diff --git a/.coveragerc b/.coveragerc
index 625961df..fe9ca39c 100644
--- a/.coveragerc
+++ b/.coveragerc
@@ -4,6 +4,7 @@ omit =
     src/pybella/data_assimilation/*
     src/pybella/inputs/*
     src/pybella/utils/debug_helpers.py
+    src/pybella/utils/slices.py
     */tests/*
     */test_*
     setup.py
diff --git a/.gitignore b/.gitignore
index 76231175..7501eb79 100644
--- a/.gitignore
+++ b/.gitignore
@@ -5,8 +5,12 @@
 *.ipynb_checkpoints*
 *.egg-info*
 *.coverage*
-profile.html
-profile.json
+profile*.html
+profile*.json
+profile*.out
+prof/*
+profiling/*
+chat*.json
 
 # Ignore everything under outputs/
 outputs/**
@@ -28,6 +32,7 @@ outputs/**
 *copy.py*
 package*json
 *.log
+*.swp
 
 # Sphinx html build
 **_build*
diff --git a/docs/source/_static/logo.svg b/docs/source/_static/logo.svg
index 44b1a947..d599f20d 100644
--- a/docs/source/_static/logo.svg
+++ b/docs/source/_static/logo.svg
@@ -45,7 +45,7 @@
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diff --git a/docs/source/apis/src.flow_solver.physics.low_mach.mpv.rst b/docs/source/apis/src.flow_solver.physics.low_mach.mpv.rst
index abfa1b22..a86a9939 100644
--- a/docs/source/apis/src.flow_solver.physics.low_mach.mpv.rst
+++ b/docs/source/apis/src.flow_solver.physics.low_mach.mpv.rst
@@ -1,7 +1,7 @@
-src.flow_solver.physics.low\_mach.mpv
+src.flow_solver.physics.low\_mach.npf
 ================================
 
-.. automodule:: src.flow_solver.physics.low_mach.mpv
+.. automodule:: src.flow_solver.physics.low_mach.npf
 
    
    
diff --git a/docs/source/apis/src.flow_solver.physics.low_mach.rst b/docs/source/apis/src.flow_solver.physics.low_mach.rst
index 3df4d745..63b298d3 100644
--- a/docs/source/apis/src.flow_solver.physics.low_mach.rst
+++ b/docs/source/apis/src.flow_solver.physics.low_mach.rst
@@ -28,6 +28,6 @@ src.flow_solver.physics.low\_mach
    :recursive:
 
    src.flow_solver.physics.low_mach.laplacian
-   src.flow_solver.physics.low_mach.mpv
+   src.flow_solver.physics.low_mach.npf
    src.flow_solver.physics.low_mach.second_projection
 
diff --git a/docs/source/content/boundary.rst b/docs/source/content/boundary.rst
index f7fbaee1..1854214a 100644
--- a/docs/source/content/boundary.rst
+++ b/docs/source/content/boundary.rst
@@ -4,7 +4,7 @@ Boundary handling
 =================
 Boundary handling for the ghosts cells (:class:`discretization.kgrid.ElemSpaceDiscr`) and nodes (:class:`discretization.kgrid.NodeSpaceDiscr`) are handled in ``boundary.py``.
 
-Cell boundarys are handled by the function :func:`inputs.boundary.set_explicit_boundary_data`. The bondary conditions are given in the initial user data file, :py:attr:`inputs.user_data.UserDataInit.bdry_type`.
+Cell boundarys are handled by the function :func:`inputs.boundary.set_data`. The bondary conditions are given in the initial user data file, :py:attr:`inputs.user_data.UserDataInit.bdry_type`.
 
 For ghost cells in directions without gravity, the ghost cells are padded by the ``np.pad()`` function.
 
diff --git a/outputs/target_lamb_wave/target_lamb_wave_151_60_stripped.h5 b/outputs/target_lamb_wave/target_lamb_wave_151_60_stripped.h5
index 7bd460b8..b5dbc90b 100644
Binary files a/outputs/target_lamb_wave/target_lamb_wave_151_60_stripped.h5 and b/outputs/target_lamb_wave/target_lamb_wave_151_60_stripped.h5 differ
diff --git a/src/pybella/__main__.py b/src/pybella/__main__.py
index 253323b7..cf3d7a60 100644
--- a/src/pybella/__main__.py
+++ b/src/pybella/__main__.py
@@ -69,7 +69,9 @@ def main():
             debug_writer = io.create_debug_writer(params.debug, writer, mem)
 
             logging.info("For ensemble member = %i..." % cnt)
-            mem = dis_time_update.do(mem, sst.ud, tout, blend, step_writer, debug_writer)
+            mem = dis_time_update.do(
+                mem, sst.ud, tout, blend, step_writer, debug_writer
+            )
 
             if sst.ud.diag:
                 if sst.ud.diag_updt_targets:
@@ -105,8 +107,6 @@ def main():
                 label = "ensemble_mem=%i_%.3f" % (n, tout)
             writer.write_all(mem, str(label) + "_after_full_step")
 
-        # synchronise_variables(mpv, Sol, elem, node, ud, th)
-        # sst.t = tout
         tout_old = np.copy(tout)
         logging.info("tout = %.3f" % tout)
 
diff --git a/src/pybella/data_assimilation/analysis.py b/src/pybella/data_assimilation/analysis.py
index 0fcf4aa4..ccff22b2 100644
--- a/src/pybella/data_assimilation/analysis.py
+++ b/src/pybella/data_assimilation/analysis.py
@@ -1,7 +1,10 @@
 import logging
-
 import numpy as np
 
+from ..utils import sim_params as params
+from ..flow_solver.utils.boundary import cell_boundary as bdry_c
+from ..flow_solver.utils.boundary import node_boundary as bdry_n
+
 from . import (
     etpf as da_etpf,
     post_processing as da_post_processing,
@@ -9,10 +12,6 @@
     utils as da_utils,
 )
 
-from ..flow_solver.utils import boundary as bdry
-
-from ..utils import sim_params as params
-
 
 def do_for_window(tout, outer_step, results, sst, writer):
     # mp = sst.model_params
@@ -30,9 +29,9 @@ def do_for_window(tout, outer_step, results, sst, writer):
         # Update ensemble with forecast
         ######################################################
         for mem in results:
-            elem, node, sol, _, mpv, th, _ = mem
-            bdry.set_explicit_boundary_data(sol, elem, sst.ud, th, mpv)
-            bdry.set_ghostnodes_p2(mpv.p2_nodes, node, sst.ud)
+            elem, node, sol, _, npf, th, _ = mem
+            bdry_c.set_ghost_cells(mem, sst.ud)
+            bdry_n.set_ghost_nodes(npf.p2_nodes, node, sst.ud)
 
         # ens.set_members(results, tout)
         sst.ensemble_state.set_members(results)
@@ -42,13 +41,13 @@ def do_for_window(tout, outer_step, results, sst, writer):
         ######################################################
         logging.info("Starting output...")
         for mem in sst.ensemble_state:
-            elem, node, sol, _, mpv, th, _ = mem
+            elem, node, sol, _, npf, th, _ = mem
             if params.label_type == "STEP":
                 step = outer_step
                 label = "ensemble_mem=%i_%.3d" % (n, step)
             else:
                 label = "ensemble_mem=%i_%.3f" % (n, tout)
-            writer.write_all(sol, mpv, elem, node, th, str(label) + "_before_da")
+            writer.write_all(sol, npf, elem, node, th, str(label) + "_before_da")
 
         ##################################################
         # LETKF with batch observations
@@ -88,7 +87,7 @@ def do_for_window(tout, outer_step, results, sst, writer):
             )
             results = da_utils.HSprojector_2t3D(results, elem, node, dp.dap, sst.N)
             # if hasattr(dap, 'converter'):
-            # results = dap.converter(results, N, mpv, elem, node, th, ud)
+            # results = dap.converter(results, N, npf, elem, node, th, ud)
 
         ##################################################
         # ETPF
@@ -120,9 +119,9 @@ def do_for_window(tout, outer_step, results, sst, writer):
     # Update ensemble with analysis
     ######################################################
     for mem in results:
-        elem, node, Sol, _, mpv, th, _, _ = mem
-        bdry.set_explicit_boundary_data(Sol, elem, sst.ud, th, mpv)
-        p2_nodes = mpv.p2_nodes
-        bdry.set_ghostnodes_p2(p2_nodes, node, sst.ud)
+        elem, node, sol, npf, th, _, _ = mem
+        bdry_c.set_ghost_cells(mem, sst.ud)
+        p2_nodes = npf.p2_nodes
+        bdry_n.set_ghost_nodes(p2_nodes, node, sst.ud)
 
     sst.ensemble_state.set_members(results)
diff --git a/src/pybella/data_assimilation/params.py b/src/pybella/data_assimilation/params.py
index 8eb4f995..0aca048b 100644
--- a/src/pybella/data_assimilation/params.py
+++ b/src/pybella/data_assimilation/params.py
@@ -4,7 +4,8 @@
 import numpy as np
 import scipy as sp
 
-from ..flow_solver.utils import boundary as bdry
+from ..flow_solver.utils.boundary import cell_boundary as bdry_c
+from ..flow_solver.utils.boundary import node_boundary as bdry_n
 
 
 class init(object):
@@ -23,15 +24,6 @@ def __init__(self, N, da_type="rloc"):
         # which attributes to inflate in ensemble inflation?
         self.attributes = ["rho", "rhou", "rhov"]
 
-        # self.obs_path = './output_travelling_vortex/output_travelling_vortex_ensemble=1_32_32_6.0_truthgen.h5'
-        # self.obs_path = './output_rising_bubble/output_rising_bubble_ensemble=1_100_50_10.0_psinc_ref.h5'
-        # self.obs_path = './output_rising_bubble/output_rising_bubble_ensemble=1_100_50_10.0_truthgen_freezelt5.h5'
-        # self.obs_path = './output_rising_bubble/output_rising_bubble_ensemble=1_100_50_10.0_comp_ref.h5'
-        # self.obs_path = './output_rising_bubble/output_rising_bubble_ensemble=1_160_80_1.0_truth_CFLfixed_ib-0.h5'
-
-        # self.obs_path = './output_swe_vortex/output_swe_vortex_ensemble=1_64_1_64_3.0_comp_1.0_pps_tra_truth.h5'
-        # self.obs_path = './output_swe_vortex/output_swe_vortex_ensemble=1_64_1_64_3.0_neg_comp_1.0_pp_tra_truth_ip.h5'
-        # self.obs_path = './output_travelling_vortex/output_travelling_vortex_ensemble=1_64_64_3.0_comp_1.0_pp_tra_truth_ip.h5'
         self.obs_path = "./output_travelling_vortex/output_travelling_vortex_ensemble=1_64_64_3.0_obs.h5"
 
         # forward operator (projector from state space to observation space)
@@ -129,7 +121,7 @@ def gen_obs_noise(self):
             self.obs_noise_seeds = [np.random.randint(10000)]
 
     @staticmethod
-    def converter(results, N, mpv, elem, node, th, ud):
+    def converter(results, N, npf, elem, node, th, ud):
         """
         Do this after data assimilation for HS balanced vortex.
 
@@ -138,7 +130,7 @@ def converter(results, N, mpv, elem, node, th, ud):
 
         g = ud.g0
         for n in range(N):
-            bdry.set_explicit_boundary_data(results[n][0], elem, ud, th, mpv)
+            bdry_c.set_ghost_cells(results[n][0], elem, ud, th, npf)
             results[n][0].rhoY[...] = (g / 2.0 * results[n][0].rho ** 2) ** th.gamminv
 
             igy = elem.igy
@@ -148,12 +140,12 @@ def converter(results, N, mpv, elem, node, th, ud):
 
             pn = sp.signal.convolve(results[n][0].rhoY[:, igy, :], kernel, mode="valid")
 
-            bdry.set_explicit_boundary_data(results[n][0], elem, ud, th, mpv)
+            bdry_c.set_ghost_cells(results[n][0], elem, ud, th, npf)
             pn = np.expand_dims(pn, 1)
             pn = np.repeat(pn, node.icy, axis=1)
 
             results[n][2].p2_nodes[1:-1, :, 1:-1] = pn
-            bdry.set_ghostnodes_p2(results[n][2].p2_nodes, node, ud)
+            bdry_n.set_ghost_nodes(results[n][2].p2_nodes, node, ud)
 
             pn = np.expand_dims(results[n][2].p2_nodes[:, igy, :], 1)
             results[n][2].p2_nodes[...] = np.repeat(pn[...], node.icy, axis=1)
diff --git a/src/pybella/data_assimilation/prepare.py b/src/pybella/data_assimilation/prepare.py
index f50ddb1e..fd396aa0 100644
--- a/src/pybella/data_assimilation/prepare.py
+++ b/src/pybella/data_assimilation/prepare.py
@@ -48,19 +48,19 @@ def initialise(sst):
         logging.info("Seeds used in generating initial ensemble spread = ", seeds)
         for n in range(sst.N):
             Sol0 = deepcopy(sst.Sol)
-            mpv0 = deepcopy(sst.mpv)
+            npf0 = deepcopy(sst.npf)
             Sol0 = sst.sol_init(
-                Sol0, mpv0, es.elem, es.node, es.th, es.ud, seed=seeds[n]
+                Sol0, npf0, es.elem, es.node, es.th, es.ud, seed=seeds[n]
             )
-            # sol_ens[n] = [Sol0, deepcopy(es.flux), mpv0, [-np.inf, es.step]]
+            # sol_ens[n] = [Sol0, deepcopy(es.flux), npf0, [-np.inf, es.step]]
             sol_ens.update_member(
-                es.elem, es.node, Sol0, mpv0, deepcopy(es.flux), es.th
+                es.elem, es.node, Sol0, npf0, deepcopy(es.flux), es.th
             )
 
             sst.ensembble_state = sol_ens
     # elif sst.restart == False:
-    # sol_ens = [[sst.sol_init(mp.Sol, mp.mpv, mp.elem, mp.node, mp.th, sst.ud), mp.flux, mp.mpv, [-np.inf, sst.step]]]
-    # sol_ens.update_member(mp.elem, mp.node, sst.sol_init(mp.Sol, mp.mpv, mp.elem, mp.node, mp.th, sst.ud), mp.mpv, deepcopy(mp.flux), mp.th)
+    # sol_ens = [[sst.sol_init(mp.Sol, mp.npf, mp.elem, mp.node, mp.th, sst.ud), mp.flux, mp.npf, [-np.inf, sst.step]]]
+    # sol_ens.update_member(mp.elem, mp.node, sst.sol_init(mp.Sol, mp.npf, mp.elem, mp.node, mp.th, sst.ud), mp.npf, deepcopy(mp.flux), mp.th)
     # for n in range(sst.N):
     #     sol_ens.get_member(n).time.t = -np.inf
 
diff --git a/src/pybella/data_assimilation/utils.py b/src/pybella/data_assimilation/utils.py
index b1a593d2..a7ea7046 100644
--- a/src/pybella/data_assimilation/utils.py
+++ b/src/pybella/data_assimilation/utils.py
@@ -6,8 +6,7 @@
 import matplotlib.pyplot as plt
 
 from ..utils import options as opts
-
-from ..flow_solver.utils import boundary as bdry
+from ..flow_solver.utils.boundary import node_boundary as bdry_n
 
 
 class ensemble(object):
@@ -83,12 +82,12 @@ def set_p2_nodes(analysis, results, N, th, node, ud, loc_c=0, loc_n=2):
         rhoY_n[1:-1, 1:-1] = (
             sp.signal.fftconvolve(rhoY, kernel, mode="valid") / kernel.sum()
         )
-        bdry.set_ghostnodes_p2(rhoY_n, node, ud)
+        bdry_n.set_ghost_nodes(rhoY_n, node, ud)
         p2_n = rhoY_n**th.gm1 - 1.0 + (p2_n - p2_n.mean())
         # p2_n = rhoY_n**th.gm1 - 1.0
         p2_n -= p2_n.mean()
         # p2_n = np.pad(p2_n,2,mode='wrap')
-        bdry.set_ghostnodes_p2(p2_n, node, ud)
+        bdry_n.set_ghost_nodes(p2_n, node, ud)
         setattr(results[n][loc_n], "p2_nodes", p2_n)
 
 
@@ -260,7 +259,7 @@ def HSprojector_3t2D(results, elem, dap, N):
     Parameters
     ----------
     results : nd.array
-        An array of ensemble size k. Each ensemble member has [Sol,flux,mpv,[window_step,step]].
+        An array of ensemble size k. Each ensemble member has [Sol,flux,npf,[window_step,step]].
     dap : data assimilation input class
         .
     N : int
diff --git a/src/pybella/flow_solver/discretisation/time_update.py b/src/pybella/flow_solver/discretisation/time_update.py
index fb62afc1..2a3d76a4 100644
--- a/src/pybella/flow_solver/discretisation/time_update.py
+++ b/src/pybella/flow_solver/discretisation/time_update.py
@@ -1,19 +1,15 @@
 import copy
 import logging
-
 import numpy as np
 
+# dependencies from pybella common
 from ...utils import options as opts
 
 # dependencies of the flow solver subpackage
-from ..utils import boundary as bdry
-from ..physics.gas_dynamics import (
-    numerical_flux as gd_flux,
-    eos as gd_eos,
-    cfl as gd_cfl,
-)
-from ..physics.gas_dynamics import explicit as gd_explicit
-from ..physics.low_mach import second_projection as lm_sp
+from ..utils.boundary import rayleigh_boundary as bdry_r
+from ..physics import cfl, eos
+from ..numerics.explicit_advection import advective_flux, compute_advection
+from ..numerics import explicit_euler, implicit_euler
 
 # for blending module
 from ...interfaces.dynamics_blending import schemes
@@ -37,21 +33,21 @@ def do(
     swe_to_lake = False
 
     while (mem.time.t < tout) and (mem.time.step < ud.stepmax):
-        bdry.set_explicit_boundary_data(mem.sol, mem.elem, ud, mem.th, mem.mpv)
-
         label = "%.3d" % mem.time.step
 
         if mem.time.step == 0 and writer != None:
             writer.write_all(mem, str(label) + "_ic")
 
-        dt, cfl, cfl_ac = gd_cfl.dynamic_timestep(mem.sol, mem.time.t, tout, mem.elem, ud, mem.th, mem.time.step)
+        dt, cfl_adv, cfl_acs = cfl.dynamic_timestep(
+            mem.sol, mem.time.t, tout, mem.elem, ud, mem.th, mem.time.step
+        )
 
         dt = prestep.apply_modifcations(dt, ud, mem.time.step)
 
         ######################################################
         # Blending : Do blending before timestep
         ######################################################
-        swe_to_lake, mem.sol, mem.mpv, mem.time.t = schemes.prepare_blending(
+        swe_to_lake, mem.sol, mem.npf, mem.time.t = schemes.prepare_blending(
             mem,
             ud,
             bld,
@@ -65,11 +61,13 @@ def do(
             debug_writer,
         )
 
-        ud.is_nonhydrostatic = gd_eos.is_nonhydrostatic(ud, mem.time.window_step)
-        ud.nonhydrostasy = gd_eos.nonhydrostasy(ud, mem.time.t, mem.time.window_step)
+        ud.is_nonhydrostatic = eos.is_nonhydrostatic(ud, mem.time.window_step)
+        ud.nonhydrostasy = eos.nonhydrostasy(ud, mem.time.t, mem.time.window_step)
 
         if ud.continuous_blending or ud.initial_blending:
-            logging.info(f"step = {mem.time.step}, window_step = {mem.time.window_step}")
+            logging.info(
+                f"step = {mem.time.step}, window_step = {mem.time.window_step}"
+            )
 
         logging.info(
             f"""
@@ -80,84 +78,65 @@ def do(
                     """
         )
 
-        Sol0 = copy.deepcopy(mem.sol)
+        sol0 = copy.deepcopy(mem.sol)
 
         debug_writer.write(f"{label}_before_flux")
 
-        gd_flux.recompute_advective_fluxes(mem)
+        advective_flux.recompute(mem)
 
-        debug_writer.populate_flux_components(f"{label}_before_advect", mem.flux, mem.elem)
         debug_writer.write(f"{label}_before_advect")
 
         if ud.do_advection:
-            gd_explicit.advect_rk(
+            compute_advection.first_order_runge_kutta(
                 mem,
                 ud,
                 0.5 * dt,
             )
 
         debug_writer.write(f"{label}_after_advect")
-        debug_writer.populate(f"{label}_after_full_step", "p2_nodes", mem.mpv.p2_nodes)
+        debug_writer.populate(f"{label}_after_full_step", "p2_nodes", mem.npf.p2_nodes)
 
-        mem.mpv.p2_nodes0[...] = mem.mpv.p2_nodes
+        mem.npf.p2_nodes0[...] = mem.npf.p2_nodes
 
-        lm_sp.euler_backward_non_advective_expl_part(mem, ud, 0.5 * dt)
+        implicit_euler.do_explicit_part(mem, ud, 0.5 * dt)
 
         debug_writer.write(f"{label}_after_ebnaexp")
 
-        Sol0_increment = Sol0 if ud.is_compressible == 0 else None
+        sol0_increment = sol0 if ud.is_compressible == 0 else None
 
-        lm_sp.euler_backward_non_advective_impl_part(
-            mem.sol,
-            mem.mpv,
-            mem.elem,
-            mem.node,
+        implicit_euler.do_implicit_part(
+            mem,
             ud,
-            mem.th,
-            mem.time.t,
             0.5 * dt,
-            mem,
-            Sol0=Sol0_increment,
+            sol0=sol0_increment,
             label=f"{label}_after_ebnaimp",
             writer=writer,
         )
 
         if ud.bdry_type[1] == opts.BdryType.RAYLEIGH:
             # top rayleight damping
-            bdry.rayleigh_damping(mem.sol, mem.mpv, ud, mem.elem, mem.node)
+            bdry_r.rayleigh_damping(mem.sol, mem.npf, ud)
 
-        bdry.apply_rayleigh_forcing(
-            mem.sol,
-            mem.mpv,
-            ud,
-            mem.elem,
-            mem.node,
-            mem.time.t,
-            mem.time.step,
-            dt,
-            mem.th,
-            bdry,
-        )
+        bdry_r.apply_rayleigh_forcing(mem, ud, dt)
 
         debug_writer.write(f"{label}_after_ebnaimp")
 
-        gd_flux.recompute_advective_fluxes(mem)
+        advective_flux.recompute(mem)
 
-        debug_writer.populate_flux_components(f"{label}_after_half_step", mem.flux, mem.elem)
         debug_writer.write(f"{label}_after_half_step")
 
-        Sol_half_new = copy.deepcopy(mem.sol)
-        mpv_half_new = copy.deepcopy(mem.mpv)
-        mem.mpv.p2_nodes_half = np.copy(mem.mpv.p2_nodes)
+        sol_half_new = copy.deepcopy(mem.sol)
+        npf_half_new = copy.deepcopy(mem.npf)
+        mem.npf.p2_nodes_half = np.copy(mem.npf.p2_nodes)
 
         if ud.is_nonhydrostatic == 0 or (
             ud.is_compressible == 1 and ud.is_nonhydrostatic == 1
         ):
-            mem.mpv.p2_nodes[...] = mem.mpv.p2_nodes0
+            mem.npf.p2_nodes[...] = mem.npf.p2_nodes0
 
-        mem.sol = copy.deepcopy(Sol0)
+        mem.sol = copy.deepcopy(sol0)
 
-        lm_sp.euler_forward_non_advective(
+        explicit_euler.do_forward_step(
             mem,
             ud,
             0.5 * dt,
@@ -168,7 +147,7 @@ def do(
         debug_writer.write(f"{label}_after_efna")
 
         if ud.do_advection:
-            gd_explicit.advect(
+            compute_advection.strange_splitting(
                 mem,
                 ud,
                 dt,
@@ -179,52 +158,38 @@ def do(
 
         debug_writer.write(f"{label}_after_full_advect")
 
-        lm_sp.euler_backward_non_advective_expl_part(mem, ud, 0.5 * dt)
+        implicit_euler.do_explicit_part(mem, ud, 0.5 * dt)
 
         debug_writer.write(f"{label}_after_full_ebnaexp")
 
-        lm_sp.euler_backward_non_advective_impl_part(
-            mem.sol,
-            mem.mpv,
-            mem.elem,
-            mem.node,
+        implicit_euler.do_implicit_part(
+            mem,
             ud,
-            mem.th,
-            mem.time.t,
             0.5 * dt,
-            mem,
             writer=writer,
             label=str(label) + "_after_full_step",
         )
 
         if ud.bdry_type[1] == opts.BdryType.RAYLEIGH:
             # top rayleight damping
-            bdry.rayleigh_damping(mem.sol, mem.mpv, ud, mem.elem, mem.node)
+            bdry_r.rayleigh_damping(mem.sol, mem.npf, ud)
 
         # bottom rayleigh forcing
-        bdry.apply_rayleigh_forcing(
-            mem.sol,
-            mem.mpv,
+        bdry_r.apply_rayleigh_forcing(
+            mem,
             ud,
-            mem.elem,
-            mem.node,
-            mem.time.t,
-            mem.time.step,
             dt,
-            mem.th,
-            bdry,
             half=False,
-            Sol_half_new=Sol_half_new,
-            mpv_half_new=mpv_half_new,
+            sol_half_new=sol_half_new,
+            npf_half_new=npf_half_new,
         )
 
         ######################################################
         # Blending : Do blending after timestep
         ######################################################
-        mem.sol, mem.mpv = schemes.blending_after_timestep(
+        mem.sol, mem.npf = schemes.blending_after_timestep(
             mem.sol,
-            mem.flux,
-            mem.mpv,
+            mem.npf,
             bld,
             mem.elem,
             mem.node,
@@ -249,7 +214,7 @@ def do(
         )
         logging.info(
             "step %i done, t = %.12f, dt = %.12f, CFL = %.8f, CFL_ac = %.8f"
-            % (mem.time.step, mem.time.t, dt, cfl, cfl_ac)
+            % (mem.time.step, mem.time.t, dt, cfl_adv, cfl_acs)
         )
         logging.info(
             "###############################################################################################"
diff --git a/src/pybella/flow_solver/physics/gas_dynamics/__init__.py b/src/pybella/flow_solver/numerics/__init__.py
similarity index 100%
rename from src/pybella/flow_solver/physics/gas_dynamics/__init__.py
rename to src/pybella/flow_solver/numerics/__init__.py
diff --git a/src/pybella/flow_solver/numerics/coriolis.py b/src/pybella/flow_solver/numerics/coriolis.py
new file mode 100644
index 00000000..955112cf
--- /dev/null
+++ b/src/pybella/flow_solver/numerics/coriolis.py
@@ -0,0 +1,138 @@
+import numba as nb
+
+
+# Refactored main function
+def multiply_inverse_terms(
+    Vec, mem, ud, dt, attrs=("rhou", "rhov", "rhow"), get_coeffs=False
+):
+    """Coriolis matrix multiplication."""
+    nonhydro = ud.nonhydrostasy
+    g = ud.gravity_strength[1]
+    Msq = ud.Msq
+
+    wh1, wv, wh2 = dt * ud.coriolis_strength
+    strat = mem.npf.HydroState_n.get_dSdy(mem.elem, mem.node)
+    Y = mem.sol.rhoY / mem.sol.rho
+    nu = -(dt**2) * (g / Msq) * strat * Y
+    shp = nu.shape
+
+    # initialise Coriolis cache is not already done
+    h11, h12, h13, h21, h22, h23, h31, h32, h33, denom = (
+        mem.cache.get_coriolis_array_views(shp)
+    )
+
+    # Get vector components by view
+    VecU = getattr(Vec, attrs[0])
+    VecV = getattr(Vec, attrs[1])
+    VecW = getattr(Vec, attrs[2])
+
+    U, V, W = mem.cache.get_velocity_array_views(VecU.shape)
+
+    _apply_coriolis_matrix_inplace(
+        h11,
+        h12,
+        h13,
+        h21,
+        h22,
+        h23,
+        h31,
+        h32,
+        h33,
+        denom,
+        VecU,
+        VecV,
+        VecW,
+        U,
+        V,
+        W,
+        wh1,
+        wh2,
+        wv,
+        nu,
+        nonhydro,
+    )
+
+    # Return coefficients
+    if get_coeffs:
+        # For 2D only
+        h11, h12, _, h21, h22, _, _, _, _, _ = mem.cache.get_coriolis_array_views(shp)
+        return (h11.T, h22.T, h12.T, h21.T)
+
+
+@nb.njit(cache=True)
+def _compute_coriolis_coefficients(
+    h11, h12, h13, h21, h22, h23, h31, h32, h33, denom, wh1, wh2, wv, nu, nonhydro
+):
+    """Compute coefficients for the H^-1 matrix multiplication.
+
+    This corresponds to equation (C11) in the mathematical formulation.
+    """
+    # Common terms
+    wh1_sq = wh1 * wh1
+    wh2_sq = wh2 * wh2
+    wv_sq = wv * wv
+    nu_nh = nu + nonhydro
+
+    # Denominator (det(H))
+    denom[...] = 1.0 / (wh1_sq + wh2_sq + nu_nh * (wv_sq + 1.0))
+
+    # H^-1 matrix elements (row-major order)
+    # Row 1: U equation coefficients
+    h11[...] = (wh1_sq + nu_nh) * denom
+    h12[...] = nonhydro * (wh1 * wv + wh2) * denom
+    h13[...] = (wh1 * wh2 - nu_nh * wv) * denom
+
+    # Row 2: V equation coefficients
+    h21[...] = (wh1 * wv - wh2) * denom
+    h22[...] = nonhydro * (1.0 + wv_sq) * denom
+    h23[...] = (wh2 * wv + wh1) * denom
+
+    # Row 3: W equation coefficients
+    h31[...] = (wh1 * wh2 + nu_nh * wv) * denom
+    h32[...] = nonhydro * (wh2 * wv - wh1) * denom
+    h33[...] = (nu_nh + wh2_sq) * denom
+
+    return h11, h12, h13, h21, h22, h23, h31, h32, h33
+
+
+@nb.njit(cache=True)
+def _apply_coriolis_matrix_inplace(
+    h11,
+    h12,
+    h13,
+    h21,
+    h22,
+    h23,
+    h31,
+    h32,
+    h33,
+    denom,
+    u_vec,
+    v_vec,
+    w_vec,
+    U,
+    V,
+    W,
+    wh1,
+    wh2,
+    wv,
+    nu,
+    nonhydro,
+):
+    """Apply H^-1 matrix multiplication in-place.
+
+    Corresponds to the equation: U^{n+1} = H^{-1}(U^{n*} - Δt_{cp}(Pθ)^* ∇π^{n+1})
+    """
+    # Get matrix coefficients
+    _compute_coriolis_coefficients(
+        h11, h12, h13, h21, h22, h23, h31, h32, h33, denom, wh1, wh2, wv, nu, nonhydro
+    )
+
+    U[...] = u_vec
+    V[...] = v_vec
+    W[...] = w_vec
+
+    # Matrix multiplication: [U_new, V_new, W_new] = H^-1 @ [U_old, V_old, W_old]
+    u_vec[...] = h11 * U + h12 * V + h13 * W
+    v_vec[...] = h21 * U + h22 * V + h23 * W
+    w_vec[...] = h31 * U + h32 * V + h33 * W
diff --git a/src/pybella/flow_solver/numerics/explicit_advection/advective_flux.py b/src/pybella/flow_solver/numerics/explicit_advection/advective_flux.py
new file mode 100644
index 00000000..ecc7ef89
--- /dev/null
+++ b/src/pybella/flow_solver/numerics/explicit_advection/advective_flux.py
@@ -0,0 +1,40 @@
+# -*- coding: utf-8 -*-
+import numpy as np
+from numba import njit
+
+from ....utils.operators import convolution
+from ....utils import slices
+
+
+def recompute(mem, **kwargs):
+    """Recompute the advective fluxes at the cell interfaces.
+
+    Parameters
+    ----------
+    mem : object
+        Memory object containing sol and flux attributes
+    **kwargs
+        Optional pre-computed velocity components ('u', 'v', 'w')
+    """
+    ndim = mem.sol.rho.ndim
+    inner_idx = slices.get_inner_slice(ndim)
+    kernels = convolution.get_flux_kernels(ndim)
+
+    # Define the component order and corresponding flux indices
+    components = ["u", "v"] if ndim == 2 else ["u", "v", "w"]
+    rho_components = ["rhou", "rhov"] if ndim == 2 else ["rhou", "rhov", "rhow"]
+
+    flux = mem.cache.get_flux_containers(mem.elem)
+
+    for i, (comp, rho_comp) in enumerate(zip(components, rho_components)):
+        # Use provided velocity or compute from momentum
+        if comp in kwargs:
+            rhoY_vel = kwargs[comp]
+        else:
+            momentum = getattr(mem.sol, rho_comp)
+            rhoY_vel = mem.sol.rhoY * momentum / mem.sol.rho
+
+        # Apply directional convolution
+        flux[i].rhoY[inner_idx] = convolution.apply_directional_convolution(
+            rhoY_vel, kernels[comp], comp, ndim
+        )
diff --git a/src/pybella/flow_solver/physics/gas_dynamics/explicit.py b/src/pybella/flow_solver/numerics/explicit_advection/compute_advection.py
similarity index 53%
rename from src/pybella/flow_solver/physics/gas_dynamics/explicit.py
rename to src/pybella/flow_solver/numerics/explicit_advection/compute_advection.py
index 2e64d80f..09f7dfe9 100644
--- a/src/pybella/flow_solver/physics/gas_dynamics/explicit.py
+++ b/src/pybella/flow_solver/numerics/explicit_advection/compute_advection.py
@@ -1,53 +1,36 @@
+import numba as nb
+
 from ....utils.slices import get_neighbor_indices
-from ...utils import boundary as bdry
-from . import recovery as gd_recovery
-from . import numerical_flux as gd_flux
+from ...utils.boundary import cell_boundary as bdry_c
+from . import recovery, riemann_solver
 
 
-def advect(mem, ud, dt, odd, label, writer=None):
+def strange_splitting(mem, ud, dt, odd, label, writer=None):
     """
     Concise implementation of Strang-splitting advection.
     This function updates the `Sol` solution container with the advected solution in-place.
     """
     time_step = 0.5 * dt
     diagnostics = [writer, mem.node, label] if writer is not None else None
-    
+
     # Define sweep configurations: (reverse_order, use_diagnostics)
     sweeps = [(not odd, not odd), (odd, odd)]
-    
+
     for reverse_order, use_diagnostics in sweeps:
         _perform_dimensional_sweep(
-            mem, ud, time_step, 
+            mem,
+            ud,
+            time_step,
             reverse=reverse_order,
-            diagnostics=diagnostics if use_diagnostics else None
+            diagnostics=diagnostics if use_diagnostics else None,
         )
-    
-    bdry.set_explicit_boundary_data(mem.sol, mem.elem, ud, mem.th, mem.mpv)
-
-
-def explicit_step_and_flux(mem, ud, lmbda, split_step, tag=None):
-    """
-    For each advection substep, solve the advection problem. For more details, see :ref:`advection_routine`. 
-    This function updates the solution `Sol` container in-place if a Strang-splitting is used, 
-    or returns the `flux` data container if a Runge-Kutta method is used.
-    """
-    flux = _compute_flux_and_recovery(mem, ud, lmbda, split_step, tag)
-    
-    # Cache neighbor indices (consider moving this to initialization if called frequently)
-    left_idx, right_idx = get_neighbor_indices(mem.elem.ndim)
-
-    if tag != "rk":
-        _update_solution_variables(mem.sol, flux, lmbda, left_idx, right_idx)
-    
-    bdry.set_explicit_boundary_data(mem.sol, mem.elem, ud, mem.th, mem.mpv, step=split_step)
 
-    if tag == "rk":
-        return flux
+    bdry_c.set_ghost_cells(mem, ud)
 
 
-def advect_rk(mem, ud, dt):
+def first_order_runge_kutta(mem, ud, dt):
     """
-    Function that runs the advection routine with a first-order Runge-Kutta update. 
+    Function that runs the advection routine with a first-order Runge-Kutta update.
     This function updates the `Sol` solution container with the advected solution in-place.
 
     Attention
@@ -56,13 +39,14 @@ def advect_rk(mem, ud, dt):
     """
     time_step = dt
     ndim = mem.elem.ndim
+    flux = mem.cache.get_flux_containers(mem.elem)
 
     # Compute fluxes for all dimensions
     for split in range(ndim):
         lmbda = time_step / mem.elem.dxyz[split]
         mem.sol.flip_forward()
         if mem.elem.iisc[split] > 1:
-            mem.flux[split] = explicit_step_and_flux(mem, ud, lmbda, split, tag="rk")
+            flux[split] = _explicit_step_and_flux(mem, ud, lmbda, split, tag="rk")
 
     # Cache neighbor indices once
     left_idx, right_idx = get_neighbor_indices(mem.elem.ndim)
@@ -71,73 +55,132 @@ def advect_rk(mem, ud, dt):
     for dim in range(ndim):
         _apply_dimensional_flux_update(mem, dim, time_step, left_idx, right_idx)
 
-    bdry.set_explicit_boundary_data(mem.sol, mem.elem, ud, mem.th, mem.mpv)
+    bdry_c.set_ghost_cells(mem, ud)
+
 
 def _update_solution_variables(sol, flux, lmbda, left_idx, right_idx, variables=None):
     """
     Helper function to update solution variables with flux differences.
-    
+
     """
     if variables is None:
-        variables = ['rho', 'rhou', 'rhov', 'rhow', 'rhoX', 'rhoY']
-    
+        variables = ["rho", "rhou", "rhov", "rhow", "rhoX", "rhoY"]
+
     for var in variables:
         flux_diff = getattr(flux, var)[left_idx] - getattr(flux, var)[right_idx]
         current_val = getattr(sol, var)
         setattr(sol, var, current_val + lmbda * flux_diff)
 
 
-def _compute_flux_and_recovery(mem, ud, lmbda, split_step, tag=None):
+def _explicit_step_and_flux(mem, ud, lmbda, split_step, tag=None):
+    """
+    For each advection substep, solve the advection problem. For more details, see :ref:`advection_routine`.
+    This function updates the solution `Sol` container in-place if a Strang-splitting is used,
+    or returns the `flux` data container if a Runge-Kutta method is used.
+    """
+    bdry_c.set_ghost_cells(mem, ud, step=split_step)
+
+    flux = mem.cache.get_flux_containers(mem.elem)[split_step]
+
+    flux = _compute_flux_and_recovery(mem, flux, ud, lmbda, split_step, tag)
+
+    # Consider caching neighbor indices
+    left_idx, right_idx = get_neighbor_indices(mem.elem.ndim)
+
+    if tag != "rk":
+        _update_solution_variables(mem.sol, flux, lmbda, left_idx, right_idx)
+
+    if tag == "rk":
+        return flux
+
+
+def _compute_flux_and_recovery(mem, flux, ud, lmbda, split_step, tag=None):
     """
     Helper function to compute flux using gradient recovery and HLL solver.
-    
+
     Returns:
         flux: Computed flux container
     """
-    flux = mem.flux[split_step]
-    
-    bdry.set_explicit_boundary_data(mem.sol, mem.elem, ud, mem.th, mem.mpv, step=split_step)
-    
-    Lefts, Rights = gd_recovery.do(mem, ud, lmbda, split_step, tag)
-    
-    flux = gd_flux.hll_solver(mem, flux, Lefts, Rights)
-    
+
+    Lefts, Rights = recovery.compute(mem, flux, ud, lmbda, split_step, tag)
+
+    flux = riemann_solver.hll(mem, flux, Lefts, Rights)
+
     return flux
 
+
 def _apply_dimensional_flux_update(mem, dim, time_step, left_idx, right_idx):
     """
     Apply flux update for a specific dimension.
     """
     lmbda = time_step / mem.elem.dxyz[dim]
     mem.sol.flip_forward()
-    
-    _update_solution_variables(mem.sol, mem.flux[dim], lmbda, left_idx, right_idx)
-    
+    flux = mem.cache.get_flux_containers(mem.elem)[dim]
+
+    _update_solution_variables(mem.sol, flux, lmbda, left_idx, right_idx)
+
     # Handle special case for vertical axis
     if dim == 1:
-        updt = lmbda * (mem.flux[dim].rhoX[left_idx] - mem.flux[dim].rhoX[right_idx])
+        updt = lmbda * (flux.rhoX[left_idx] - flux.rhoX[right_idx])
         setattr(mem.sol, "pwchi", updt)
 
+
 def _perform_dimensional_sweep(mem, ud, time_step, reverse=False, diagnostics=None):
     """
     Perform a dimensional sweep in either forward or reverse order.
-    
+
     """
     elem, Sol = mem.elem, mem.sol
     ndim = elem.ndim
-    
+
     # Determine dimension order
-    dim_range = range(ndim-1, -1, -1) if reverse else range(ndim)
-    
+    dim_range = range(ndim - 1, -1, -1) if reverse else range(ndim)
+
     for split in dim_range:
         lmbda = time_step / elem.dxyz[split]
-        
+
         # Handle solution flipping based on sweep direction
         if reverse:
             if elem.iisc[split] > 1:
-                explicit_step_and_flux(mem, ud, lmbda, split, diagnostics)
+                _explicit_step_and_flux(mem, ud, lmbda, split, diagnostics)
             Sol.flip_backward()
         else:
             Sol.flip_forward()
             if elem.iisc[split] > 1:
-                explicit_step_and_flux(mem, ud, lmbda, split, diagnostics)
+                _explicit_step_and_flux(mem, ud, lmbda, split, diagnostics)
+
+
+# def _update_solution_variables(sol, flux, lmbda, left_idx, right_idx, variables=None):
+#     """
+#     Wrapper to update solution variables using JIT-compiled array math.
+#     """
+#     if variables is None:
+#         variables = ["rho", "rhou", "rhov", "rhow", "rhoX", "rhoY"]
+
+#     sol_arrays = [getattr(sol, var) for var in variables]
+#     flux_arrays = [getattr(flux, var) for var in variables]
+
+#     _update_solution_arrays_jit(sol_arrays, flux_arrays, lmbda, left_idx, right_idx)
+
+
+# @nb.njit(cache=True)
+# def _update_solution_arrays_jit(
+#     sol_vars, flux_vars, lmbda, left_idx, right_idx
+# ):
+#     """
+#     Vectorized update of solution variables using pre-extracted arrays.
+
+#     Parameters
+#     ----------
+#     sol_vars : List[np.ndarray]
+#         Solution arrays (e.g., sol.rho, sol.rhou, ...)
+#     flux_vars : List[np.ndarray]
+#         Corresponding flux arrays (e.g., flux.rho, flux.rhou, ...)
+#     lmbda : float
+#         CFL-like prefactor
+#     left_idx, right_idx : Tuple of index arrays
+#         Indices into inner cells (e.g., from `get_interface_indices`)
+#     """
+#     for i in range(len(sol_vars)):
+#         flux_diff = flux_vars[i][left_idx] - flux_vars[i][right_idx]
+#         sol_vars[i][...] += lmbda * flux_diff
diff --git a/src/pybella/flow_solver/physics/gas_dynamics/recovery.py b/src/pybella/flow_solver/numerics/explicit_advection/recovery.py
similarity index 73%
rename from src/pybella/flow_solver/physics/gas_dynamics/recovery.py
rename to src/pybella/flow_solver/numerics/explicit_advection/recovery.py
index 483ad62e..9e2b82ae 100644
--- a/src/pybella/flow_solver/physics/gas_dynamics/recovery.py
+++ b/src/pybella/flow_solver/numerics/explicit_advection/recovery.py
@@ -4,14 +4,12 @@
 from ....utils import options as opts
 from ....utils.slices import get_neighbor_indices, get_interface_indices
 
-from ...utils import variable as var
 
-def do(mem, ud, lmbda, split_step, tag=None):
+def compute(mem, flux, ud, lmbda, split_step, tag=None):
     """
     Reconstruct the limited slopes at the cell interfaces.
 
     """
-    flux = mem.flux[split_step]
     gamm = mem.th.gamm
 
     order_two = 1  # always 1
@@ -34,25 +32,35 @@ def do(mem, ud, lmbda, split_step, tag=None):
     )
 
     shape = mem.sol.u.shape
-    
+
     # Get cached objects
     cache = mem.cache.get_recovery_objects(shape, ud)
-    Diffs, Ampls, Lefts, Rights, Slopes = cache['Diffs'], cache['Ampls'], cache['Lefts'], cache['Rights'], cache['Slopes']
-    
+    Diffs, Ampls, Lefts, Rights, Slopes = (
+        cache["Diffs"],
+        cache["Ampls"],
+        cache["Lefts"],
+        cache["Rights"],
+        cache["Slopes"],
+    )
+
     # Compute differences
     _compute_differences(mem.sol, rights_idx, lefts_idx, Diffs)
-    
+
     # Compute slopes
     slopes_obj = _slopes(Diffs, Slopes, ud, mem.elem)
-    
+
     # Compute left-side amplitudes and values
-    _compute_amplitudes(slopes_obj, lmbda, u, Ampls, sign_factor=1.0, lambda_factor=-1.0)
+    _compute_amplitudes(
+        slopes_obj, lmbda, u, Ampls, sign_factor=1.0, lambda_factor=-1.0
+    )
     _compute_reconstructed_values(mem.sol, Ampls, order_two, Lefts)
-    
+
     # Compute right-side amplitudes and values
-    _compute_amplitudes(slopes_obj, lmbda, u, Ampls, sign_factor=-1.0, lambda_factor=1.0)
-    _compute_reconstructed_values(mem.sol, Ampls, order_two,Rights)
-    
+    _compute_amplitudes(
+        slopes_obj, lmbda, u, Ampls, sign_factor=-1.0, lambda_factor=1.0
+    )
+    _compute_reconstructed_values(mem.sol, Ampls, order_two, Rights)
+
     # Return velocity components
     vel = [mem.sol.u, mem.sol.v, mem.sol.w]
 
@@ -60,7 +68,7 @@ def do(mem, ud, lmbda, split_step, tag=None):
     reconstructed_rhoy = _compute_rhoy_reconstruction(
         mem, Lefts, Rights, lefts_idx, rights_idx, vel, split_step, order_two, lmbda
     )
-    
+
     # Compute pressure reconstruction
     _compute_pressure_reconstruction(
         Lefts, Rights, lefts_idx, rights_idx, reconstructed_rhoy, gamm
@@ -71,35 +79,37 @@ def do(mem, ud, lmbda, split_step, tag=None):
 
     return Lefts, Rights
 
+
 def _slopes(Diffs, Slopes, ud, elem):
     """Reconstruct piecewise linear slopes in cells."""
     # Configuration
     variable_config = {
-        'u': ud.limiter_type_velocity,
-        'v': ud.limiter_type_velocity, 
-        'w': ud.limiter_type_velocity,
-        'X': ud.limiter_type_scalars,
-        'Y': ud.limiter_type_scalars
+        "u": ud.limiter_type_velocity,
+        "v": ud.limiter_type_velocity,
+        "w": ud.limiter_type_velocity,
+        "X": ud.limiter_type_scalars,
+        "Y": ud.limiter_type_scalars,
     }
-    
+
     # TBD: Consider moving indices to cache
     lefts_idx, rights_idx = get_neighbor_indices(elem.ndim)
-    
+
     # Process each variable
     for var_name, limiter_type in variable_config.items():
         diff_data = getattr(Diffs, var_name)
-        
+
         # Extract amplitudes
         al = diff_data[lefts_idx][lefts_idx]
         ar = diff_data[lefts_idx][rights_idx]
-        
+
         # Calculate and assign slopes
         slope_data = _limiters(limiter_type, al, ar)
         getattr(Slopes, var_name)[..., 1:-1] = slope_data
-    
+
     return Slopes
 
-@njit
+
+@njit(cache=True)
 def _limiters(limiter_type, al, ar):
     """
     Applies the limiter type specified in the initial conditions to recovery the slope.
@@ -130,58 +140,70 @@ def _get_conservatives(U):
 
 def _compute_differences(sol, rights_idx, lefts_idx, diffs):
     """Compute differences between right and left indices for all fields."""
-    fields = ['u', 'v', 'w', 'X']
+    fields = ["u", "v", "w", "X"]
     for field in fields:
-        getattr(diffs, field)[..., :-1] = getattr(sol, field)[rights_idx] - getattr(sol, field)[lefts_idx]
-    
+        getattr(diffs, field)[..., :-1] = (
+            getattr(sol, field)[rights_idx] - getattr(sol, field)[lefts_idx]
+        )
+
     # Y field has special handling (reciprocal differences)
     diffs.Y[..., :-1] = 1.0 / sol.Y[rights_idx] - 1.0 / sol.Y[lefts_idx]
 
 
 def _compute_amplitudes(slopes, lmbda, u, ampls, sign_factor=1.0, lambda_factor=1.0):
     """Compute amplitudes for all fields with given sign and lambda factors."""
-    fields = ['u', 'v', 'w', 'X', 'Y']
+    fields = ["u", "v", "w", "X", "Y"]
     factor = sign_factor * 0.5 * (1.0 + lambda_factor * lmbda * u)
-    
+
     for field in fields:
         getattr(ampls, field)[...] = factor * getattr(slopes, field)
 
 
 def _compute_reconstructed_values(sol, ampls, order_two, result):
     """Compute reconstructed values for all fields."""
-    fields = ['u', 'v', 'w', 'X']
+    fields = ["u", "v", "w", "X"]
     for field in fields:
-        getattr(result, field)[...] = getattr(sol, field) + order_two * getattr(ampls, field)
-    
+        getattr(result, field)[...] = getattr(sol, field) + order_two * getattr(
+            ampls, field
+        )
+
     # Y field has special handling (reciprocal computation)
     result.Y[...] = 1.0 / (1.0 / sol.Y + order_two * ampls.Y)
 
-def _compute_rhoy_reconstruction(mem, lefts, rights, lefts_idx, rights_idx, 
-                                vel, split_step, order_two, lmbda):
+
+def _compute_rhoy_reconstruction(
+    mem, lefts, rights, lefts_idx, rights_idx, vel, split_step, order_two, lmbda
+):
     """Compute rhoY reconstruction for both left and right sides."""
     # Use existing arrays for in-place operations
     # First compute on lefts.rhoY, then copy to rights.rhoY
-    
+
     # Start with average in lefts array
     lefts.rhoY[lefts_idx] = 0.5 * (mem.sol.rhoY[lefts_idx] + mem.sol.rhoY[rights_idx])
-    
+
     # Subtract velocity correction in-place
-    lefts.rhoY[lefts_idx] -= order_two * 0.5 * lmbda * (
-        vel[split_step][rights_idx] * mem.sol.rhoY[rights_idx] -
-        vel[split_step][lefts_idx] * mem.sol.rhoY[lefts_idx]
+    lefts.rhoY[lefts_idx] -= (
+        order_two
+        * 0.5
+        * lmbda
+        * (
+            vel[split_step][rights_idx] * mem.sol.rhoY[rights_idx]
+            - vel[split_step][lefts_idx] * mem.sol.rhoY[lefts_idx]
+        )
     )
-    
+
     # Copy result to rights
     rights.rhoY[rights_idx] = lefts.rhoY[lefts_idx]
-    
+
     return lefts.rhoY[lefts_idx]
 
 
-def _compute_pressure_reconstruction(lefts, rights, lefts_idx, rights_idx, 
-                                   reconstructed_rhoy, gamm):
+def _compute_pressure_reconstruction(
+    lefts, rights, lefts_idx, rights_idx, reconstructed_rhoy, gamm
+):
     """Compute pressure reconstruction using power law."""
-    reconstructed_p0 = reconstructed_rhoy ** gamm
-    lefts.p0[lefts_idx] = reconstructed_p0
-    rights.p0[rights_idx] = reconstructed_p0
-    
-    return reconstructed_p0
\ No newline at end of file
+    reconstructed_p0 = reconstructed_rhoy**gamm
+    lefts.p[lefts_idx] = reconstructed_p0
+    rights.p[rights_idx] = reconstructed_p0
+
+    return reconstructed_p0
diff --git a/src/pybella/flow_solver/numerics/explicit_advection/riemann_solver.py b/src/pybella/flow_solver/numerics/explicit_advection/riemann_solver.py
new file mode 100644
index 00000000..88f35532
--- /dev/null
+++ b/src/pybella/flow_solver/numerics/explicit_advection/riemann_solver.py
@@ -0,0 +1,81 @@
+import numpy as np
+import numba as nb
+from ....utils import slices
+
+
+def hll(mem, flux, Lefts, Rights):
+    """
+    HLL solver for the Riemann problem. Chooses the advected quantities from `Lefts` or `Rights` based on the direction given by `flux`.
+
+    Returns
+    -------
+    :py:class:`management.variable.States`
+        `flux` data container with the solution of the Riemann problem.
+
+    """
+    ndim = mem.sol.rho.ndim
+    left_idx, right_idx, _ = slices.get_interface_indices(ndim)
+    remove_cols_idx = slices.get_last_dim_inner_slice(ndim)
+
+    # Compute primitive variables
+    Lefts.primitives(mem.th)
+    Rights.primitives(mem.th)
+
+    # Compute upwind weights
+    upwind = 0.5 * (1.0 + np.sign(flux.rhoY))
+    upl = upwind[right_idx]
+    upr = 1.0 - upwind[left_idx]
+
+    # Pre-compute common weights
+    left_weight = upl[left_idx] / Lefts.Y[left_idx]
+    right_weight = upr[right_idx] / Rights.Y[right_idx]
+
+    # Define flux components to compute
+    flux_components = [
+        ("rhou", "u"),
+        ("rho", None, 1.0),  # state_value=1.0
+        ("rhov", "v"),
+        ("rhow", "w"),
+        ("rhoX", "X"),
+    ]
+
+    # Compute all flux components
+    for component in flux_components:
+        flux_attr = component[0]
+        state_attr = component[1] if len(component) > 1 else None
+        state_value = component[2] if len(component) > 2 else 1.0
+
+        # Get state values
+        if state_attr is not None:
+            left_val = getattr(Lefts, state_attr)[left_idx]
+            right_val = getattr(Rights, state_attr)[right_idx]
+        else:
+            left_val = right_val = state_value
+
+        _compute_flux_component(
+            getattr(flux, flux_attr),
+            flux.rhoY,
+            left_weight,
+            right_weight,
+            left_val,
+            right_val,
+            remove_cols_idx,
+        )
+
+    return flux
+
+
+@nb.njit(cache=True)
+def _compute_flux_component(
+    flux_values,
+    rhoY_values,
+    left_weight,
+    right_weight,
+    left_val,
+    right_val,
+    remove_cols_idx,
+):
+    """Numba-optimised flux component computation."""
+    flux_values[remove_cols_idx] = rhoY_values[remove_cols_idx] * (
+        left_weight * left_val + right_weight * right_val
+    )
diff --git a/src/pybella/flow_solver/numerics/explicit_euler.py b/src/pybella/flow_solver/numerics/explicit_euler.py
new file mode 100644
index 00000000..44f79d14
--- /dev/null
+++ b/src/pybella/flow_solver/numerics/explicit_euler.py
@@ -0,0 +1,81 @@
+import numpy as np
+
+from ...utils.operators import convolution, divergence, gradient
+from ..utils.boundary import cell_boundary as bdry_c
+from ..utils.boundary import node_boundary as bdry_n
+from ..utils.boundary import common as bdry
+
+
+def do_forward_step(mem, ud, dt, writer=None, label=None, debug=False):
+    # Unpack frequently used variables
+    th, sol, npf, node, elem = mem.th, mem.sol, mem.npf, mem.node, mem.elem
+    ndim = elem.ndim
+
+    nonhydro = ud.nonhydrostasy
+    g, Msq = ud.gravity_strength[1], ud.Msq
+    Ginv = th.Gammainv
+    corr_h1, corr_v, corr_h2 = ud.coriolis_strength
+    u0, v0, w0 = ud.u_wind_speed, ud.v_wind_speed, ud.w_wind_speed
+
+    # Reusable derived quantities
+    rho, rhoY, rhoX = sol.rho, sol.rhoY, sol.rhoX
+    rhou, rhov, rhow = sol.rhou, sol.rhov, sol.rhow
+
+    # Pressure and derivatives
+    p2n = npf.p2_nodes
+    dp2n = np.zeros_like(p2n)
+
+    S0c = npf.HydroState.get_S0c(elem)
+    dSdy = npf.HydroState_n.get_dSdy(elem, node)
+
+    # Compute divergence
+    npf.rhs[...] = divergence.compute_at_nodes(npf.rhs, elem, sol, ud)
+    if not hasattr(ud, "ATMOSPHERIC_EXTENSION"):
+        bdry.scale_wall_node_values(npf.rhs, node, ud, 2.0)
+
+    if debug:
+        writer.populate(str(label), "rhs", npf.rhs)
+
+    # Compute compressibility kernel
+    kernel = convolution.get_averaging_kernel(ndim, width=2)
+    dpidP = (th.gm1 / Msq) * convolution.apply_convolution_kernel(
+        rhoY ** (th.gamm - 2.0), kernel=kernel, normalize=True, use_numba=True
+    )
+
+    rhoYovG = Ginv * rhoY
+    dbuoy = rhoY * (rhoX / rho)
+
+    # Pressure gradients
+    dpdx, dpdy, dpdz = gradient.compute_at_nodes(p2n, ndim, node.dxyz)
+
+    # Wind perturbations
+    drhou = rhou - u0 * rho
+    drhov = rhov - v0 * rho
+    drhow = rhow - w0 * rho
+    v = rhov / rho
+
+    # Momentum update (u, v, w)
+    rhou -= dt * (rhoYovG * dpdx - corr_h2 * drhov + corr_v * drhow)
+    rhov -= (
+        dt
+        * (
+            rhoYovG * dpdy
+            + (g / Msq) * dbuoy * nonhydro
+            - corr_h1 * drhow
+            + corr_h2 * drhou
+        )
+        * (1 - ud.is_ArakawaKonor)
+    )
+
+    if ndim == 3:
+        rhow -= dt * (rhoYovG * dpdz - corr_v * drhou + corr_h1 * drhov)
+
+    # Scalar update (rhoX)
+    sol.rhoX[...] = (rho * (rho / rhoY - S0c)) - dt * (v * dSdy) * rho
+
+    # Compressibility correction to p2
+    dp2n[node.i1] -= dt * dpidP * npf.rhs
+    npf.p2_nodes += ud.compressibility * dp2n
+
+    # Boundary conditions
+    bdry_n.set_ghost_nodes(npf.p2_nodes, node, ud)
diff --git a/src/pybella/flow_solver/numerics/implicit_euler.py b/src/pybella/flow_solver/numerics/implicit_euler.py
new file mode 100644
index 00000000..7fa9ba2b
--- /dev/null
+++ b/src/pybella/flow_solver/numerics/implicit_euler.py
@@ -0,0 +1,242 @@
+import numpy as np
+import scipy as sp
+
+from ...utils.operators import convolution, divergence, gradient
+from ...utils.operators.laplacian import preconditioner, lap2D_manual, lap3D
+from ..utils.boundary import cell_boundary as bdry_c
+from ..utils.boundary import node_boundary as bdry_n
+from ..utils.boundary import common as bdry
+from . import coriolis
+
+
+class solver_counter(object):
+    """
+    taken from https://stackoverflow.com/questions/33512081/getting-the-number-of-iterations-of-scipys-gmres-iterative-method
+
+    """
+
+    def __init__(self):
+        self.niter = 0
+
+    def __call__(self, rk=None):
+        self.niter += 1
+        self.rk = rk
+
+
+def do_explicit_part(mem, ud, dt):
+    nonhydro = ud.nonhydrostasy
+    g = ud.gravity_strength[1]
+    Msq = ud.Msq
+
+    dbuoy = mem.sol.rhoY * (mem.sol.rhoX / mem.sol.rho)
+    mem.sol.rhov = (nonhydro * mem.sol.rhov) - dt * (g / Msq) * dbuoy
+
+    mem.sol.mod_bg_wind(ud, -1.0)
+
+    coriolis.multiply_inverse_terms(mem.sol, mem, ud, dt)
+
+    mem.sol.mod_bg_wind(ud, +1.0)
+
+
+def do_implicit_part(
+    mem,
+    ud,
+    dt,
+    sol0=None,
+    writer=None,
+    label=None,
+    debug=False,
+):
+    """
+    Optimized version with reduced redundancy and improved structure.
+    """
+    # Early return optimization - disable writer if not debugging
+    if not debug:
+        writer = None
+
+    nc = mem.node.sc
+
+    # Helper function to reduce writer boilerplate
+    def write_debug_data(key, data):
+        if writer is not None:
+            writer.populate(str(label), key, data)
+
+    # Initial debug output
+    write_debug_data("p2_initial", mem.npf.p2_nodes)
+
+    # Set boundary data and compute operator coefficients (consolidated)
+    sol_for_boundary = sol0 if sol0 is not None else mem.sol
+    bdry_c.set_ghost_cells(mem, ud, sol=sol_for_boundary)
+    operator_coefficients_nodes(mem, ud, dt)
+
+    # Debug output for w components
+    if writer is not None:
+        write_debug_data("hcenter", mem.npf.wcenter)
+        write_debug_data("wplusx", mem.npf.wplus[0])
+        write_debug_data("wplusy", mem.npf.wplus[1])
+
+        # Handle 3D case more cleanly
+        wplusz_data = (
+            mem.npf.wplus[2] if mem.elem.ndim == 3 else np.zeros_like(mem.npf.wplus[0])
+        )
+        write_debug_data("wplusz", wplusz_data)
+
+    # Boundary and correction operations
+    # bdry.set_ghost_nodes(mem.npf.p2_nodes, mem.node, ud)
+    _correction_nodes(mem, ud, dt, mem.npf.p2_nodes, 0)
+    bdry_c.set_ghost_cells(mem, ud)
+
+    # Compute RHS
+    mem.npf.rhs[...] = divergence.compute_at_nodes(mem.npf.rhs, mem.elem, mem.sol, ud)
+    write_debug_data("rhs", mem.npf.rhs)
+
+    mem.npf.rhs /= dt
+
+    # Handle compressibility - simplified logic
+    _apply_compressibility_correction(mem, ud)
+
+    write_debug_data("rhs_nodes", mem.npf.rhs)
+
+    # Prepare and solve linear system
+    lap, rhs_inner = _prepare_linear_system(mem, ud, dt)
+
+    # Solve using BiCGSTAB
+    counter = solver_counter()
+    p2, _ = sp.sparse.linalg.bicgstab(
+        lap, rhs_inner, atol=ud.tol, maxiter=ud.max_iterations, callback=counter
+    )
+
+    # Reshape solution and apply
+    p2_full = _reshape_solution(p2, mem, ud, nc)
+    write_debug_data("p2_full", p2_full)
+
+    # # Final boundary and correction operations
+    # bdry.set_ghost_nodes(p2_full, mem.node, ud)
+    _correction_nodes(mem, ud, dt, p2_full, 1)
+
+    mem.npf.p2_nodes[...] += p2_full
+    bdry_n.set_ghost_nodes(mem.npf.p2_nodes, mem.node, ud)
+    bdry_c.set_ghost_cells(mem, ud)
+
+
+def _correction_nodes(mem, ud, dt, p, updt_chi):
+    ndim = mem.node.ndim
+    Gammainv = mem.th.Gammainv
+
+    dSdy = mem.npf.HydroState_n.get_dSdy(mem.elem, mem.node)
+
+    Dpx, Dpy, Dpz = gradient.compute_at_nodes(p, mem.elem.ndim, mem.node.dxyz)
+
+    thinv = mem.sol.rho / mem.sol.rhoY
+
+    Y = mem.sol.rhoY / mem.sol.rho
+    coeff = Gammainv * mem.sol.rhoY * Y
+
+    mem.npf.u[...] = -dt * coeff * Dpx
+    mem.npf.v[...] = -dt * coeff * Dpy
+    mem.npf.w[...] = -dt * coeff * Dpz
+
+    coriolis.multiply_inverse_terms(mem.npf, mem, ud, dt, attrs=["u", "v", "w"])
+
+    mem.sol.rhou += thinv * mem.npf.u
+    mem.sol.rhov += thinv * mem.npf.v
+    mem.sol.rhow += thinv * mem.npf.w if ndim == 3 else 0.0
+    mem.sol.rhoX += -updt_chi * dt * dSdy * mem.sol.rhov
+
+
+def operator_coefficients_nodes(mem, ud, dt):
+    Gammainv = mem.th.Gammainv
+    ndim = mem.node.ndim
+
+    ccenter = -ud.Msq * mem.th.gm1inv / (dt**2)
+    cexp = 2.0 - mem.th.gamm
+
+    Y = mem.sol.rhoY / mem.sol.rho
+    coeff = Gammainv * mem.sol.rhoY * Y
+
+    for dim in range(ndim):
+        mem.npf.wplus[dim][...] = coeff
+
+    kernel = convolution.get_averaging_kernel(ndim, width=2)
+
+    mem.npf.wcenter = ccenter * convolution.apply_convolution_kernel(
+        mem.sol.rhoY**cexp, kernel
+    )
+
+    if not hasattr(ud, "ATMOSPHERIC_EXTENSION"):
+        bdry.scale_wall_node_values(mem.npf.wcenter, mem.node, ud)
+
+
+def _apply_compressibility_correction(mem, ud):
+    """
+    Extracted compressibility logic for better readability.
+    """
+    if ud.is_compressible == 0:
+        if ud.is_ArakawaKonor:
+            mem.npf.rhs -= mem.npf.wcenter * mem.npf.dp2_nodes
+            mem.npf.wcenter[...] = 0.0
+        else:
+            # Simplified - this was redundant multiplication
+            mem.npf.wcenter[...] *= ud.compressibility
+    else:
+        mem.npf.wcenter *= ud.compressibility
+
+
+def _prepare_linear_system(mem, ud, dt):
+    """
+    Prepare the linear system components based on dimensionality.
+    """
+    if mem.elem.ndim == 2:
+        return _prepare_2d_system(mem, ud, dt)
+    else:  # 3D case
+        return _prepare_3d_system(mem, ud, dt)
+
+
+def _prepare_2d_system(mem, ud, dt):
+    """Prepare 2D linear system."""
+    Vec = mem.npf
+    coriolis_params = coriolis.multiply_inverse_terms(
+        Vec, mem, ud, dt, attrs=("u", "v", "w"), get_coeffs=True
+    )
+
+    diag_inv = preconditioner.prepare_diag(mem.npf, mem.node)
+    mem.npf.rhs *= diag_inv
+
+    p2 = mem.npf.p2_nodes[mem.node.i2].T
+    lap = lap2D_manual.get_linop(mem.npf, mem.node, coriolis_params, diag_inv, ud)
+    sh = p2.shape[0] * p2.shape[1]
+
+    lap = sp.sparse.linalg.LinearOperator((sh, sh), lap)
+    rhs_inner = mem.npf.rhs[mem.node.i1].T.ravel()
+
+    return lap, rhs_inner
+
+
+def _prepare_3d_system(mem, ud, dt):
+    """Prepare 3D linear system."""
+    # Note: diag_inv appears to be used but not defined in 3D case
+    # This might be a bug in the original code
+    diag_inv = None  # TODO: Verify if this should be computed for 3D
+
+    lap = lap3D.get_linop(mem.elem, mem.node, mem.npf, ud, diag_inv, dt)
+    p2 = mem.npf.p2_nodes  # Define p2 for 3D case
+    sh = p2.reshape(-1).shape[0]
+
+    lap = sp.sparse.linalg.LinearOperator((sh, sh), lap)
+    rhs_inner = mem.npf.rhs[mem.node.i1].ravel()
+
+    return lap, rhs_inner, sh
+
+
+def _reshape_solution(p2, mem, ud, nc):
+    """
+    Reshape the solution vector back to the appropriate format.
+    """
+    p2_full = np.zeros(nc).squeeze()
+
+    if mem.elem.ndim == 2:
+        p2_full[mem.node.i2] = p2.reshape(mem.npf.rhs[mem.node.i1].T.shape).T
+    else:  # 3D case
+        p2_full[mem.node.i1] = p2.reshape(ud.inx + 2, ud.iny + 2, ud.inz + 2)
+
+    return p2_full
diff --git a/src/pybella/flow_solver/physics/gas_dynamics/cfl.py b/src/pybella/flow_solver/physics/cfl.py
similarity index 71%
rename from src/pybella/flow_solver/physics/gas_dynamics/cfl.py
rename to src/pybella/flow_solver/physics/cfl.py
index e1eb709f..2274e72f 100644
--- a/src/pybella/flow_solver/physics/gas_dynamics/cfl.py
+++ b/src/pybella/flow_solver/physics/cfl.py
@@ -1,11 +1,12 @@
 import numpy as np
 
+
 def dynamic_timestep(Sol, time, time_output, elem, ud, th, step):
     """
     Calculate dynamic timestep for CFD simulation.
 
     Documentation to be homogenised.
-    
+
     Args:
         Sol: Solution object containing flow variables
         time: Current simulation time
@@ -14,79 +15,111 @@ def dynamic_timestep(Sol, time, time_output, elem, ud, th, step):
         ud: User data object with CFL and timestep parameters
         th: Thermodynamic properties
         step: Current step number
-    
+
     Returns:
         If acoustic_timestep == 1: dt (float)
         Else: tuple of (dt, cfl, cfl_ac)
     """
     machine_epsilon = np.finfo(float).eps
-    
+
     # Calculate thermodynamic properties
-    p = Sol.rhoY ** th.gamm
+    p = Sol.rhoY**th.gamm
     c = np.sqrt(th.gamm * p / Sol.rho) / np.sqrt(ud.Msq)
-    
+
     # Calculate velocity components
     u = np.abs(Sol.rhou / Sol.rho)
     v = np.abs(Sol.rhov / Sol.rho)
     w = np.abs(Sol.rhow / Sol.rho)
-    
+
     # Find maximum velocities (with minimum threshold)
     u_max = max(u.max(), machine_epsilon)
     v_max = max(v.max(), machine_epsilon)
     w_max = max(w.max(), machine_epsilon)
-    
+
     # Calculate acoustic velocities
     upc_max = max((u + c).max(), machine_epsilon)
     vpc_max = max((v + c).max(), machine_epsilon)
     wpc_max = max((w + c).max(), machine_epsilon)
-    
+
     if ud.acoustic_timestep == 1:
         return _calculate_acoustic_timestep(
-            ud.CFL, elem, upc_max, vpc_max, wpc_max, 
-            time, time_output, ud, step, machine_epsilon
+            ud.CFL,
+            elem,
+            upc_max,
+            vpc_max,
+            wpc_max,
+            time,
+            time_output,
+            ud,
+            step,
+            machine_epsilon,
         )
     else:
-        return _calculate_convective_timestep(
-            ud.CFL, elem, u_max, v_max, w_max, upc_max, vpc_max, wpc_max,
-            time, time_output, ud, step, machine_epsilon
+        return _calculate_advective_timestep(
+            ud.CFL,
+            elem,
+            u_max,
+            v_max,
+            w_max,
+            upc_max,
+            vpc_max,
+            wpc_max,
+            time,
+            time_output,
+            ud,
+            step,
+            machine_epsilon,
         )
 
 
-def _calculate_acoustic_timestep(CFL, elem, upc_max, vpc_max, wpc_max, 
-                                time, time_output, ud, step, machine_epsilon):
+def _calculate_acoustic_timestep(
+    CFL, elem, upc_max, vpc_max, wpc_max, time, time_output, ud, step, machine_epsilon
+):
     """Calculate timestep based on acoustic CFL condition."""
     # Calculate directional timesteps
     dt_directions = [
         CFL * elem.dx / upc_max,
         CFL * elem.dy / vpc_max,
-        CFL * elem.dz / wpc_max
+        CFL * elem.dz / wpc_max,
     ]
     dt_cfl = min(dt_directions)
-    
+
     # Apply ramping factor
     ramp_factor = ud.dtfixed0 + min(step, 1.0) * (ud.dtfixed - ud.dtfixed0)
     dt = min(dt_cfl, ramp_factor)
-    
+
     # Ensure we don't overshoot the output time
     remaining_time = time_output - time
     if dt > remaining_time:
         dt = remaining_time + machine_epsilon
-    
+
     return dt
 
 
-def _calculate_convective_timestep(CFL, elem, u_max, v_max, w_max, 
-                                  upc_max, vpc_max, wpc_max,
-                                  time, time_output, ud, step, machine_epsilon):
+def _calculate_advective_timestep(
+    CFL,
+    elem,
+    u_max,
+    v_max,
+    w_max,
+    upc_max,
+    vpc_max,
+    wpc_max,
+    time,
+    time_output,
+    ud,
+    step,
+    machine_epsilon,
+):
     """Calculate timestep based on convective CFL condition."""
     # Calculate directional timesteps
     dt_directions = [
         CFL * elem.dx / u_max,
         CFL * elem.dy / v_max,
-        CFL * elem.dz / w_max
+        CFL * elem.dz / w_max,
     ]
     dt_cfl = min(dt_directions)
-    
+
     # Apply ramping and step scaling for positive steps
     if step >= 0:
         ramp_factor = ud.dtfixed0 + min(step, 1.0) * (ud.dtfixed - ud.dtfixed0)
@@ -94,18 +127,14 @@ def _calculate_convective_timestep(CFL, elem, u_max, v_max, w_max,
         dt *= min(float(step + 1), 1.0)
     else:
         dt = dt_cfl
-    
+
     # Ensure we don't overshoot the output time
     remaining_time = time_output - time
     if dt > remaining_time:
         dt = remaining_time
-    
+
     # Calculate CFL numbers for output
     cfl = CFL * dt / dt_cfl
-    cfl_ac = max(
-        dt * upc_max / elem.dx,
-        dt * vpc_max / elem.dy,
-        dt * wpc_max / elem.dz
-    )
-    
-    return dt, cfl, cfl_ac
\ No newline at end of file
+    cfl_ac = max(dt * upc_max / elem.dx, dt * vpc_max / elem.dy, dt * wpc_max / elem.dz)
+
+    return dt, cfl, cfl_ac
diff --git a/src/pybella/flow_solver/physics/gas_dynamics/eos.py b/src/pybella/flow_solver/physics/eos.py
similarity index 84%
rename from src/pybella/flow_solver/physics/gas_dynamics/eos.py
rename to src/pybella/flow_solver/physics/eos.py
index f7c00226..3e91d304 100644
--- a/src/pybella/flow_solver/physics/gas_dynamics/eos.py
+++ b/src/pybella/flow_solver/physics/eos.py
@@ -1,7 +1,5 @@
 import numpy as np
 
-from ...utils import boundary as bdry
-
 
 def nonhydrostasy(ud, t, step):
     if step >= 0:
@@ -71,14 +69,3 @@ def rhoe(rho, u, v, w, p, ud, th):
     gm1inv = th.gm1inv
 
     return p * gm1inv + 0.5 * Msq * rho * (u**2 + v**2 + w**2)
-
-
-def synchronise_variables(mpv, Sol, elem, node, ud, th):
-    scale_factor = 1.0 / ud.Msq
-
-    if ud.is_compressible:
-        p2bg = mpv.HydroState.p20[0, :].reshape(1, -1)
-        p2bg = np.repeat(p2bg, elem.icx, axis=0)
-        mpv.p2_cells = scale_factor * Sol.rhoY**th.gm1 - p2bg
-
-    bdry.set_ghostcells_p2(mpv.p2_cells, elem, ud)
diff --git a/src/pybella/flow_solver/physics/gas_dynamics/numerical_flux.py b/src/pybella/flow_solver/physics/gas_dynamics/numerical_flux.py
deleted file mode 100644
index 80b31e04..00000000
--- a/src/pybella/flow_solver/physics/gas_dynamics/numerical_flux.py
+++ /dev/null
@@ -1,106 +0,0 @@
-# -*- coding: utf-8 -*-
-import numpy as np
-from numba import njit
-
-from ....utils.operators import get_flux_convolution_kernels, apply_directional_convolution
-from ....utils.slices import get_inner_slice, get_interface_indices, get_last_dim_inner_slice
-
-def recompute_advective_fluxes(mem, **kwargs):
-    """Recompute the advective fluxes at the cell interfaces.
-    
-    Parameters
-    ----------
-    mem : object
-        Memory object containing sol and flux attributes
-    **kwargs
-        Optional pre-computed velocity components ('u', 'v', 'w')
-    """
-    ndim = mem.sol.rho.ndim
-    inner_idx = get_inner_slice(ndim)
-    kernels = get_flux_convolution_kernels(ndim)
-    
-    # Define the component order and corresponding flux indices
-    components = ['u', 'v'] if ndim == 2 else ['u', 'v', 'w']
-    rho_components = ['rhou', 'rhov'] if ndim == 2 else ['rhou', 'rhov', 'rhow']
-    
-    for i, (comp, rho_comp) in enumerate(zip(components, rho_components)):
-        # Use provided velocity or compute from momentum
-        if comp in kwargs:
-            rhoY_vel = kwargs[comp]
-        else:
-            momentum = getattr(mem.sol, rho_comp)
-            rhoY_vel = mem.sol.rhoY * momentum / mem.sol.rho
-        
-        # Apply directional convolution
-        mem.flux[i].rhoY[inner_idx] = apply_directional_convolution(
-            rhoY_vel, kernels[comp], comp, ndim
-        )
-
-@njit(cache=True)
-def _compute_flux_component(flux_values, rhoY_values, left_weight, right_weight, 
-                                  left_val, right_val, remove_cols_idx):
-    """Numba-optimised flux component computation."""
-    flux_values[remove_cols_idx] = rhoY_values[remove_cols_idx] * (
-        left_weight * left_val + right_weight * right_val
-    )
-
-def hll_solver(mem, flux, Lefts, Rights):
-    """
-    HLL solver for the Riemann problem. Chooses the advected quantities from `Lefts` or `Rights` based on the direction given by `flux`.
-
-    Returns
-    -------
-    :py:class:`management.variable.States`
-        `flux` data container with the solution of the Riemann problem.
-    
-    """
-    ndim = mem.sol.rho.ndim
-    left_idx, right_idx, _ = get_interface_indices(ndim)
-    remove_cols_idx = get_last_dim_inner_slice(ndim)
-
-    # Compute primitive variables
-    Lefts.primitives(mem.th)
-    Rights.primitives(mem.th)
-
-    # Compute upwind weights
-    upwind = 0.5 * (1.0 + np.sign(flux.rhoY))
-    upl = upwind[right_idx]
-    upr = 1.0 - upwind[left_idx]
-    
-    # Pre-compute common weights
-    left_weight = upl[left_idx] / Lefts.Y[left_idx]
-    right_weight = upr[right_idx] / Rights.Y[right_idx]
-
-    # Define flux components to compute
-    flux_components = [
-        ('rhou', 'u'),
-        ('rho', None, 1.0),  # state_value=1.0
-        ('rhov', 'v'),
-        ('rhow', 'w'),
-        ('rhoX', 'X')
-    ]
-    
-    # Compute all flux components
-    for component in flux_components:
-        flux_attr = component[0]
-        state_attr = component[1] if len(component) > 1 else None
-        state_value = component[2] if len(component) > 2 else 1.0
-        
-        # Get state values
-        if state_attr is not None:
-            left_val = getattr(Lefts, state_attr)[left_idx]
-            right_val = getattr(Rights, state_attr)[right_idx]
-        else:
-            left_val = right_val = state_value
-        
-        _compute_flux_component(
-            getattr(flux, flux_attr),
-            flux.rhoY,
-            left_weight,
-            right_weight, 
-            left_val,
-            right_val,
-            remove_cols_idx
-        )
-
-    return flux
\ No newline at end of file
diff --git a/src/pybella/flow_solver/physics/hydrostatics.py b/src/pybella/flow_solver/physics/hydrostatics.py
index 6aa8e215..b45a92f5 100644
--- a/src/pybella/flow_solver/physics/hydrostatics.py
+++ b/src/pybella/flow_solver/physics/hydrostatics.py
@@ -1,7 +1,7 @@
 import numpy as np
 import numba as nb
 
-from ..utils import boundary as bdry
+from ..utils.boundary import node_boundary as bdry_n
 
 
 def column(HydroState, HydroState_n, Y, Y_n, elem, node, th, ud):
@@ -80,7 +80,7 @@ def column(HydroState, HydroState_n, Y, Y_n, elem, node, th, ud):
     HydroState_n.p20[xc_idx, igy + 1 :] = pi_hydro_n[:, igy:] / ud.Msq
 
 
-def integrated_state(mpv, elem, node, th, ud):
+def integrated_state(npf, elem, node, th, ud):
     """
     Compute hydrostatic background state for atmospheric model.
     Handles arbitrary stratification profiles and proper numerical integration.
@@ -138,25 +138,25 @@ def integrated_state(mpv, elem, node, th, ud):
         rhoY_hydro = pi_hydro**gm1_inv
 
         # Update cell solutions
-        mpv.HydroState.rhoY0[:] = rhoY_hydro
-        mpv.HydroState.rho0[:] = rhoY_hydro * S_ps
-        mpv.HydroState.p0[:] = p_hydro
-        mpv.HydroState.p20[:] = pi_hydro / ud.Msq
-        mpv.HydroState.S0[:] = S_ps
-        mpv.HydroState.S10[:] = 0.0
-        mpv.HydroState.Y0[:] = 1.0 / S_ps
+        npf.HydroState.rhoY0[:] = rhoY_hydro
+        npf.HydroState.rho0[:] = rhoY_hydro * S_ps
+        npf.HydroState.p0[:] = p_hydro
+        npf.HydroState.p20[:] = pi_hydro / ud.Msq
+        npf.HydroState.S0[:] = S_ps
+        npf.HydroState.S10[:] = 0.0
+        npf.HydroState.Y0[:] = 1.0 / S_ps
 
         ############################
         # Update node hydrostates
         ############################
 
         # Bottom reference node (y=0)
-        mpv.HydroState_n.Y0[igy] = ud.stratification(0.0)
-        mpv.HydroState_n.rhoY0[igy] = rhoY0
-        mpv.HydroState_n.rho0[igy] = rhoY0 / ud.stratification(0.0)
-        mpv.HydroState_n.S0[igy] = 1.0 / mpv.HydroState_n.Y0[igy]
-        mpv.HydroState_n.p0[igy] = p0
-        mpv.HydroState_n.p20[igy] = pi0 / ud.Msq
+        npf.HydroState_n.Y0[igy] = ud.stratification(0.0)
+        npf.HydroState_n.rhoY0[igy] = rhoY0
+        npf.HydroState_n.rho0[igy] = rhoY0 / ud.stratification(0.0)
+        npf.HydroState_n.S0[igy] = 1.0 / npf.HydroState_n.Y0[igy]
+        npf.HydroState_n.p0[igy] = p0
+        npf.HydroState_n.p20[igy] = pi0 / ud.Msq
 
         # Ghost cells below bottom (negative heights)
         Sn_integral_p = np.zeros(igy)
@@ -179,46 +179,46 @@ def integrated_state(mpv, elem, node, th, ud):
         rhoY_hydro_n = pi_hydro_n**gm1_inv
 
         # Update node solutions - below reference
-        mpv.HydroState_n.rhoY0[:igy] = rhoY_hydro_n[:igy]
-        mpv.HydroState_n.Y0[: igy + 1] = ud.stratification(
+        npf.HydroState_n.rhoY0[:igy] = rhoY_hydro_n[:igy]
+        npf.HydroState_n.Y0[: igy + 1] = ud.stratification(
             0.5 * (y_ps[: igy + 1] + y_ps[: igy + 1] - elem.dy)
         )
-        mpv.HydroState_n.rho0[:igy] = rhoY_hydro_n[:igy] / mpv.HydroState_n.Y0[:igy]
-        mpv.HydroState_n.S0[:igy] = 1.0 / mpv.HydroState_n.Y0[:igy]
-        mpv.HydroState_n.p0[:igy] = rhoY_hydro_n[:igy] ** th.gamm
-        mpv.HydroState_n.p20[:igy] = pi_hydro_n[:igy] / ud.Msq
+        npf.HydroState_n.rho0[:igy] = rhoY_hydro_n[:igy] / npf.HydroState_n.Y0[:igy]
+        npf.HydroState_n.S0[:igy] = 1.0 / npf.HydroState_n.Y0[:igy]
+        npf.HydroState_n.p0[:igy] = rhoY_hydro_n[:igy] ** th.gamm
+        npf.HydroState_n.p20[:igy] = pi_hydro_n[:igy] / ud.Msq
 
         # Update node solutions - above reference
-        mpv.HydroState_n.rhoY0[igy + 1 :] = rhoY_hydro_n[igy:]
-        mpv.HydroState_n.Y0[igy + 1 :] = ud.stratification(
+        npf.HydroState_n.rhoY0[igy + 1 :] = rhoY_hydro_n[igy:]
+        npf.HydroState_n.Y0[igy + 1 :] = ud.stratification(
             0.5 * (y_ps[igy:] + y_ps[igy:] + elem.dy)
         )
-        mpv.HydroState_n.rho0[igy + 1 :] = (
-            rhoY_hydro_n[igy:] / mpv.HydroState_n.Y0[igy + 1 :]
+        npf.HydroState_n.rho0[igy + 1 :] = (
+            rhoY_hydro_n[igy:] / npf.HydroState_n.Y0[igy + 1 :]
         )
-        mpv.HydroState_n.S0[igy + 1 :] = 1.0 / mpv.HydroState_n.Y0[igy + 1 :]
-        mpv.HydroState_n.p0[igy + 1 :] = rhoY_hydro_n[igy:] ** th.gamm
-        mpv.HydroState_n.p20[igy + 1 :] = pi_hydro_n[igy:] / ud.Msq
+        npf.HydroState_n.S0[igy + 1 :] = 1.0 / npf.HydroState_n.Y0[igy + 1 :]
+        npf.HydroState_n.p0[igy + 1 :] = rhoY_hydro_n[igy:] ** th.gamm
+        npf.HydroState_n.p20[igy + 1 :] = pi_hydro_n[igy:] / ud.Msq
 
     else:
         # No gravity case - uniform atmosphere
-        mpv.HydroState.p20[:] = 1.0
-        mpv.HydroState.p0[:] = 1.0
-        mpv.HydroState.rho0[:] = 1.0
-        mpv.HydroState.rhoY0[:] = 1.0
-        mpv.HydroState.Y0[:] = 1.0
-        mpv.HydroState.S0[:] = 1.0
-        mpv.HydroState.S10[:] = 0.0
-
-        mpv.HydroState_n.p20[:] = 1.0
-        mpv.HydroState_n.p0[:] = 1.0
-        mpv.HydroState_n.rho0[:] = 1.0
-        mpv.HydroState_n.rhoY0[:] = 1.0
-        mpv.HydroState_n.Y0[:] = 1.0
-        mpv.HydroState_n.S0[:] = 1.0
-
-
-def analytical_state(mpv, elem, node, th, ud):
+        npf.HydroState.p20[:] = 1.0
+        npf.HydroState.p0[:] = 1.0
+        npf.HydroState.rho0[:] = 1.0
+        npf.HydroState.rhoY0[:] = 1.0
+        npf.HydroState.Y0[:] = 1.0
+        npf.HydroState.S0[:] = 1.0
+        npf.HydroState.S10[:] = 0.0
+
+        npf.HydroState_n.p20[:] = 1.0
+        npf.HydroState_n.p0[:] = 1.0
+        npf.HydroState_n.rho0[:] = 1.0
+        npf.HydroState_n.rhoY0[:] = 1.0
+        npf.HydroState_n.Y0[:] = 1.0
+        npf.HydroState_n.S0[:] = 1.0
+
+
+def analytical_state(npf, elem, node, th, ud):
     g = ud.gravity_strength[1]
     Gamma = th.Gamma
     Hex = 1.0 / (th.Gamma * g)
@@ -233,12 +233,12 @@ def analytical_state(mpv, elem, node, th, ud):
     p_n = pi_n**th.Gammainv
     rho_n = P_n / Y_n
 
-    mpv.HydroState_n.p20[...] = pi_n / ud.Msq
-    mpv.HydroState_n.p0[...] = p_n
-    mpv.HydroState_n.rho0[...] = rho_n
-    mpv.HydroState_n.rhoY0[...] = P_n
-    mpv.HydroState_n.Y0[...] = Y_n
-    mpv.HydroState_n.S0[...] = 1.0 / Y_n
+    npf.HydroState_n.p20[...] = pi_n / ud.Msq
+    npf.HydroState_n.p0[...] = p_n
+    npf.HydroState_n.rho0[...] = rho_n
+    npf.HydroState_n.rhoY0[...] = P_n
+    npf.HydroState_n.Y0[...] = Y_n
+    npf.HydroState_n.S0[...] = 1.0 / Y_n
 
     pi_cp = np.exp(-(elem.y + 0.5 * dy) / Hex)
     pi_cm = np.exp(-(elem.y - 0.5 * dy) / Hex)
@@ -249,15 +249,15 @@ def analytical_state(mpv, elem, node, th, ud):
     p_c = pi_c**th.Gammainv
     rho_c = P_c / Y_c
 
-    mpv.HydroState.p20[...] = pi_c / ud.Msq
-    mpv.HydroState.p0[...] = p_c
-    mpv.HydroState.rho0[...] = rho_c
-    mpv.HydroState.rhoY0[...] = P_c
-    mpv.HydroState.Y0[...] = Y_c
-    mpv.HydroState.S0[...] = 1.0 / Y_c
+    npf.HydroState.p20[...] = pi_c / ud.Msq
+    npf.HydroState.p0[...] = p_c
+    npf.HydroState.rho0[...] = rho_c
+    npf.HydroState.rhoY0[...] = P_c
+    npf.HydroState.Y0[...] = Y_c
+    npf.HydroState.S0[...] = 1.0 / Y_c
 
 
-def initial_pressure(Sol, mpv, elem, node, ud, th):
+def initial_pressure(Sol, npf, elem, node, ud, th):
     Gammainv = th.Gammainv
     igy = node.igy
     igx = node.igx
@@ -282,7 +282,7 @@ def initial_pressure(Sol, mpv, elem, node, ud, th):
     bdpdx[xn_idx] = np.sum(
         0.5
         * (Pm * thm + Pc * thc)
-        * (mpv.p2_cells[x_idx_c, y_idx] - mpv.p2_cells[x_idx_m, y_idx])
+        * (npf.p2_cells[x_idx_c, y_idx] - npf.p2_cells[x_idx_m, y_idx])
         * dy,
         axis=1,
     )
@@ -303,10 +303,9 @@ def initial_pressure(Sol, mpv, elem, node, ud, th):
     x_idx = slice(igx, -igx + 1)
     y_idx = slice(igy, -igy + 1)
 
-    mpv.p2_cells[x_idx, y_idx] += pibot[x_idx].reshape(
+    npf.p2_cells[x_idx, y_idx] += pibot[x_idx].reshape(
         -1, 1
-    ) - 1.0 * mpv.HydroState.p20[y_idx].reshape(1, -1)
-    bdry.set_ghostcells_p2(mpv.p2_cells, elem, ud)
+    ) - 1.0 * npf.HydroState.p20[y_idx].reshape(1, -1)
 
     icxn = node.icx
     icyn = node.icy
@@ -324,7 +323,7 @@ def initial_pressure(Sol, mpv, elem, node, ud, th):
     beta *= Gammainv / height
 
     bdpdx[1:] = np.sum(
-        Pc * thc * (mpv.p2_nodes[1:-1, igy:-igy] - mpv.p2_nodes[:-2, igy:-igy]) * dy,
+        Pc * thc * (npf.p2_nodes[1:-1, igy:-igy] - npf.p2_nodes[:-2, igy:-igy]) * dy,
         axis=1,
     )
     bdpdx *= Gammainv / height / dx
@@ -343,33 +342,33 @@ def initial_pressure(Sol, mpv, elem, node, ud, th):
 
     x_idx = slice(igx, -igx + 1)
     y_idx = slice(igy, -igy + 1)
-    mpv.p2_nodes[x_idx, y_idx] += pibot[x_idx].reshape(
+    npf.p2_nodes[x_idx, y_idx] += pibot[x_idx].reshape(
         -1, 1
-    ) - 1.0 * mpv.HydroState_n.p20[y_idx].reshape(1, -1)
+    ) - 1.0 * npf.HydroState_n.p20[y_idx].reshape(1, -1)
 
-    mpv.dp2_nodes[:, :] = mpv.p2_nodes
+    npf.dp2_nodes[:, :] = npf.p2_nodes
 
     # guess initial node value (at left-most node)
-    mpv.p2_nodes[igx, igy:-igy] = mpv.dp2_nodes[igx, igy:-igy]
+    npf.p2_nodes[igx, igy:-igy] = npf.dp2_nodes[igx, igy:-igy]
 
-    mpv.p2_nodes[:, :] = __loop_over_array(
-        igx, igy, icxn, icyn, mpv.p2_nodes, mpv.dp2_nodes
+    npf.p2_nodes[:, :] = __loop_over_array(
+        igx, igy, icxn, icyn, npf.p2_nodes, npf.dp2_nodes
     )
 
     assert ((node.icx + 1) % 2) == 1
-    delp2 = 0.5 * (mpv.p2_nodes[-igx - 1, igy:-igy] - mpv.p2_nodes[igx, igy:-igy])
+    delp2 = 0.5 * (npf.p2_nodes[-igx - 1, igy:-igy] - npf.p2_nodes[igx, igy:-igy])
     delp2 = delp2.reshape(1, -1)
-    sgn = np.ones_like(mpv.p2_nodes[:, 0][igy:-igy]).reshape(-1, 1)
+    sgn = np.ones_like(npf.p2_nodes[:, 0][igy:-igy]).reshape(-1, 1)
 
     sgn[1::2] *= -1
 
-    mpv.p2_nodes[igx:-igx, igy:-igy] += sgn * delp2
-    bdry.set_ghostnodes_p2(mpv.p2_nodes, node, ud)
+    npf.p2_nodes[igx:-igx, igy:-igy] += sgn * delp2
+    bdry_n.set_ghost_nodes(npf.p2_nodes, node, ud)
 
-    mpv.dp2_nodes[:, :] = 0.0
+    npf.dp2_nodes[:, :] = 0.0
 
     inner_domain = (slice(igx, -igx), slice(igy, -igy))
-    pi = ud.Msq * (mpv.p2_cells[inner_domain] + 1.0 * mpv.HydroState.p20[igy:-igy])
+    pi = ud.Msq * (npf.p2_cells[inner_domain] + 1.0 * npf.HydroState.p20[igy:-igy])
     Y = Sol.rhoY[inner_domain] / Sol.rho[inner_domain]
     rhoold = np.copy(Sol.rho[inner_domain])
     Sol.rhoY[inner_domain] = pi**th.gm1inv
diff --git a/src/pybella/flow_solver/physics/low_mach/laplacian.py b/src/pybella/flow_solver/physics/low_mach/laplacian.py
deleted file mode 100644
index dcc1821b..00000000
--- a/src/pybella/flow_solver/physics/low_mach/laplacian.py
+++ /dev/null
@@ -1,1880 +0,0 @@
-import numpy as np
-import scipy as sp
-import numba as nb
-
-from ....utils import options as opts
-
-
-def stencil_9pt(elem, node, mpv, Sol, ud, diag_inv, dt, coriolis_params):
-    igx = elem.igx
-    igy = elem.igy
-
-    icxn = node.icx
-    icyn = node.icy
-
-    iicxn = icxn - (2 * igx)
-    iicyn = icyn - (2 * igy)
-
-    iicxn, iicyn = iicyn, iicxn
-
-    dx = node.dy
-    dy = node.dx
-
-    inner_domain = (slice(igx, -igx), slice(igy, -igy))
-    i1 = node.i1
-
-    hplusx = mpv.wplus[1][i1].reshape(
-        -1,
-    )
-    hplusy = mpv.wplus[0][i1].reshape(
-        -1,
-    )
-    hcenter = mpv.wcenter[i1].reshape(
-        -1,
-    )
-
-    diag_inv = diag_inv[i1].reshape(
-        -1,
-    )
-
-    oodx = 1.0 / (dx)
-    oody = 1.0 / (dy)
-
-    x_periodic = ud.bdry_type[1] == opts.BdryType.PERIODIC
-    y_periodic = ud.bdry_type[0] == opts.BdryType.PERIODIC
-
-    x_wall = (
-        ud.bdry_type[1] == opts.BdryType.WALL
-        or ud.bdry_type[1] == opts.BdryType.RAYLEIGH
-    )
-    y_wall = (
-        ud.bdry_type[0] == opts.BdryType.WALL
-        or ud.bdry_type[0] == opts.BdryType.RAYLEIGH
-    )
-
-    #### Compute Coriolis parameters:
-    # nonhydro = ud.nonhydrostasy
-    # g = ud.gravity_strength[1]
-    # Msq = ud.Msq
-    # dy = elem.dy
-
-    # wh1, wv, wh2 = dt * ud.coriolis_strength
-
-    # igs = elem.igs
-
-    # ndim = node.ndim
-
-    # nindim = np.empty((ndim),dtype='object')
-    # innerdim = np.copy(nindim)
-    # innerdim1 = np.copy(nindim)
-    # eindim = np.empty((ndim),dtype='object')
-
-    # for dim in range(ndim):
-    #     is_periodic = ud.bdry_type[dim] == BdryType.PERIODIC
-    #     nindim[dim] = slice(igs[dim]-is_periodic,-igs[dim]+is_periodic)
-    #     innerdim[dim] = slice(igs[dim],-igs[dim])
-    #     eindim[dim] = slice(igs[dim]-is_periodic,-igs[dim]+is_periodic-1)
-
-    #     if dim == 1:
-    #         y_idx = slice(igs[dim]-is_periodic,-igs[dim]+is_periodic-1)
-    #         right_idx = None if -igs[dim]+is_periodic == 0 else -igs[dim]+is_periodic
-    #         y_idx1 = slice(igs[dim]-is_periodic+1, right_idx)
-
-    #     innerdim1[dim] = slice(igs[dim]-1, (-igs[dim]+1))
-
-    # strat = (mpv.HydroState_n.S0[y_idx1] - mpv.HydroState_n.S0[y_idx]) / dy
-
-    # nindim = tuple(nindim)
-    # eindim = tuple(eindim)
-    # innerdim = tuple(innerdim)
-    # innerdim1 = tuple(innerdim1)
-
-    # for dim in range(0,elem.ndim,2):
-    #     is_periodic = ud.bdry_type[dim] != BdryType.PERIODIC
-    #     strat = np.expand_dims(strat, dim)
-    #     strat = np.repeat(strat, elem.sc[dim]-int(2*is_periodic+igs[dim]), axis=dim)
-
-    # Y = Sol.rhoY[nindim] / Sol.rho[nindim]
-
-    # nu = np.zeros_like(mpv.wcenter)
-    # nu[eindim] = -dt**2 * (g / Msq) * strat * Y
-
-    # nu = nu[inner_domain].reshape(-1,)
-
-    # denom = 1.0 / (wh1**2 + wh2**2 + (nu + nonhydro) * (wv**2 + 1))
-
-    # coeff_uu = (wh1**2 + nu + nonhydro) * denom
-    # coeff_uv = nonhydro * (wh1 * wv + wh2) * denom
-    # coeff_vu = (wh1 * wv - wh2) * denom
-    # coeff_vv = nonhydro * (1 + wv**2) * denom
-
-    # coriolis_params = (coeff_vv, coeff_vu, coeff_uv, coeff_uu)
-    # coriolis_params = np.array(coriolis_params, dtype=np.float64)
-
-    return lambda p: lap2D_gather(
-        p,
-        igx,
-        igy,
-        iicxn,
-        iicyn,
-        hplusx,
-        hplusy,
-        hcenter,
-        oodx,
-        oody,
-        x_periodic,
-        y_periodic,
-        x_wall,
-        y_wall,
-        diag_inv,
-        coriolis_params,
-    )
-
-    # ndim = elem.ndim
-    # periodicity = np.zeros(ndim, dtype='int')
-    # for dim in range(0,ndim,2):
-    #     periodicity[dim] = ud.bdry_type[dim] == BdryType.PERIODIC
-
-    # # proj = (slice(None,),slice(None,),igz)
-    # i0 = (slice(0,-1),slice(0,-1))
-    # i1 = (slice(1,-1),slice(1,-1))
-    # i2 = (slice(igx,-igx),slice(igy,-igy))
-
-    # hplusx = mpv.wplus[0][i0][i1]
-    # hplusy = mpv.wplus[1][i0][i1]
-    # hcenter = mpv.wcenter[i2]
-    # diag_inv = diag_inv[i1]
-
-    # dxy = (dx, dy)
-
-    # #### Compute Coriolis parameters:
-    # nonhydro = ud.nonhydrostasy
-    # g = ud.gravity_strength[1]
-    # Msq = ud.Msq
-    # dy = elem.dy
-
-    # wh1, wv, wh2 = dt * ud.coriolis_strength
-
-    # first_nodes_row_right_idx = (slice(1,None))
-    # first_nodes_row_left_idx = (slice(0,-1))
-
-    # strat = (mpv.HydroState_n.S0[first_nodes_row_right_idx] - mpv.HydroState_n.S0[first_nodes_row_left_idx]) / dy
-
-    # for dim in range(0,elem.ndim,2):
-    #     strat = np.expand_dims(strat, dim)
-    #     strat = np.repeat(strat, elem.sc[dim], axis=dim)
-
-    # Y = Sol.rhoY / Sol.rho
-    # nu = -dt**2 * (g / Msq) * strat * Y
-
-    # coeff_uu = (wh1**2 + nu + nonhydro)
-    # coeff_uv = nonhydro * (wh1 * wv + wh2)
-    # coeff_vu = (wh1 * wv - wh2)
-    # coeff_vv = nonhydro * (1 + wv**2)
-
-    # coriolis_params = (coeff_uu[i1], coeff_uv, coeff_vu, coeff_vv)
-
-    # return lambda p : lap2Dc(p, hplusx, hplusy, hcenter, dxy, periodicity, diag_inv, coriolis_params)
-
-
-@nb.jit(nopython=True, nogil=False, cache=True)
-def lap2D_gather(
-    p,
-    igx,
-    igy,
-    iicxn,
-    iicyn,
-    hplusx,
-    hplusy,
-    hcenter,
-    oodx,
-    oody,
-    x_periodic,
-    y_periodic,
-    x_wall,
-    y_wall,
-    diag_inv,
-    coriolis,
-):
-    ngnc = (iicxn) * (iicyn)
-    lap = np.zeros((ngnc))
-    cnt_x = 0
-    cnt_y = 0
-
-    nine_pt = 0.25 * (2.0) * 1.0
-    cyy, cxx, cyx, cxy = coriolis
-    oodx2 = 0.5 * oodx**2
-    oody2 = 0.5 * oody**2
-
-    for idx in range(iicxn * iicyn):
-        ne_topleft = idx - iicxn - 1
-        ne_topright = idx - iicxn
-        ne_botleft = idx - 1
-        ne_botright = idx
-
-        # get indices of the 9pt stencil
-        topleft_idx = idx - iicxn - 1
-        midleft_idx = idx - 1
-        botleft_idx = idx + iicxn - 1
-
-        topmid_idx = idx - iicxn
-        midmid_idx = idx
-        botmid_idx = idx + iicxn
-
-        topright_idx = idx - iicxn + 1
-        midright_idx = idx + 1
-        botright_idx = idx + iicxn + 1
-
-        if cnt_x == 0:
-            topleft_idx += iicxn - 1
-            midleft_idx += iicxn - 1
-            botleft_idx += iicxn - 1
-
-            ne_topleft += iicxn - 1
-            ne_botleft += iicxn - 1
-
-        if cnt_x == (iicxn - 1):
-            topright_idx -= iicxn - 1
-            midright_idx -= iicxn - 1
-            botright_idx -= iicxn - 1
-
-            ne_topright -= iicxn - 1
-            ne_botright -= iicxn - 1
-
-        if cnt_y == 0:
-            topleft_idx += (iicxn) * (iicyn - 1)
-            topmid_idx += (iicxn) * (iicyn - 1)
-            topright_idx += (iicxn) * (iicyn - 1)
-
-            ne_topleft += (iicxn) * (iicyn - 1)
-            ne_topright += (iicxn) * (iicyn - 1)
-
-        if cnt_y == (iicyn - 1):
-            botleft_idx -= (iicxn) * (iicyn - 1)
-            botmid_idx -= (iicxn) * (iicyn - 1)
-            botright_idx -= (iicxn) * (iicyn - 1)
-
-            ne_botleft -= (iicxn) * (iicyn - 1)
-            ne_botright -= (iicxn) * (iicyn - 1)
-
-        topleft = p[topleft_idx]
-        midleft = p[midleft_idx]
-        botleft = p[botleft_idx]
-
-        topmid = p[topmid_idx]
-        midmid = p[midmid_idx]
-        botmid = p[botmid_idx]
-
-        topright = p[topright_idx]
-        midright = p[midright_idx]
-        botright = p[botright_idx]
-
-        hplusx_topleft = hplusx[ne_topleft]
-        hplusx_botleft = hplusx[ne_botleft]
-        hplusy_topleft = hplusy[ne_topleft]
-        hplusy_botleft = hplusy[ne_botleft]
-
-        hplusx_topright = hplusx[ne_topright]
-        hplusx_botright = hplusx[ne_botright]
-        hplusy_topright = hplusy[ne_topright]
-        hplusy_botright = hplusy[ne_botright]
-
-        cxx_tl = cxx[ne_topleft]
-        cxx_tr = cxx[ne_topright]
-        cxx_bl = cxx[ne_botleft]
-        cxx_br = cxx[ne_botright]
-
-        cxy_tl = cxy[ne_topleft]
-        cxy_tr = cxy[ne_topright]
-        cxy_bl = cxy[ne_botleft]
-        cxy_br = cxy[ne_botright]
-
-        cyx_tl = cyx[ne_topleft]
-        cyx_tr = cyx[ne_topright]
-        cyx_bl = cyx[ne_botleft]
-        cyx_br = cyx[ne_botright]
-
-        cyy_tl = cyy[ne_topleft]
-        cyy_tr = cyy[ne_topright]
-        cyy_bl = cyy[ne_botleft]
-        cyy_br = cyy[ne_botright]
-
-        if x_wall and (cnt_x == 0):
-            hplusx_topleft = 0.0
-            hplusy_topleft = 0.0
-            hplusx_botleft = 0.0
-            hplusy_botleft = 0.0
-
-        if x_wall and (cnt_x == (iicxn - 1)):
-            hplusx_topright = 0.0
-            hplusy_topright = 0.0
-            hplusx_botright = 0.0
-            hplusy_botright = 0.0
-
-        if y_wall and (cnt_y == 0):
-            hplusx_topleft = 0.0
-            hplusy_topleft = 0.0
-            hplusx_topright = 0.0
-            hplusy_topright = 0.0
-
-        if y_wall and (cnt_y == (iicyn - 1)):
-            hplusx_botleft = 0.0
-            hplusy_botleft = 0.0
-            hplusx_botright = 0.0
-            hplusy_botright = 0.0
-
-        # dp2dxdy1 = ((midmid - midleft) - (topmid - topleft)) * nine_pt
-        # dp2dxdy2 = ((midright - midmid) - (topright - topmid)) * nine_pt
-        # dp2dxdy3 = ((botmid - botleft) - (midmid - midleft)) * nine_pt
-        # dp2dxdy4 = ((botright - botmid) - (midright - midmid)) * nine_pt
-
-        # lap[idx] = - hplusx_topleft * oodx2 * ((midmid - midleft) - dp2dxdy1) \
-        #         -  hplusy_topleft * oody2 * ((midmid - topmid) - dp2dxdy1) \
-        #         +  hplusx_topright * oodx2 * ((midright - midmid) - dp2dxdy2) \
-        #         -  hplusy_topright * oody2 * ((midmid - topmid) + dp2dxdy2) \
-        #         -  hplusx_botleft * oodx2 * ((midmid - midleft) + dp2dxdy3) \
-        #         +  hplusy_botleft * oody2 * ((botmid - midmid) - dp2dxdy3) \
-        #         +  hplusx_botright * oodx2 * ((midright - midmid) + dp2dxdy4) \
-        #         +  hplusy_botright * oody2 * ((botmid - midmid) + dp2dxdy4) \
-        #         +  hcenter[idx] * p[idx]
-
-        Dx_tl = 0.5 * (topmid - topleft + midmid - midleft) * hplusx_topleft
-        Dx_tr = 0.5 * (topright - topmid + midright - midmid) * hplusx_topright
-        Dx_bl = 0.5 * (botmid - botleft + midmid - midleft) * hplusx_botleft
-        Dx_br = 0.5 * (botright - botmid + midright - midmid) * hplusx_botright
-
-        Dy_tl = 0.5 * (midmid - topmid + midleft - topleft) * hplusy_topleft
-        Dy_tr = 0.5 * (midright - topright + midmid - topmid) * hplusy_topright
-        Dy_bl = 0.5 * (botmid - midmid + botleft - midleft) * hplusy_botleft
-        Dy_br = 0.5 * (botright - midright + botmid - midmid) * hplusy_botright
-
-        fac = 1.0
-        Dxx = (
-            0.5
-            * (cxx_tr * Dx_tr - cxx_tl * Dx_tl + cxx_br * Dx_br - cxx_bl * Dx_bl)
-            * oodx
-            * oodx
-            * fac
-        )
-        Dyy = (
-            0.5
-            * (cyy_br * Dy_br - cyy_tr * Dy_tr + cyy_bl * Dy_bl - cyy_tl * Dy_tl)
-            * oody
-            * oody
-            * fac
-        )
-        Dyx = (
-            0.5
-            * (cyx_br * Dy_br - cyx_bl * Dy_bl + cyx_tr * Dy_tr - cyx_tl * Dy_tl)
-            * oody
-            * oodx
-            * fac
-        )
-        Dxy = (
-            0.5
-            * (cxy_br * Dx_br - cxy_tr * Dx_tr + cxy_bl * Dy_bl - cxy_tl * Dx_tl)
-            * oodx
-            * oody
-            * fac
-        )
-
-        lap[idx] = Dxx + Dyy + Dyx + Dxy + hcenter[idx] * p[idx]
-
-        # fac = 1.0
-        # lap[idx] = - fac * hplusx_topleft * oodx2 * ((midmid - midleft)) \
-        #         -  fac * hplusy_topleft * oody2 * ((midmid - topmid)) \
-        #         +  fac * hplusx_topright * oodx2 * ((midright - midmid)) \
-        #         -  fac * hplusy_topright * oody2 * ((midmid - topmid)) \
-        #         -  fac * hplusx_botleft * oodx2 * ((midmid - midleft)) \
-        #         +  fac * hplusy_botleft * oody2 * ((botmid - midmid)) \
-        #         +  fac * hplusx_botright * oodx2 * ((midright - midmid)) \
-        #         +  fac * hplusy_botright * oody2 * ((botmid - midmid)) \
-        #         +  hcenter[idx] * p[idx]
-
-        lap[idx] *= diag_inv[idx]
-
-        cnt_x += 1
-        if cnt_x % iicxn == 0:
-            cnt_y += 1
-            cnt_x = 0
-
-    return lap
-
-
-@nb.jit(nopython=True, nogil=False, cache=True)
-def lap2D(
-    p,
-    igx,
-    igy,
-    iicxn,
-    iicyn,
-    hplusx,
-    hplusy,
-    hcenter,
-    oodx2,
-    oody2,
-    x_periodic,
-    y_periodic,
-    x_wall,
-    y_wall,
-    diag_inv,
-):
-    ngnc = (iicxn) * (iicyn)
-    lap = np.zeros((ngnc))
-    cnt_x = 0
-    cnt_y = 0
-
-    nine_pt = 0.25 * (2.0) * 1.0
-
-    for idx in range(iicxn * iicyn):
-        ne_topleft = idx - iicxn - 1
-        ne_topright = idx - iicxn
-        ne_botleft = idx - 1
-        ne_botright = idx
-
-        # get indices of the 9pt stencil
-        topleft_idx = idx - iicxn - 1
-        midleft_idx = idx - 1
-        botleft_idx = idx + iicxn - 1
-
-        topmid_idx = idx - iicxn
-        midmid_idx = idx
-        botmid_idx = idx + iicxn
-
-        topright_idx = idx - iicxn + 1
-        midright_idx = idx + 1
-        botright_idx = idx + iicxn + 1
-
-        if cnt_x == 0:
-            topleft_idx += iicxn - 1
-            midleft_idx += iicxn - 1
-            botleft_idx += iicxn - 1
-
-            # if x_periodic:
-            #     topmid_idx += iicxn - 1
-            #     midmid_idx += iicxn - 1
-            #     botmid_idx += iicxn - 1
-
-            ne_topleft += iicxn - 1
-            ne_botleft += iicxn - 1
-
-        if cnt_x == (iicxn - 1):
-            topright_idx -= iicxn - 1
-            midright_idx -= iicxn - 1
-            botright_idx -= iicxn - 1
-
-            # if x_periodic:
-            #     topmid_idx -= iicxn - 1
-            #     midmid_idx -= iicxn - 1
-            #     botmid_idx -= iicxn - 1
-
-            ne_topright -= iicxn - 1
-            ne_botright -= iicxn - 1
-
-        if cnt_y == 0:
-            topleft_idx += (iicxn) * (iicyn - 1)
-            topmid_idx += (iicxn) * (iicyn - 1)
-            topright_idx += (iicxn) * (iicyn - 1)
-
-            # if y_periodic:
-            #     midleft_idx += ((iicxn) * (iicyn - 1))
-            #     midmid_idx += ((iicxn) * (iicyn - 1))
-            #     midright_idx += ((iicxn) * (iicyn - 1))
-
-            ne_topleft += (iicxn) * (iicyn - 1)
-            ne_topright += (iicxn) * (iicyn - 1)
-
-        if cnt_y == (iicyn - 1):
-            botleft_idx -= (iicxn) * (iicyn - 1)
-            botmid_idx -= (iicxn) * (iicyn - 1)
-            botright_idx -= (iicxn) * (iicyn - 1)
-
-            # if y_periodic:
-            #     midleft_idx -= ((iicxn) * (iicyn - 1))
-            #     midmid_idx -= ((iicxn) * (iicyn - 1))
-            #     midright_idx -= ((iicxn) * (iicyn - 1))
-
-            ne_botleft -= (iicxn) * (iicyn - 1)
-            ne_botright -= (iicxn) * (iicyn - 1)
-
-        topleft = p[topleft_idx]
-        midleft = p[midleft_idx]
-        botleft = p[botleft_idx]
-
-        topmid = p[topmid_idx]
-        midmid = p[midmid_idx]
-        botmid = p[botmid_idx]
-
-        topright = p[topright_idx]
-        midright = p[midright_idx]
-        botright = p[botright_idx]
-
-        hplusx_topleft = hplusx[ne_topleft]
-        hplusx_botleft = hplusx[ne_botleft]
-        hplusy_topleft = hplusy[ne_topleft]
-        hplusy_botleft = hplusy[ne_botleft]
-
-        hplusx_topright = hplusx[ne_topright]
-        hplusx_botright = hplusx[ne_botright]
-        hplusy_topright = hplusy[ne_topright]
-        hplusy_botright = hplusy[ne_botright]
-
-        if x_wall and (cnt_x == 0):
-            hplusx_topleft = 0.0
-            hplusy_topleft = 0.0
-            hplusx_botleft = 0.0
-            hplusy_botleft = 0.0
-
-        if x_wall and (cnt_x == (iicxn - 1)):
-            hplusx_topright = 0.0
-            hplusy_topright = 0.0
-            hplusx_botright = 0.0
-            hplusy_botright = 0.0
-
-        if y_wall and (cnt_y == 0):
-            hplusx_topleft = 0.0
-            hplusy_topleft = 0.0
-            hplusx_topright = 0.0
-            hplusy_topright = 0.0
-
-        if y_wall and (cnt_y == (iicyn - 1)):
-            hplusx_botleft = 0.0
-            hplusy_botleft = 0.0
-            hplusx_botright = 0.0
-            hplusy_botright = 0.0
-
-        dp2dxdy1 = ((midmid - midleft) - (topmid - topleft)) * nine_pt
-        dp2dxdy2 = ((midright - midmid) - (topright - topmid)) * nine_pt
-        dp2dxdy3 = ((botmid - botleft) - (midmid - midleft)) * nine_pt
-        dp2dxdy4 = ((botright - botmid) - (midright - midmid)) * nine_pt
-
-        lap[idx] = (
-            -hplusx_topleft * oodx2 * ((midmid - midleft) - dp2dxdy1)
-            - hplusy_topleft * oody2 * ((midmid - topmid) - dp2dxdy1)
-            + hplusx_topright * oodx2 * ((midright - midmid) - dp2dxdy2)
-            - hplusy_topright * oody2 * ((midmid - topmid) + dp2dxdy2)
-            - hplusx_botleft * oodx2 * ((midmid - midleft) + dp2dxdy3)
-            + hplusy_botleft * oody2 * ((botmid - midmid) - dp2dxdy3)
-            + hplusx_botright * oodx2 * ((midright - midmid) + dp2dxdy4)
-            + hplusy_botright * oody2 * ((botmid - midmid) + dp2dxdy4)
-            + hcenter[idx] * p[idx]
-        )
-
-        # if cnt_x == 0 and x_wall:
-        #     lap[idx] *= 2.
-        # if (cnt_x == iicxn - 1) and x_wall:
-        #     lap[idx] *= 2.
-
-        # if cnt_y == 0 and y_wall:
-        #     lap[idx] *= 2.
-        # if (cnt_y == iicyn - 1) and y_wall:
-        #     lap[idx] *= 2.
-
-        lap[idx] *= diag_inv[idx]
-
-        cnt_x += 1
-        if cnt_x % iicxn == 0:
-            cnt_y += 1
-            cnt_x = 0
-
-    return lap
-
-
-def stencil_9pt_numba_test(mpv, node, coriolis, diag_inv, ud):
-    dx = node.dx
-    dy = node.dy
-
-    hplusx = mpv.wplus[0]
-    hplusy = mpv.wplus[1]
-    hcenter = mpv.wcenter
-
-    coeffs = (hplusx.T, hplusy.T, hcenter.T)
-
-    shp = node.iisc
-
-    dummy_p = np.zeros((node.isc[1], node.isc[0]))
-
-    ### Need to clean this up, but the Numba stencil is used in the Helmholtz solve for radiative BC!
-    if hasattr(ud, "ATMOSPHERIC_EXTENSION"):
-        return lambda p: lap2D_numba_test(
-            p, dummy_p, dx, dy, coeffs, diag_inv.T, coriolis, shp
-        )
-
-    ###################
-    else:
-        x_wall = (
-            ud.bdry_type[0] == opts.BdryType.WALL
-            or ud.bdry_type[0] == opts.BdryType.RAYLEIGH
-        )
-        y_wall = (
-            ud.bdry_type[1] == opts.BdryType.WALL
-            or ud.bdry_type[1] == opts.BdryType.RAYLEIGH
-        )
-
-        y_rayleigh = ud.bdry_type[1] == opts.BdryType.RAYLEIGH
-
-        cor_slc = (slice(1, -1), slice(1, -1))
-        coeff_slc = (slice(1, -1), slice(1, -1))
-
-        coeffs = (
-            hplusx[coeff_slc].T.reshape(
-                -1,
-            ),
-            hplusy[coeff_slc].T.reshape(
-                -1,
-            ),
-            hcenter[node.i1].T.reshape(
-                -1,
-            ),
-        )
-
-        coriolis = (
-            coriolis[0][cor_slc].reshape(
-                -1,
-            ),
-            coriolis[1][cor_slc].reshape(
-                -1,
-            ),
-            coriolis[2][cor_slc].reshape(
-                -1,
-            ),
-            coriolis[3][cor_slc].reshape(
-                -1,
-            ),
-        )
-
-        return lambda p: lap2D_gather_new(
-            p,
-            node.iicx,
-            node.iicy,
-            coeffs,
-            dx,
-            dy,
-            y_rayleigh,
-            x_wall,
-            y_wall,
-            diag_inv[node.i1].T.reshape(
-                -1,
-            ),
-            coriolis,
-        )
-
-
-@nb.jit(nopython=True, cache=False)
-def lap2D_numba_test(p, dp, dx, dy, coeffs, diag_inv, coriolis, shp):
-    p = p.reshape(shp[1], shp[0])
-    dp[1:-1, 1:-1] = p
-
-    # dp = p
-    dp = periodic(dp)
-    dp = kernel_9pt(
-        dp,
-        dx,
-        dy,
-        coeffs[0],
-        coeffs[1],
-        coeffs[2],
-        diag_inv,
-        coriolis[0],
-        coriolis[1],
-        coriolis[2],
-        coriolis[3],
-    )
-    # p = dp
-    # dp = periodic(dp)
-    p = dp[1:-1, 1:-1]
-
-    return p.ravel()
-
-
-@nb.njit(cache=True)
-def lap2D_gather_new(
-    p, iicxn, iicyn, coeffs, dx, dy, y_rayleigh, x_wall, y_wall, diag_inv, coriolis
-):
-    ngnc = (iicxn) * (iicyn)
-    lap = np.zeros((ngnc))
-    cnt_x = 0
-    cnt_y = 0
-
-    oodx = 1.0 / dx
-    oody = 1.0 / dy
-    cxx, cyy, cxy, cyx = coriolis
-
-    hplusx, hplusy, hcenter = coeffs
-
-    for idx in range(iicxn * iicyn):
-        # ne_topleft = idx - (iicxn - 1)
-        # ne_topright = idx - (iicxn)
-        # ne_botleft = idx - 1
-        # ne_botright = idx
-
-        nr_row = idx // iicxn
-        col_idx = idx - (nr_row * iicxn)
-
-        ne_row_idx = nr_row * (iicxn + 1)
-        ne_col_idx = col_idx
-        ne_idx = ne_row_idx + ne_col_idx
-
-        # ne_topleft = ne_idx - (iicxn + 1) - 1
-        # ne_topright = ne_idx - (iicxn + 1)
-        # ne_botleft = ne_idx - 1
-        # ne_botright = ne_idx
-
-        ne_topleft = ne_idx
-        ne_topright = ne_idx + 1
-        ne_botleft = ne_idx + (iicxn + 1)
-        ne_botright = ne_idx + (iicxn + 1) + 1
-
-        # get indices of the 9pt stencil
-        topleft_idx = idx - iicxn - 1
-        midleft_idx = idx - 1
-        botleft_idx = idx + iicxn - 1
-
-        topmid_idx = idx - iicxn
-        midmid_idx = idx
-        botmid_idx = idx + iicxn
-
-        topright_idx = idx - iicxn + 1
-        midright_idx = idx + 1
-        botright_idx = idx + iicxn + 1
-
-        if cnt_x == 0:
-            topleft_idx += iicxn - 1
-            midleft_idx += iicxn - 1
-            botleft_idx += iicxn - 1
-
-            # ne_topleft += iicxn - 1
-            # ne_botleft += iicxn - 1
-
-            # ne_topleft += iicxn + 1
-            # ne_botleft += iicxn + 1
-
-        if cnt_x == (iicxn - 1):
-            topright_idx -= iicxn - 1
-            midright_idx -= iicxn - 1
-            botright_idx -= iicxn - 1
-
-            # ne_topright -= iicxn - 1
-            # ne_botright -= iicxn - 1
-
-            # ne_topright -= iicxn + 1
-            # ne_botright -= iicxn + 1
-
-        if cnt_y == 0:
-            topleft_idx += (iicxn) * (iicyn - 1)
-            topmid_idx += (iicxn) * (iicyn - 1)
-            topright_idx += (iicxn) * (iicyn - 1)
-
-            # ne_topleft += ((iicxn + 1) * (iicyn))
-            # ne_topright += ((iicxn + 1) * (iicyn))
-
-            # ne_topleft += ((iicxn + 2) * (iicyn + 1))
-            # ne_topright += ((iicxn + 2) * (iicyn + 1))
-
-        # if cnt_y == (iicyn - 1) and not y_rayleigh:
-        if cnt_y == (iicyn - 1):
-            botleft_idx -= (iicxn) * (iicyn - 1)
-            botmid_idx -= (iicxn) * (iicyn - 1)
-            botright_idx -= (iicxn) * (iicyn - 1)
-
-            # ne_botleft -= ((iicxn + 1) * (iicyn))
-            # ne_botright -= ((iicxn + 1) * (iicyn))
-
-            # ne_botleft -= ((iicxn + 2) * (iicyn + 1))
-            # ne_botright -= ((iicxn + 2) * (iicyn + 1))
-
-        ############
-        # top BC handling for rayleigh
-        ############
-        # if cnt_y == (iicyn - 1) and y_rayleigh:
-        #     botleft_idx = topleft_idx
-        #     botmid_idx = topmid_idx
-        #     botright_idx = topright_idx
-
-        topleft = p[topleft_idx]
-        midleft = p[midleft_idx]
-        botleft = p[botleft_idx]
-
-        topmid = p[topmid_idx]
-        midmid = p[midmid_idx]
-        botmid = p[botmid_idx]
-
-        topright = p[topright_idx]
-        midright = p[midright_idx]
-        botright = p[botright_idx]
-
-        hplusx_topleft = hplusx[ne_topleft]
-        hplusx_botleft = hplusx[ne_botleft]
-        hplusy_topleft = hplusy[ne_topleft]
-        hplusy_botleft = hplusy[ne_botleft]
-
-        hplusx_topright = hplusx[ne_topright]
-        hplusx_botright = hplusx[ne_botright]
-        hplusy_topright = hplusy[ne_topright]
-        hplusy_botright = hplusy[ne_botright]
-
-        cxx_tl = cxx[ne_topleft]
-        cxx_tr = cxx[ne_topright]
-        cxx_bl = cxx[ne_botleft]
-        cxx_br = cxx[ne_botright]
-
-        cxy_tl = cxy[ne_topleft]
-        cxy_tr = cxy[ne_topright]
-        cxy_bl = cxy[ne_botleft]
-        cxy_br = cxy[ne_botright]
-
-        cyx_tl = cyx[ne_topleft]
-        cyx_tr = cyx[ne_topright]
-        cyx_bl = cyx[ne_botleft]
-        cyx_br = cyx[ne_botright]
-
-        cyy_tl = cyy[ne_topleft]
-        cyy_tr = cyy[ne_topright]
-        cyy_bl = cyy[ne_botleft]
-        cyy_br = cyy[ne_botright]
-
-        if x_wall and (cnt_x == 0):
-            hplusx_topleft = 0.0
-            hplusy_topleft = 0.0
-            hplusx_botleft = 0.0
-            hplusy_botleft = 0.0
-
-        if x_wall and (cnt_x == (iicxn - 1)):
-            hplusx_topright = 0.0
-            hplusy_topright = 0.0
-            hplusx_botright = 0.0
-            hplusy_botright = 0.0
-
-        if y_wall and (cnt_y == 0):
-            hplusx_topleft = 0.0
-            hplusy_topleft = 0.0
-            hplusx_topright = 0.0
-            hplusy_topright = 0.0
-
-        if y_wall and (cnt_y == (iicyn - 1)):
-            hplusx_botleft = 0.0
-            hplusy_botleft = 0.0
-            hplusx_botright = 0.0
-            hplusy_botright = 0.0
-
-        # if y_rayleigh and (cnt_y == 0):
-        #     hplusx_topleft = 0.
-        #     hplusy_topleft = 0.
-        #     hplusx_topright = 0.
-        #     hplusy_topright = 0.
-
-        Dx_tl = 0.5 * (topmid - topleft + midmid - midleft) * hplusx_topleft
-        Dx_tr = 0.5 * (topright - topmid + midright - midmid) * hplusx_topright
-        Dx_bl = 0.5 * (botmid - botleft + midmid - midleft) * hplusx_botleft
-        Dx_br = 0.5 * (botright - botmid + midright - midmid) * hplusx_botright
-
-        Dy_tl = 0.5 * (midmid - topmid + midleft - topleft) * hplusy_topleft
-        Dy_tr = 0.5 * (midright - topright + midmid - topmid) * hplusy_topright
-        Dy_bl = 0.5 * (botmid - midmid + botleft - midleft) * hplusy_botleft
-        Dy_br = 0.5 * (botright - midright + botmid - midmid) * hplusy_botright
-
-        fac = 1.0
-        Dxx = (
-            0.5
-            * (cxx_tr * Dx_tr - cxx_tl * Dx_tl + cxx_br * Dx_br - cxx_bl * Dx_bl)
-            * oodx
-            * oodx
-            * fac
-        )
-        Dyy = (
-            0.5
-            * (cyy_br * Dy_br - cyy_tr * Dy_tr + cyy_bl * Dy_bl - cyy_tl * Dy_tl)
-            * oody
-            * oody
-            * fac
-        )
-        Dyx = (
-            0.5
-            * (cxy_br * Dy_br - cxy_bl * Dy_bl + cxy_tr * Dy_tr - cxy_tl * Dy_tl)
-            * oody
-            * oodx
-            * fac
-        )
-        Dxy = (
-            0.5
-            * (cyx_br * Dx_br - cyx_tr * Dx_tr + cyx_bl * Dx_bl - cyx_tl * Dx_tl)
-            * oodx
-            * oody
-            * fac
-        )
-
-        lap[idx] = Dxx + Dyy + Dyx + Dxy + hcenter[idx] * p[idx]
-
-        lap[idx] *= diag_inv[idx]
-
-        cnt_x += 1
-        if cnt_x % iicxn == 0:
-            cnt_y += 1
-            cnt_x = 0
-
-    return lap
-
-
-@nb.stencil
-def kernel_9pt(a, dx, dy, hpx, hpy, hpc, diag_inv, cxx, cyy, cxy, cyx):
-    oodx = 1.0 / dx
-    oody = 1.0 / dy
-
-    topleft = a[1, -1]
-    topmid = a[1, 0]
-    topright = a[1, 1]
-
-    midleft = a[0, -1]
-    midmid = a[0, 0]
-    midright = a[0, 1]
-
-    botleft = a[-1, -1]
-    botmid = a[-1, 0]
-    botright = a[-1, 1]
-
-    # shftr = 1
-    # shftc = 0
-    # blr = 0 - shftr
-    # blc = 0 - shftc
-    # brr = 0 - shftr
-    # brc = 1 - shftc
-    # tlr = 1 - shftr
-    # tlc = 0 - shftc
-    # trr = 1 - shftr
-    # trc = 1 - shftc
-
-    # hpx_bl = hpx[blr,blc]
-    # hpx_br = hpx[brr,brc]
-    # hpx_tl = hpx[tlr,tlc]
-    # hpx_tr = hpx[trr,trc]
-
-    # hpy_bl = hpy[blr,blc]
-    # hpy_br = hpy[brr,brc]
-    # hpy_tl = hpy[tlr,tlc]
-    # hpy_tr = hpy[trr,trc]
-
-    # cxx_bl = cxx[blr,blc]
-    # cxx_br = cxx[brr,brc]
-    # cxx_tl = cxx[tlr,tlc]
-    # cxx_tr = cxx[trr,trc]
-
-    # cyy_bl = cyy[blr,blc]
-    # cyy_br = cyy[brr,brc]
-    # cyy_tl = cyy[tlr,tlc]
-    # cyy_tr = cyy[trr,trc]
-
-    # cxy_bl = cxy[blr,blc]
-    # cxy_br = cxy[brr,brc]
-    # cxy_tl = cxy[tlr,tlc]
-    # cxy_tr = cxy[trr,trc]
-
-    # cyx_bl = cyx[blr,blc]
-    # cyx_br = cyx[brr,brc]
-    # cyx_tl = cyx[tlr,tlc]
-    # cyx_tr = cyx[trr,trc]
-
-    hpx_bl = hpx[0, 0]
-    hpx_br = hpx[0, 1]
-    hpx_tl = hpx[1, 0]
-    hpx_tr = hpx[1, 1]
-
-    hpy_bl = hpy[0, 0]
-    hpy_br = hpy[0, 1]
-    hpy_tl = hpy[1, 0]
-    hpy_tr = hpy[1, 1]
-
-    cxx_bl = cxx[0, 0]
-    cxx_br = cxx[0, 1]
-    cxx_tl = cxx[1, 0]
-    cxx_tr = cxx[1, 1]
-
-    cyy_bl = cyy[0, 0]
-    cyy_br = cyy[0, 1]
-    cyy_tl = cyy[1, 0]
-    cyy_tr = cyy[1, 1]
-
-    cxy_bl = cxy[0, 0]
-    cxy_br = cxy[0, 1]
-    cxy_tl = cxy[1, 0]
-    cxy_tr = cxy[1, 1]
-
-    cyx_bl = cyx[0, 0]
-    cyx_br = cyx[0, 1]
-    cyx_tl = cyx[1, 0]
-    cyx_tr = cyx[1, 1]
-
-    Dx_tl = 0.5 * (topmid - topleft + midmid - midleft) * hpx_tl
-    Dx_tr = 0.5 * (topright - topmid + midright - midmid) * hpx_tr
-    Dx_bl = 0.5 * (botmid - botleft + midmid - midleft) * hpx_bl
-    Dx_br = 0.5 * (botright - botmid + midright - midmid) * hpx_br
-
-    Dy_tl = 0.5 * (topmid - midmid + topleft - midleft) * hpy_tl
-    Dy_tr = 0.5 * (topright - midright + topmid - midmid) * hpy_tr
-    Dy_bl = 0.5 * (midmid - botmid + midleft - botleft) * hpy_bl
-    Dy_br = 0.5 * (midright - botright + midmid - botmid) * hpy_br
-
-    # print(hpx_tl, hpx_tr, hpx_bl, hpx_br)
-    # print(hpy_tl, hpy_tr, hpy_bl, hpy_br)
-    # print("")
-
-    Dxx = (
-        0.5
-        * (cxx_tr * Dx_tr - cxx_tl * Dx_tl + cxx_br * Dx_br - cxx_bl * Dx_bl)
-        * oodx
-        * oodx
-    )
-    Dyy = (
-        0.5
-        * (cyy_tr * Dy_tr - cyy_br * Dy_br + cyy_tl * Dy_tl - cyy_bl * Dy_bl)
-        * oody
-        * oody
-    )
-    Dyx = (
-        0.5
-        * (cxy_br * Dy_br - cxy_bl * Dy_bl + cxy_tr * Dy_tr - cxy_tl * Dy_tl)
-        * oody
-        * oodx
-    )
-    Dxy = (
-        0.5
-        * (cyx_tr * Dx_tr - cyx_br * Dx_br + cyx_tl * Dx_tl - cyx_bl * Dx_bl)
-        * oodx
-        * oody
-    )
-
-    return ((Dxx + Dyy + Dyx + Dxy) + hpc[0, 0] * a[0, 0]) * diag_inv[0, 0]
-
-
-@nb.njit(cache=True)
-def periodic(arr):
-    # periodic padding
-    arr[:, 0] = arr[:, -3]
-    arr[:, -1] = arr[:, 2]
-
-    # wall padding
-    arr[0, :] = arr[2, :]
-    arr[-1, :] = arr[-3, :]
-
-    return arr
-
-
-def stencil_27pt(elem, node, mpv, ud, diag_inv, dt):
-    oodxyz = node.dxyz
-    oodxyz = 1.0 / (oodxyz**2)
-    oodx2, oody2, oodz2 = oodxyz[0], oodxyz[1], oodxyz[2]
-    odx, odz = 1.0 / node.dx, 1.0 / node.dz
-
-    i0 = (slice(0, -1), slice(0, -1), slice(0, -1))
-    i1 = (slice(1, -1), slice(1, -1), slice(1, -1))
-    i2 = (slice(2, -2), slice(2, -2), slice(2, -2))
-
-    ndim = elem.ndim
-    periodicity = np.empty(ndim, dtype="int")
-    for dim in range(ndim):
-        periodicity[dim] = ud.bdry_type[dim] == opts.BdryType.PERIODIC
-
-    hplusx = mpv.wplus[0][i0][i1]
-    hplusy = mpv.wplus[1][i0][i1]
-    hplusz = mpv.wplus[2][i0][i1]
-
-    hcenter = mpv.wcenter[i2]
-    diag_inv = diag_inv[i1]
-
-    corrf = dt * ud.coriolis_strength[0]
-
-    return lambda p: lap3D(
-        p,
-        hplusx,
-        hplusy,
-        hplusz,
-        hcenter,
-        oodx2,
-        oody2,
-        oodz2,
-        periodicity,
-        diag_inv,
-        corrf,
-        odx,
-        odz,
-    )
-
-
-@nb.jit(nopython=True, cache=True, nogil=False)
-def lap3D(
-    p0,
-    hplusx,
-    hplusy,
-    hplusz,
-    hcenter,
-    oodx2,
-    oody2,
-    oodz2,
-    periodicity,
-    diag_inv,
-    corrf,
-    odx,
-    odz,
-):
-    shx, shy, shz = hcenter.shape
-    p = p0.reshape(shz + 2, shy + 2, shx + 2)
-
-    coeff = 1.0 / 16
-    lap = np.zeros_like(p)
-
-    # cut out four cubes from the 3d array corresponding to the nodes... in each axial direction.
-    toplefts = [
-        (slice(0, None), slice(0, -1), slice(0, -1)),
-        (slice(0, -1), slice(0, None), slice(0, -1)),
-        (slice(0, -1), slice(0, -1), slice(0, None)),
-    ]
-    toprights = [
-        (slice(0, None), slice(0, -1), slice(1, None)),
-        (slice(1, None), slice(0, None), slice(0, -1)),
-        (slice(0, -1), slice(1, None), slice(0, None)),
-    ]
-
-    botlefts = [
-        (slice(0, None), slice(1, None), slice(0, -1)),
-        (slice(0, -1), slice(0, None), slice(1, None)),
-        (slice(1, None), slice(0, -1), slice(0, None)),
-    ]
-    botrights = [
-        (slice(0, None), slice(1, None), slice(1, None)),
-        (slice(1, None), slice(0, None), slice(1, None)),
-        (slice(1, None), slice(1, None), slice(0, None)),
-    ]
-
-    cnt = 0
-    for bc in periodicity:
-        if bc == True and cnt == 0:
-            tmp = p[1, :, :]
-            p[0, :, :] = p[-3, :, :]
-            p[-1, :, :] = p[2, :, :]
-            p[1, :, :] = p[-2, :, :]
-            p[-2, :, :] = tmp
-        elif bc == False and cnt == 0:
-            hplusx[0, :, :] = 0.0
-            hplusx[-1, :, :] = 0.0
-            hplusy[0, :, :] = 0.0
-            hplusy[-1, :, :] = 0.0
-            hplusz[0, :, :] = 0.0
-            hplusz[-1, :, :] = 0.0
-        if bc == True and cnt == 1:
-            tmp = p[:, 1, :]
-            p[:, 0, :] = p[:, -3, :]
-            p[:, -1, :] = p[:, 2, :]
-            p[:, 1, :] = p[:, -2, :]
-            p[:, -2, :] = tmp
-        elif bc == False and cnt == 1:
-            hplusx[:, 0, :] = 0.0
-            hplusx[:, -1, :] = 0.0
-            hplusy[:, 0, :] = 0.0
-            hplusy[:, -1, :] = 0.0
-            hplusz[:, 0, :] = 0.0
-            hplusz[:, -1, :] = 0.0
-        if bc == True and cnt == 2:
-            tmp = p[:, :, 1]
-            p[:, :, 0] = p[:, :, -3]
-            p[:, :, -1] = p[:, :, 2]
-            p[:, :, 1] = p[:, :, -2]
-            p[:, :, -2] = tmp
-        elif bc == False and cnt == 2:
-            hplusx[:, :, 0] = 0.0
-            hplusx[:, :, -1] = 0.0
-            hplusy[:, :, 0] = 0.0
-            hplusy[:, :, -1] = 0.0
-            hplusz[:, :, 0] = 0.0
-            hplusz[:, :, -1] = 0.0
-        cnt += 1
-
-    leftz = p[:, :, :-1]
-    rightz = p[:, :, 1:]
-
-    z_fluxes = rightz - leftz
-
-    lefty = p[:, :-1, :]
-    righty = p[:, 1:, :]
-
-    y_fluxes = righty - lefty
-
-    leftx = p[:-1, :, :]
-    rightx = p[1:, :, :]
-
-    x_fluxes = rightx - leftx
-
-    x_flx = (
-        x_fluxes[toplefts[0]]
-        + x_fluxes[toprights[0]]
-        + x_fluxes[botlefts[0]]
-        + x_fluxes[botrights[0]]
-    )
-    y_flx = (
-        y_fluxes[toplefts[1]]
-        + y_fluxes[toprights[1]]
-        + y_fluxes[botlefts[1]]
-        + y_fluxes[botrights[1]]
-    )
-    z_flx = (
-        z_fluxes[toplefts[2]]
-        + z_fluxes[toprights[2]]
-        + z_fluxes[botlefts[2]]
-        + z_fluxes[botrights[2]]
-    )
-
-    hxzp = hplusx * z_flx
-    hxzpm = hxzp[:-1, :, :]
-    hxzpm = (
-        hxzpm[toplefts[0]]
-        + hxzpm[toprights[0]]
-        + hxzpm[botlefts[0]]
-        + hxzpm[botrights[0]]
-    )
-    hxzpp = hxzp[1:, :, :]
-    hxzpp = (
-        hxzpp[toplefts[0]]
-        + hxzpp[toprights[0]]
-        + hxzpp[botlefts[0]]
-        + hxzpp[botrights[0]]
-    )
-
-    hzxp = hplusz * x_flx
-    hzxpm = hzxp[:, :, :-1]
-    hzxpm = (
-        hzxpm[toplefts[2]]
-        + hzxpm[toprights[2]]
-        + hzxpm[botlefts[2]]
-        + hzxpm[botrights[2]]
-    )
-    hzxpp = hzxp[:, :, 1:]
-    hzxpp = (
-        hzxpp[toplefts[2]]
-        + hzxpp[toprights[2]]
-        + hzxpp[botlefts[2]]
-        + hzxpp[botrights[2]]
-    )
-
-    x_flx = hplusx * x_flx
-    x_flxm = x_flx[:-1, :, :]
-    x_flxm = (
-        x_flxm[toplefts[0]]
-        + x_flxm[toprights[0]]
-        + x_flxm[botlefts[0]]
-        + x_flxm[botrights[0]]
-    )
-    x_flxp = x_flx[1:, :, :]
-    x_flxp = (
-        x_flxp[toplefts[0]]
-        + x_flxp[toprights[0]]
-        + x_flxp[botlefts[0]]
-        + x_flxp[botrights[0]]
-    )
-
-    y_flx = hplusy * y_flx
-    y_flxm = y_flx[:, :-1, :]
-    y_flxm = (
-        y_flxm[toplefts[1]]
-        + y_flxm[toprights[1]]
-        + y_flxm[botlefts[1]]
-        + y_flxm[botrights[1]]
-    )
-    y_flxp = y_flx[:, 1:, :]
-    y_flxp = (
-        y_flxp[toplefts[1]]
-        + y_flxp[toprights[1]]
-        + y_flxp[botlefts[1]]
-        + y_flxp[botrights[1]]
-    )
-
-    z_flx = hplusz * z_flx
-    z_flxm = z_flx[:, :, :-1]
-    z_flxm = (
-        z_flxm[toplefts[2]]
-        + z_flxm[toprights[2]]
-        + z_flxm[botlefts[2]]
-        + z_flxm[botrights[2]]
-    )
-    z_flxp = z_flx[:, :, 1:]
-    z_flxp = (
-        z_flxp[toplefts[2]]
-        + z_flxp[toprights[2]]
-        + z_flxp[botlefts[2]]
-        + z_flxp[botrights[2]]
-    )
-
-    lap[1:-1, 1:-1, 1:-1] = (
-        oodx2 * coeff * (-x_flxm + x_flxp)
-        + oody2 * coeff * (-y_flxm + y_flxp)
-        + oodz2 * coeff * (-z_flxm + z_flxp)
-        + +1.0 * odx * odz * coeff * corrf * (hxzpp - hxzpm)
-        + -1.0 * odx * odz * coeff * corrf * (hzxpp - hzxpm)
-        + hcenter * p[1:-1, 1:-1, 1:-1]
-    )
-
-    lap = lap * diag_inv
-
-    return lap
-
-
-def stencil_hs(elem, node, mpv, ud, diag_inv, dt):
-    oodx2 = 1.0 / node.dx**2
-    oodz2 = 1.0 / node.dz**2
-    odx, odz = 1.0 / node.dx, 1.0 / node.dz
-    igy = elem.igs[1]
-
-    proj = (
-        slice(
-            None,
-        ),
-        igy,
-        slice(
-            None,
-        ),
-    )
-    i0 = (slice(0, -1), slice(0, -1))
-    i1 = (slice(1, -1), slice(1, -1))
-    i2 = (slice(2, -2), slice(2, -2))
-
-    ndim = elem.ndim
-    periodicity = np.empty(ndim, dtype="int")
-    for dim in range(0, ndim, 2):
-        periodicity[dim] = ud.bdry_type[dim] == opts.BdryType.PERIODIC
-
-    hplusx = mpv.wplus[0][proj][i0][i1]
-    hplusz = mpv.wplus[2][proj][i0][i1]
-    hcenter = mpv.wcenter[proj][i2]
-    diag_inv = diag_inv[proj][i1]
-
-    corrf = dt * ud.coriolis_strength[1]
-
-    return lambda p: lapHS(
-        p, hplusx, hplusz, hcenter, oodx2, oodz2, periodicity, diag_inv, corrf, odx, odz
-    )
-
-
-@nb.jit(nopython=True, cache=True, nogil=True)
-def lapHS(
-    p0, hplusx, hplusz, hcenter, oodx2, oodz2, periodicity, diag_inv, corrf, odx, odz
-):
-    shx, shz = hcenter.shape
-    p = p0.reshape(shx + 2, shz + 2)
-
-    coeff = 1.0 / 4
-    lap = np.zeros_like(p)
-
-    cnt = 0
-    for bc in periodicity:
-        if bc == True and cnt == 0:
-            tmp = p[1, :]
-            p[0, :] = p[-3, :]
-            p[-1, :] = p[2, :]
-            p[1, :] = p[-2, :]
-            p[-2, :] = tmp
-
-            # p[0,:] = p[-4,:]
-            # p[-1,:] = p[3,:]
-            # p[1,:] = p[-3,:]
-            # p[-2,:] = p[2,:]
-        elif bc == False and cnt == 0:
-            hplusx[0, :] = 0.0
-            hplusx[-1, :] = 0.0
-            hplusz[0, :] = 0.0
-            hplusz[-1, :] = 0.0
-        if bc == True and cnt == 2:
-            tmp = p[:, 1]
-            p[:, 0] = p[:, -3]
-            p[:, -1] = p[:, 2]
-            p[:, 1] = p[:, -2]
-            p[:, -2] = tmp
-            # p[:,0] = p[:,-4]
-            # p[:,-1] = p[:,3]
-            # p[:,1] = p[:,-3]
-            # p[:,-2] = p[:,2]
-        elif bc == False and cnt == 2:
-            hplusx[:, 0] = 0.0
-            hplusx[:, -1] = 0.0
-            hplusz[:, 0] = 0.0
-            hplusz[:, -1] = 0.0
-        cnt += 1
-
-    leftz = p[:, :-1]
-    rightz = p[:, 1:]
-
-    z_fluxes = rightz - leftz
-
-    leftx = p[:-1, :]
-    rightx = p[1:, :]
-
-    x_fluxes = rightx - leftx
-
-    x_flx = x_fluxes[:, :-1] + x_fluxes[:, 1:]
-    z_flx = z_fluxes[:-1, :] + z_fluxes[1:, :]
-
-    hxzp = hplusx * z_flx
-    hxzpm = hxzp[:-1, :]
-    hxzpm = hxzpm[:, :-1] + hxzpm[:, 1:]
-    # hxzpm = hxzpm[:-1,:] + hxzpm[1:,:]
-    hxzpp = hxzp[1:, :]
-    hxzpp = hxzpp[:, :-1] + hxzpp[:, 1:]
-    # hxzpp = hxzpp[:-1,:] + hxzpp[1:,:]
-
-    hzxp = hplusz * x_flx
-    hzxpm = hzxp[:, :-1]
-    hzxpm = hzxpm[:-1, :] + hzxpm[1:, :]
-    # hzxpm = hzxpm[:,:-1] + hzxpm[:,1:]
-    hzxpp = hzxp[:, 1:]
-    hzxpp = hzxpp[:-1, :] + hzxpp[1:, :]
-    # hzxpp = hzxpp[:,:-1] + hzxpp[:,1:]
-
-    x_flx = hplusx * x_flx
-    x_flxm = x_flx[:-1, :]
-    x_flxm = x_flxm[:, :-1] + x_flxm[:, 1:]
-    x_flxp = x_flx[1:, :]
-    x_flxp = x_flxp[:, :-1] + x_flxp[:, 1:]
-
-    z_flx = hplusz * z_flx
-    z_flxm = z_flx[:, :-1]
-    z_flxm = z_flxm[:-1, :] + z_flxm[1:, :]
-    z_flxp = z_flx[:, 1:]
-    z_flxp = z_flxp[:-1, :] + z_flxp[1:, :]
-
-    lap[1:-1, 1:-1] = (
-        oodx2 * coeff * (-x_flxm + x_flxp)
-        + oodz2 * coeff * (-z_flxm + z_flxp)
-        + +1.0 * odx * odz * coeff * corrf * (hxzpp - hxzpm)
-        + -1.0 * odx * odz * coeff * corrf * (hzxpp - hzxpm)
-        + hcenter * p[1:-1, 1:-1]
-    )
-
-    lap = lap * diag_inv
-
-    return lap
-
-
-def stencil_vs(elem, node, mpv, ud, diag_inv, dt):
-    igx = elem.igx
-    igy = elem.igy
-    igz = elem.igz
-
-    icxn = node.icx
-    icyn = node.icy
-
-    iicxn = icxn - (2 * igx)
-    iicyn = icyn - (2 * igy)
-
-    iicxn, iicyn = iicyn, iicxn
-
-    dx = node.dy
-    dy = node.dx
-
-    oodx2 = 0.5 / (dx**2)
-    oody2 = 0.5 / (dy**2)
-
-    xx, yy = 1, 0
-
-    proj = (
-        slice(
-            None,
-        ),
-        slice(
-            None,
-        ),
-        igz,
-    )
-    i0 = (slice(0, -1), slice(0, -1))
-    i1 = (slice(1, -1), slice(1, -1))
-    i2 = (slice(igx, -igx), slice(igy, -igy))
-
-    VS = True
-
-    if not VS:
-        x_periodic = ud.bdry_type[xx] == opts.BdryType.PERIODIC
-        y_periodic = ud.bdry_type[yy] == opts.BdryType.PERIODIC
-
-        x_wall = ud.bdry_type[xx] == opts.BdryType.WALL
-        y_wall = ud.bdry_type[yy] == opts.BdryType.WALL
-
-        hplusx = mpv.wplus[xx][proj][i2].reshape(
-            -1,
-        )
-        hplusy = mpv.wplus[yy][proj][i2].reshape(
-            -1,
-        )
-        hcenter = mpv.wcenter[proj][i2].reshape(
-            -1,
-        )
-        diag_inv = diag_inv[proj][i2].reshape(
-            -1,
-        )
-
-        return lambda p: lap2D(
-            p,
-            igx,
-            igy,
-            iicxn,
-            iicyn,
-            hplusx,
-            hplusy,
-            hcenter,
-            oodx2,
-            oody2,
-            x_periodic,
-            y_periodic,
-            x_wall,
-            y_wall,
-            diag_inv,
-        )
-
-    if VS:
-        oodx2 = 1.0 / node.dx**2
-        oody2 = 1.0 / node.dy**2
-
-        ndim = elem.ndim
-        periodicity = np.zeros(ndim, dtype="int")
-        for dim in range(0, ndim, 2):
-            periodicity[dim] = ud.bdry_type[dim] == opts.BdryType.PERIODIC
-
-        hplusx = mpv.wplus[0][proj][i0][i1]
-        hplusy = mpv.wplus[1][proj][i0][i1]
-        hcenter = mpv.wcenter[proj][i2]
-        diag_inv = diag_inv[proj][i1]
-
-        return lambda p: lapVS(
-            p, hplusx, hplusy, hcenter, oodx2, oody2, periodicity, diag_inv
-        )
-
-
-@nb.jit(nopython=True, cache=True, nogil=False)
-def lapVS(p0, hplusx, hplusy, hcenter, oodx2, oody2, periodicity, diag_inv):
-    shx, shy = hcenter.shape
-    p = p0.reshape(shx + 2, shy + 2)
-
-    coeff = 1.0 / 4
-    lap = np.zeros_like(p)
-
-    cnt = 0
-    for bc in periodicity:
-        if bc == True and cnt == 0:
-            p[0, :] = p[-3, :]
-            p[-1, :] = p[2, :]
-
-        elif bc == False and cnt == 0:
-            hplusx[0, :] = 0.0
-            hplusx[-1, :] = 0.0
-            hplusy[0, :] = 0.0
-            hplusy[-1, :] = 0.0
-
-            # p[0,:] = p[2,:]
-            # p[-1,:] = p[-3,:]
-
-        if bc == True and cnt == 1:
-            p[:, 0] = p[:, -3]
-            p[:, -1] = p[:, 2]
-
-        elif bc == False and cnt == 1:
-            hplusx[:, 0] = 0.0
-            hplusx[:, -1] = 0.0
-            hplusy[:, 0] = 0.0
-            hplusy[:, -1] = 0.0
-
-            # p[:,0] = p[:,2]
-            # p[:,-1] = p[:,-3]
-
-        cnt += 1
-
-    lefty = p[:, :-1]
-    righty = p[:, 1:]
-
-    y_fluxes = righty - lefty
-
-    leftx = p[:-1, :]
-    rightx = p[1:, :]
-
-    x_fluxes = rightx - leftx
-
-    x_flx = x_fluxes[:, :-1] + x_fluxes[:, 1:]
-    y_flx = y_fluxes[:-1, :] + y_fluxes[1:, :]
-
-    x_flx = hplusx * x_flx
-    x_flxm = x_flx[:-1, :]
-    x_flxm = x_flxm[:, :-1] + x_flxm[:, 1:]
-    x_flxp = x_flx[1:, :]
-    x_flxp = x_flxp[:, :-1] + x_flxp[:, 1:]
-
-    y_flx = hplusy * y_flx
-    y_flxm = y_flx[:, :-1]
-    y_flxm = y_flxm[:-1, :] + y_flxm[1:, :]
-    y_flxp = y_flx[:, 1:]
-    y_flxp = y_flxp[:-1, :] + y_flxp[1:, :]
-
-    lap[1:-1, 1:-1] = (
-        oodx2 * coeff * (-x_flxm + x_flxp)
-        + oody2 * coeff * (-y_flxm + y_flxp)
-        + hcenter * p[1:-1, 1:-1]
-    )
-
-    lap = lap * diag_inv
-
-    return lap
-
-
-def precon_diag_prepare(mpv, elem, node, ud, coriolis):
-    dx, dy, dz = node.dx, node.dy, node.dz
-
-    x_periodic = ud.bdry_type[0] == opts.BdryType.PERIODIC
-    y_periodic = ud.bdry_type[1] == opts.BdryType.PERIODIC
-    z_periodic = ud.bdry_type[2] == opts.BdryType.PERIODIC
-    periodicity = (x_periodic, y_periodic, z_periodic)
-    # igx = node.igx
-    # igy = node.igy
-    igs = node.igs
-    ndim = elem.ndim
-
-    # idx_e = (slice(igx - x_periodic,-igx + x_periodic - 1),slice(igy - y_periodic, -igy + y_periodic - 1))
-    idx_periodic = [slice(None)] * elem.ndim
-    idx_n, idx_e = np.copy(idx_periodic), np.copy(idx_periodic)
-
-    for dim in range(ndim):
-        if ud.bdry_type[dim] == opts.BdryType.PERIODIC:
-            idx_periodic[dim] = slice(1, -1)
-
-        idx_e[dim] = slice(
-            igs[dim] - periodicity[dim], -igs[dim] + periodicity[dim] - 1
-        )
-        idx_n[dim] = slice(igs[dim], -igs[dim])
-
-    idx_periodic, idx_e, idx_n = tuple(idx_periodic), tuple(idx_e), tuple(idx_n)
-
-    # idx_n = (slice(igx,-igx), slice(igy,-igy))
-
-    hplusxx = mpv.wplus[0]  # * (coriolis[0].T)
-    hplusyy = mpv.wplus[1]  # * (coriolis[1].T)
-    hplusxy = mpv.wplus[0]  # * (coriolis[3].T)
-    hplusyx = mpv.wplus[1]  # * (coriolis[2].T)
-
-    if ndim == 3:
-        hplusz = mpv.wplus[2]
-
-    nine_pt = 0.25 * (2.0) * 1.0
-    nine_pt = 0.5 * 0.5
-    if ndim == 2:
-        coeff = 1.0 - nine_pt
-    elif ndim == 3:
-        coeff = 0.0625
-    else:
-        assert 0, "ndim = 1?"
-
-    wxx = coeff / (dx**2)
-    wyy = coeff / (dy**2)
-    wzz = coeff / (dz**2)
-
-    wxy = coeff / (dx * dy)
-    wyx = coeff / (dy * dx)
-
-    diag_kernel = np.array(np.ones([2] * ndim))
-
-    # diag = np.zeros((node.sc)).squeeze()
-    # diag[idx_n] = -wx * signal.fftconvolve(hplusx[idx_e],diag_kernel,mode='full')[idx_periodic]
-    # diag[idx_n] -= wy * signal.fftconvolve(hplusy[idx_e],diag_kernel,mode='full')[idx_periodic]
-    # if ndim == 3:
-    #     diag[idx_n] -= wz * signal.fftconvolve(hplusz[idx_e],diag_kernel,mode='full')[idx_periodic]
-
-    # diag[idx_n] += mpv.wcenter[idx_n]
-    # diag[idx_n] = 1.0 / diag[idx_n]
-
-    diag = np.zeros_like(mpv.wcenter)
-    diag[...] = -wxx * sp.signal.fftconvolve(hplusxx, diag_kernel, mode="valid")
-    diag[...] -= wyy * sp.signal.fftconvolve(hplusyy, diag_kernel, mode="valid")
-    diag[...] -= wxy * sp.signal.fftconvolve(hplusxy, diag_kernel, mode="valid")
-    diag[...] -= wyx * sp.signal.fftconvolve(hplusyx, diag_kernel, mode="valid")
-    if ndim == 3:
-        diag[...] -= wzz * sp.signal.fftconvolve(hplusz, diag_kernel, mode="valid")
-
-    diag[...] += mpv.wcenter
-    diag[...] = 1.0 / diag
-
-    return diag
-
-
-def stencil_3pt(elem, node, ud):
-    # 1d stencil for exner pressure perturbation constraint in 2d
-    igx = elem.igx
-    igy = elem.igy
-
-    icxn = node.icx
-    icyn = node.icy
-
-    iicxn = icxn - (2 * igx)
-    iicyn = icyn - (2 * igy)
-
-    iicxn, iicyn = iicyn, iicxn
-
-    dx = node.dx
-    # print(node.dx)
-
-    oodx2 = 1.0 / (dx**2)
-
-    # x_periodic = ud.bdry_type[1] == BdryType.PERIODIC
-    x_periodic = ud.bdry_type[0] == opts.BdryType.PERIODIC
-    x_wall = ud.bdry_type[0] == opts.BdryType.WALL
-
-    return lambda p: lap2D_exner(p, iicxn, iicyn, oodx2, x_periodic, x_wall)
-
-
-@nb.jit(nopython=True, nogil=True, cache=True)
-def lap2D_exner(p, iicxn, iicyn, oodx2, x_periodic, x_wall):
-    ngnc = (iicxn) * (iicyn)
-    lap = np.zeros((ngnc))
-    cnt_x = 0
-    cnt_y = 0
-
-    for idx in range(iicxn * iicyn):
-        # left_idx = idx - 1
-        # mid_idx = idx
-        # right_idx = idx + 1
-
-        # if cnt_x == 0:
-        #     left_idx += iicxn - 1
-
-        #     if x_periodic:
-        #         mid_idx += iicxn - 1
-
-        # if cnt_x == (iicxn - 1):
-        #     right_idx -= iicxn - 1
-
-        #     if x_periodic:
-        #         mid_idx -= iicxn - 1
-
-        right_idx = idx - iicxn
-        mid_idx = idx
-        left_idx = idx + iicxn
-
-        if cnt_y == 0:
-            if x_periodic:
-                right_idx += (iicxn) * (iicyn - 1)
-                mid_idx += (iicxn) * (iicyn - 1)
-
-        if cnt_y == (iicyn - 1):
-            if x_periodic:
-                left_idx -= (iicxn) * (iicyn - 1)
-                mid_idx -= (iicxn) * (iicyn - 1)
-
-        left = p[left_idx]
-        mid = p[mid_idx]
-        right = p[right_idx]
-
-        lap[idx] = oodx2 * (left - 2.0 * mid + right)
-
-        cnt_x += 1
-        if cnt_x % iicxn == 0:
-            cnt_y += 1
-            cnt_x = 0
-
-    return lap
-
-
-def stencil_5pt(elem, node, ud):
-    igx = elem.igx
-    igy = elem.igy
-
-    icxn = node.icx
-    icyn = node.icy
-
-    iicxn = icxn - (2 * igx)
-    iicyn = icyn - (2 * igy)
-
-    iicxn, iicyn = iicyn, iicxn
-
-    dx = node.dy
-    dy = node.dx
-
-    oodx2 = 1.0 / (dx**2)
-    oody2 = 1.0 / (dy**2)
-
-    # oodx2 = 1.0
-    # oody2 = 1.0
-
-    x_periodic = ud.bdry_type[1] == opts.BdryType.PERIODIC
-    y_periodic = ud.bdry_type[0] == opts.BdryType.PERIODIC
-
-    x_wall = ud.bdry_type[1] == opts.BdryType.WALL
-    y_wall = ud.bdry_type[0] == opts.BdryType.WALL
-
-    return lambda p: lap2D_5pt(
-        p, iicxn, iicyn, oodx2, oody2, x_periodic, y_periodic, x_wall, y_wall
-    )
-
-
-@nb.jit(nopython=True, nogil=True, cache=True)
-def lap2D_5pt(p, iicxn, iicyn, oodx2, oody2, x_periodic, y_periodic, x_wall, y_wall):
-    ngnc = (iicxn) * (iicyn)
-    lap = np.zeros((ngnc))
-    cnt_x = 0
-    cnt_y = 0
-
-    for idx in range(iicxn * iicyn):
-        # get indices of the 9pt stencil
-        midleft_idx = idx - 1
-        topmid_idx = idx - iicxn
-        midmid_idx = idx
-        botmid_idx = idx + iicxn
-        midright_idx = idx + 1
-
-        if cnt_x == 0:
-            midleft_idx += iicxn - 1
-            if x_periodic:
-                topmid_idx += iicxn - 1
-                midmid_idx += iicxn - 1
-                botmid_idx += iicxn - 1
-
-        if cnt_x == (iicxn - 1):
-            midright_idx -= iicxn - 1
-
-            if x_periodic:
-                topmid_idx -= iicxn - 1
-                midmid_idx -= iicxn - 1
-                botmid_idx -= iicxn - 1
-
-        if cnt_y == 0:
-            topmid_idx += (iicxn) * (iicyn - 1)
-
-            if y_periodic:
-                midleft_idx += (iicxn) * (iicyn - 1)
-                midmid_idx += (iicxn) * (iicyn - 1)
-                midright_idx += (iicxn) * (iicyn - 1)
-
-        if cnt_y == (iicyn - 1):
-            botmid_idx -= (iicxn) * (iicyn - 1)
-
-            if y_periodic:
-                midleft_idx -= (iicxn) * (iicyn - 1)
-                midmid_idx -= (iicxn) * (iicyn - 1)
-                midright_idx -= (iicxn) * (iicyn - 1)
-
-        midleft = p[midleft_idx]
-        topmid = p[topmid_idx]
-        midmid = p[midmid_idx]
-        botmid = p[botmid_idx]
-        midright = p[midright_idx]
-
-        if x_wall and (cnt_x == 0):
-            midleft = 0.0
-
-        if x_wall and (cnt_x == (iicxn - 1)):
-            midright = 0.0
-
-        if y_wall and (cnt_y == 0):
-            topmid = 0.0
-
-        if y_wall and (cnt_y == (iicyn - 1)):
-            botmid = 0.0
-
-        lap[idx] = oodx2 * (midleft - 2.0 * midmid + midright) + oody2 * (
-            topmid - 2.0 * midmid + botmid
-        )
-
-        cnt_x += 1
-        if cnt_x % iicxn == 0:
-            cnt_y += 1
-            cnt_x = 0
-
-    return lap
diff --git a/src/pybella/flow_solver/physics/low_mach/mpv.py b/src/pybella/flow_solver/physics/low_mach/mpv.py
deleted file mode 100644
index 4e08a7af..00000000
--- a/src/pybella/flow_solver/physics/low_mach/mpv.py
+++ /dev/null
@@ -1,36 +0,0 @@
-import numpy as np
-
-from ...utils import variable as var
-
-
-class MPV(object):
-    def __init__(self, elem, node, ud):
-        sc = elem.sc
-        sn = node.sc
-
-        self.p0 = 1.0
-        self.p00 = 1.0
-
-        self.p2_cells = np.zeros((sc))
-        self.dp2_cells = np.zeros((sc))
-        self.p2_nodes = np.zeros((sn))
-        self.p2_nodes0 = np.zeros((sn))
-        self.dp2_nodes = np.zeros((sn))
-
-        self.u = np.zeros((sc))
-        self.v = np.zeros((sc))
-        self.w = np.zeros((sc))
-
-        self.rhs = np.zeros((node.isc))
-        self.wcenter = np.zeros((node.isc))
-        self.wplus = np.zeros(([elem.ndim] + list(sc)))
-
-        self.HydroState = var.States([sc[1]], ud)
-        self.HydroState_n = var.States([sn[1]], ud)
-
-        self.squeezer()
-
-    def squeezer(self):
-        for key, value in vars(self).items():
-            if type(value) == np.ndarray:
-                setattr(self, key, value.squeeze())
diff --git a/src/pybella/flow_solver/physics/low_mach/second_projection.py b/src/pybella/flow_solver/physics/low_mach/second_projection.py
deleted file mode 100644
index fc9e4523..00000000
--- a/src/pybella/flow_solver/physics/low_mach/second_projection.py
+++ /dev/null
@@ -1,580 +0,0 @@
-import itertools as it
-
-import numpy as np
-import scipy as sp
-from numba import njit
-
-from ....utils import options as opts
-from ....utils import operators
-
-from ...utils import boundary as bdry
-from . import laplacian as lm_lp
-
-
-class solver_counter(object):
-    """
-    taken from https://stackoverflow.com/questions/33512081/getting-the-number-of-iterations-of-scipys-gmres-iterative-method
-
-    """
-
-    def __init__(self, disp=True):
-        self.niter = 0
-
-    def __call__(self, rk=None):
-        self.niter += 1
-        self.rk = rk
-
-
-def euler_forward_non_advective(mem, ud, dt, writer=None, label=None, debug=False):
-    # Unpack frequently used variables
-    th, sol, mpv, node, elem = mem.th, mem.sol, mem.mpv, mem.node, mem.elem
-    ndim = elem.ndim
-
-    nonhydro = ud.nonhydrostasy
-    g, Msq = ud.gravity_strength[1], ud.Msq
-    Ginv = th.Gammainv
-    corr_h1, corr_v, corr_h2 = ud.coriolis_strength
-    u0, v0, w0 = ud.u_wind_speed, ud.v_wind_speed, ud.w_wind_speed
-
-    # Reusable derived quantities
-    rho, rhoY, rhoX = sol.rho, sol.rhoY, sol.rhoX
-    rhou, rhov, rhow = sol.rhou, sol.rhov, sol.rhow
-
-    # Pressure and derivatives
-    p2n = mpv.p2_nodes
-    dp2n = np.zeros_like(p2n)
-
-    S0c = mpv.HydroState.get_S0c(elem)
-    dSdy = mpv.HydroState_n.get_dSdy(elem, node)
-
-    # Compute divergence
-    mpv.rhs[...] = divergence_nodes(mpv.rhs, elem, node, sol, ud)
-    if not hasattr(ud, "ATMOSPHERIC_EXTENSION"):
-        bdry.scale_wall_node_values(mpv.rhs, node, ud, 2.0)
-
-    if debug:
-        writer.populate(str(label), "rhs", mpv.rhs)
-
-    # Compute compressibility kernel
-    kernel = operators.get_averaging_kernel(ndim, width=2)
-    dpidP = (th.gm1 / Msq) * operators.apply_convolution_kernel(
-        rhoY ** (th.gamm - 2.0),
-        kernel=kernel,
-        normalize=True,
-        use_numba=True
-    )
-
-    rhoYovG = Ginv * rhoY
-    dbuoy = rhoY * (rhoX / rho)
-
-    # Pressure gradients
-    dpdx, dpdy, dpdz = operators.compute_gradient_nodes(p2n, ndim, node.dxyz)
-
-    # Wind perturbations
-    drhou = rhou - u0 * rho
-    drhov = rhov - v0 * rho
-    drhow = rhow - w0 * rho
-    v = rhov / rho
-
-    # Momentum update (u, v, w)
-    rhou -= dt * (rhoYovG * dpdx - corr_h2 * drhov + corr_v * drhow)
-    rhov -= dt * (
-        rhoYovG * dpdy
-        + (g / Msq) * dbuoy * nonhydro
-        - corr_h1 * drhow
-        + corr_h2 * drhou
-    ) * (1 - ud.is_ArakawaKonor)
-
-    if ndim == 3:
-        rhow -= dt * (rhoYovG * dpdz - corr_v * drhou + corr_h1 * drhov)
-
-    # Scalar update (rhoX)
-    sol.rhoX[...] = (rho * (rho / rhoY - S0c)) - dt * (v * dSdy) * rho
-
-    # Compressibility correction to p2
-    dp2n[node.i1] -= dt * dpidP * mpv.rhs
-    mpv.p2_nodes += ud.compressibility * dp2n
-
-    # Boundary conditions
-    bdry.set_ghostnodes_p2(mpv.p2_nodes, node, ud)
-    bdry.set_explicit_boundary_data(sol, elem, ud, th, mpv)
-
-
-def euler_backward_non_advective_expl_part(mem, ud, dt):
-    nonhydro = ud.nonhydrostasy
-    g = ud.gravity_strength[1]
-    Msq = ud.Msq
-
-    dbuoy = mem.sol.rhoY * (mem.sol.rhoX / mem.sol.rho)
-    mem.sol.rhov = (nonhydro * mem.sol.rhov) - dt * (g / Msq) * dbuoy
-
-    mem.sol.mod_bg_wind(ud, -1.0)
-
-    multiply_inverse_coriolis(mem.sol, mem, ud, dt)
-
-    mem.sol.mod_bg_wind(ud, +1.0)
-
-    bdry.set_explicit_boundary_data(mem.sol, mem.elem, ud, mem.th, mem.mpv)
-
-def euler_backward_non_advective_impl_part(
-    Sol,
-    mpv,
-    elem,
-    node,
-    ud,
-    th,
-    t,
-    dt,
-    mem,
-    Sol0=None,
-    writer=None,
-    label=None,
-    debug=False,
-):
-    if not debug:
-        writer = None
-    nc = node.sc
-    rhs = np.zeros_like(mpv.p2_nodes)
-    rhs = mpv.rhs
-
-    # if elem.ndim == 2:
-    #     # p2 = np.copy(mpv.p2_nodes[node.igx:-node.igx,node.igy:-node.igy])
-    #     p2 = mpv.p2_nodes[node.p_isc]
-    # elif elem.ndim == 3:
-    #     p2 = np.copy(mpv.p2_nodes[1:-1,1:-1,1:-1])
-
-    if writer != None:
-        writer.populate(str(label), "p2_initial", mpv.p2_nodes)
-
-    if Sol0 is not None:
-        bdry.set_explicit_boundary_data(Sol0, elem, ud, th, mpv)
-        operator_coefficients_nodes(elem, node, Sol0, mpv, ud, th, dt)
-    else:
-        bdry.set_explicit_boundary_data(Sol, elem, ud, th, mpv)
-        operator_coefficients_nodes(elem, node, Sol, mpv, ud, th, dt)
-
-    i0 = node.ndim * [slice(0, -1)]
-    i0 = tuple(i0)
-
-    if writer != None:
-        writer.populate(str(label), "hcenter", mpv.wcenter)
-        writer.populate(str(label), "wplusx", mpv.wplus[0])
-        writer.populate(str(label), "wplusy", mpv.wplus[1])
-        (
-            writer.populate(str(label), "wplusz", mpv.wplus[2])
-            if elem.ndim == 3
-            else writer.populate(str(label), "wplusz", np.zeros_like(mpv.wplus[0]))
-        )
-
-    bdry.set_ghostnodes_p2(mpv.p2_nodes, node, ud)
-    correction_nodes(mem, ud, dt, mem.mpv.p2_nodes, 0)
-    bdry.set_explicit_boundary_data(Sol, elem, ud, th, mpv)
-
-    rhs[...] = divergence_nodes(rhs, elem, node, Sol, ud)
-
-    if writer != None:
-        writer.populate(str(label), "rhs", rhs)
-
-    rhs /= dt
-
-    if ud.is_compressible == 1:
-        rhs = rhs_from_p_old(rhs, node, mpv)
-    # if
-    elif ud.is_compressible == 0:
-        if ud.is_ArakawaKonor:
-            rhs -= mpv.wcenter * mpv.dp2_nodes
-            mpv.wcenter[...] = 0.0
-        else:
-            rhs_new = rhs_from_p_old(rhs, node, mpv)
-            rhs = ud.compressibility * rhs_new + (1.0 - ud.compressibility) * rhs
-            mpv.wcenter[...] *= ud.compressibility
-    else:
-        mpv.wcenter *= ud.compressibility
-
-    if writer != None:
-        writer.populate(str(label), "rhs_nodes", rhs)
-
-    mpv.rhs[...] = rhs
-
-    VS = True
-
-    # prepare initial left-hand side and the laplacian stencil
-    if elem.ndim == 2:
-        Vec = mpv
-        coriolis_params = multiply_inverse_coriolis(
-            Vec, mem, ud, dt, attrs=("u", "v", "w"), get_coeffs=True
-        )
-        # lap = stencil_9pt(elem,node,mpv,Sol,ud,diag_inv,dt,coriolis_params)
-        # sh = (ud.inx)*(ud.iny)
-
-        diag_inv = lm_lp.precon_diag_prepare(mpv, elem, node, ud, coriolis_params)
-        rhs *= diag_inv
-
-        # diag_inv = np.ones_like(mpv.rhs)
-
-        p2 = mpv.p2_nodes[node.i2].T
-        lap = lm_lp.stencil_9pt_numba_test(mpv, node, coriolis_params, diag_inv, ud)
-        sh = p2.shape[0] * p2.shape[1]
-
-        # p2 = np.copy(mpv.p2_nodes[1:-1,1:-1])
-        # sh = p2.reshape(-1).shape[0]
-
-    elif elem.ndim == 3 and elem.icy - 2 * elem.igs[1] <= 2:
-        # horizontal slice hack
-        p2 = np.copy(mpv.p2_nodes[1:-1, elem.igs[1], 1:-1])
-        lap = lm_lp.stencil_hs(elem, node, mpv, ud, diag_inv, dt)
-        sh = p2.reshape(-1).shape[0]
-
-    elif elem.ndim == 3 and elem.iicy > 1 and elem.iicz == 1:
-        # vertical slice hack
-
-        if not VS:
-            p2 = np.copy(
-                mpv.p2_nodes[..., elem.igz][node.igx : -node.igx, node.igy : -node.igy]
-            )
-            lap = lm_lp.stencil_vs(elem, node, mpv, ud, diag_inv, dt)
-            sh = (node.iicx) * (node.iicy)
-        if VS:
-            p2 = np.copy(mpv.p2_nodes[1:-1, 1:-1, elem.igs[2]])
-            lap = lm_lp.stencil_vs(elem, node, mpv, ud, diag_inv, dt)
-            sh = p2.reshape(-1).shape[0]
-
-    elif elem.ndim == 3 and elem.icy - 2 * elem.igs[1] > 2:
-        lap = lm_lp.stencil_27pt(elem, node, mpv, ud, diag_inv, dt)
-        sh = p2.reshape(-1).shape[0]
-
-    lap = sp.sparse.linalg.LinearOperator((sh, sh), lap)
-    # lap = LinearOperator(sh,lap)
-
-    counter = solver_counter()
-
-    # prepare right-hand side
-    if elem.ndim == 2:
-        # rhs_inner = rhs[node.igx:-node.igx,node.igy:-node.igy].ravel()
-        # rhs_inner = rhs[1:-1,1:-1].ravel()
-        rhs_inner = rhs[1:-1, 1:-1].T.ravel()
-        # rhs_inner = rhs.T.ravel()
-    elif elem.ndim == 3 and elem.iicy > 1 and elem.iicz == 1:
-        if not VS:
-            rhs_inner = rhs[..., elem.igs[2]][
-                node.igx : -node.igx, node.igy : -node.igy
-            ].ravel()
-        if VS:
-            rhs_inner = rhs[1:-1, 1:-1, elem.igs[2]].ravel()
-
-    elif elem.ndim == 3 and elem.icy - 2 * elem.igs[1] > 2:
-        rhs_inner = rhs[1:-1, 1:-1, 1:-1].ravel()
-    else:
-        rhs_inner = rhs[1:-1, elem.igs[1], 1:-1].ravel()
-
-    # p2, _ = bicgstab(lap,rhs_inner,tol=ud.tol,maxiter=ud.max_iterations,callback=counter)
-
-    p2, _ = sp.sparse.linalg.bicgstab(
-        lap, rhs_inner, atol=ud.tol, maxiter=ud.max_iterations, callback=counter
-    )
-    # p2, _ = gmres(lap,rhs_inner,tol=ud.tol,maxiter=ud.max_iterations)
-    # p2,info = bicgstab(lap,rhs.ravel(),x0=p2.ravel(),tol=1e-16,maxiter=6000,callback=counter)
-    # print("Convergence info = %i, no. of iterations = %i" %(info,counter.niter))
-
-    # global total_calls, total_iter
-    # total_iter += counter.niter
-    # total_calls += 1
-    # logging.info(counter.niter)
-    # logging.info(
-    #     "Total calls to BiCGStab routine = %i, total iterations = %i"
-    #     % (total_calls, total_iter)
-    # )
-
-    p2_full = np.zeros(nc).squeeze()
-    if elem.ndim == 2:
-        # p2_full[node.igx:-node.igx,node.igy:-node.igy] = p2.reshape(ud.inx,ud.iny)
-        # p2_full[node.i2] = p2.reshape(rhs[node.i1].shape[0],rhs[node.i1].shape[1])
-        p2_full[node.i2] = p2.reshape(rhs[node.i1].shape[1], rhs[node.i1].shape[0]).T
-        # p2_full[node.i1] = p2.reshape(rhs.shape[1],rhs.shape[0]).T
-        # p2 = p2.reshape(ud.inx+2, ud.iny+2)
-        # p2_full[1:-1,1:-1] = p2
-    elif elem.ndim == 3 and elem.icy - 2 * elem.igs[1] <= 2:
-        # horizontal slice hack
-        p2 = p2.reshape(ud.inx + 2, ud.inz + 2)
-        p2 = np.expand_dims(p2, 1)
-        p2 = np.repeat(p2, node.icy, axis=1)
-        p2_full[1:-1, :, 1:-1] = p2
-    elif elem.ndim == 3 and elem.iicy > 1 and elem.iicz == 1:
-        if not VS:
-            p2 = p2.reshape(node.iicx, node.iicy)
-            p2 = np.repeat(p2[..., np.newaxis], node.icz, axis=2)
-            p2_full[node.igx : -node.igx, node.igy : -node.igy] = p2
-        if VS:
-            p2 = p2.reshape(ud.inx + 2, ud.iny + 2)
-            p2 = np.expand_dims(p2, 2)
-            p2 = np.repeat(p2, node.icz, axis=2)
-            p2_full[1:-1, 1:-1, :] = p2
-
-    elif elem.ndim == 3 and elem.icy - 2 * elem.igs[1] > 2:
-        p2_full[1:-1, 1:-1, 1:-1] = p2.reshape(ud.inx + 2, ud.iny + 2, ud.inz + 2)
-    if writer != None:
-        writer.populate(str(label), "p2_full", p2_full)
-
-    bdry.set_ghostnodes_p2(p2_full, node, ud)
-    correction_nodes(mem, ud, dt, p2_full, 1)
-
-    mpv.p2_nodes[...] += p2_full
-    bdry.set_ghostnodes_p2(mpv.p2_nodes, node, ud)
-    bdry.set_explicit_boundary_data(Sol, elem, ud, th, mpv)
-
-
-def correction_nodes(mem, ud, dt, p, updt_chi):
-    ndim = mem.node.ndim
-    Gammainv = mem.th.Gammainv
-
-    dSdy = mem.mpv.HydroState_n.get_dSdy(mem.elem, mem.node)
-
-    Dpx, Dpy, Dpz = operators.compute_gradient_nodes(p, mem.elem.ndim, mem.node.dxyz)
-
-    thinv = mem.sol.rho / mem.sol.rhoY
-
-    Y = mem.sol.rhoY / mem.sol.rho
-    coeff = Gammainv * mem.sol.rhoY * Y
-
-    mem.mpv.u = -dt * coeff * Dpx
-    mem.mpv.v = -dt * coeff * Dpy
-    mem.mpv.w = -dt * coeff * Dpz
-
-    multiply_inverse_coriolis(mem.mpv, mem, ud, dt, attrs=["u", "v", "w"])
-
-    mem.sol.rhou += thinv * mem.mpv.u
-    mem.sol.rhov += thinv * mem.mpv.v
-    mem.sol.rhow += thinv * mem.mpv.w if ndim == 3 else 0.0
-    mem.sol.rhoX += -updt_chi * dt * dSdy * mem.sol.rhov
-
-    assert True
-
-
-def operator_coefficients_nodes(elem, node, Sol, mpv, ud, th, dt):
-    g = ud.gravity_strength[1]
-    Msq = ud.Msq
-    Gammainv = th.Gammainv
-
-    ndim = node.ndim
-    nonhydro = ud.nonhydrostasy
-    dy = elem.dy
-
-    wh1, wv, wh2 = dt * ud.coriolis_strength
-
-    ccenter = -ud.Msq * th.gm1inv / (dt**2)
-    cexp = 2.0 - th.gamm
-
-    igs = elem.igs
-
-    strat = mpv.HydroState_n.get_dSdy(elem, node)
-
-    Y = Sol.rhoY / Sol.rho
-    coeff = Gammainv * Sol.rhoY * Y
-
-    nu = np.zeros_like(mpv.wcenter)
-    nu = -(dt**2) * (g / Msq) * strat * Y
-
-    setattr(mpv, "nu_c", nu)
-    nu = nu
-
-    for dim in range(ndim):
-        ## Assuming 2D vertical slice!
-        if dim == 1:
-            mpv.wplus[dim][...] = coeff  # * gimp #* (wv**2 + 1.0)
-        else:
-            mpv.wplus[dim][...] = coeff  # * fimp #* (wh1**2 + nu + nonhydro)
-
-    kernel = np.ones([2] * ndim)
-
-    mpv.wcenter = (
-        ccenter
-        * sp.signal.fftconvolve(Sol.rhoY**cexp, kernel, mode="valid")
-        / kernel.sum()
-    )
-
-    tmp_wplus = sp.signal.fftconvolve(mpv.wplus[0], kernel, mode="valid") / kernel.sum()
-
-    # set_ghostcells_p2(mpv.wplus[0], elem, ud)
-    # set_ghostcells_p2(mpv.wplus[1], elem, ud)
-    # set_ghostnodes_p2(mpv.wcenter, node, ud, igs=(1,1))
-    # mpv.wcenter[:,0] = mpv.wcenter[:,1]
-    # mpv.wcenter[:,-1] = mpv.wcenter[:,-2]
-
-    assert True
-    if not hasattr(ud, "ATMOSPHERIC_EXTENSION"):
-        bdry.scale_wall_node_values(mpv.wcenter, node, ud)
-
-def rhs_from_p_old(rhs, node, mpv):
-    igs = node.igs
-    ndim = node.ndim
-
-    assert ndim != 1, "Not implemented for 1D"
-
-    # inner_idx = np.empty((ndim), dtype=object)
-    # for dim in range(ndim):
-    #     inner_idx[dim] = slice(igs[dim],-igs[dim])
-
-    # inner_idx = tuple(inner_idx)
-    # rhs_n = np.zeros_like(rhs)
-    # rhs_hh = mpv.wcenter[inner_idx] * mpv.p2_nodes[inner_idx]
-    # rhs_n[inner_idx] = rhs[inner_idx] + 0.0 * rhs_hh
-
-    inner_idx = np.empty((ndim), dtype=object)
-    for dim in range(ndim):
-        inner_idx[dim] = slice(igs[dim], -igs[dim])
-
-    inner_idx = tuple(inner_idx)
-    rhs_n = np.zeros_like(rhs)
-    rhs_hh = mpv.wcenter * mpv.p2_nodes[node.i1]
-    rhs_n = rhs + 0.0 * rhs_hh
-    return rhs_n
-
-@njit(cache=True)
-def _compute_coriolis_coefficients(wh1, wh2, wv, nu, nonhydro):
-    """Compute coefficients for the H^-1 matrix multiplication.
-    
-    This corresponds to equation (C11) in the mathematical formulation.
-    """
-    # Common terms
-    wh1_sq = wh1 * wh1
-    wh2_sq = wh2 * wh2
-    wv_sq = wv * wv
-    nu_nh = nu + nonhydro
-    
-    # Denominator (det(H))
-    denom = 1.0 / (wh1_sq + wh2_sq + nu_nh * (wv_sq + 1.0))
-    
-    # H^-1 matrix elements (row-major order)
-    # Row 1: U equation coefficients
-    h11 = (wh1_sq + nu_nh) * denom
-    h12 = nonhydro * (wh1 * wv + wh2) * denom
-    h13 = (wh1 * wh2 - nu_nh * wv) * denom
-    
-    # Row 2: V equation coefficients  
-    h21 = (wh1 * wv - wh2) * denom
-    h22 = nonhydro * (1.0 + wv_sq) * denom
-    h23 = (wh2 * wv + wh1) * denom
-    
-    # Row 3: W equation coefficients
-    h31 = (wh1 * wh2 + nu_nh * wv) * denom
-    h32 = nonhydro * (wh2 * wv - wh1) * denom
-    h33 = (nu_nh + wh2_sq) * denom
-    
-    return h11, h12, h13, h21, h22, h23, h31, h32, h33
-
-@njit(cache=True)
-def apply_coriolis_matrix_inplace(u_vec, v_vec, w_vec, U,V,W, wh1, wh2, wv, nu, nonhydro):
-    """Apply H^-1 matrix multiplication in-place.
-    
-    Corresponds to the equation: U^{n+1} = H^{-1}(U^{n*} - Δt_{cp}(Pθ)^* ∇π^{n+1})
-    """
-    # Get matrix coefficients
-    h11, h12, h13, h21, h22, h23, h31, h32, h33 = _compute_coriolis_coefficients(
-        wh1, wh2, wv, nu, nonhydro
-    )
-
-    U[...] = u_vec
-    V[...] = v_vec
-    W[...] = w_vec
-    
-    # Matrix multiplication: [U_new, V_new, W_new] = H^-1 @ [U_old, V_old, W_old]
-    u_vec[...] = h11 * U + h12 * V + h13 * W
-    v_vec[...] = h21 * U + h22 * V + h23 * W
-    w_vec[...] = h31 * U + h32 * V + h33 * W
-
-# Refactored main function
-def multiply_inverse_coriolis(
-    Vec, mem, ud, dt, attrs=("rhou", "rhov", "rhow"), get_coeffs=False
-):
-    """Coriolis matrix multiplication."""
-    nonhydro = ud.nonhydrostasy
-    g = ud.gravity_strength[1]
-    Msq = ud.Msq
-
-    wh1, wv, wh2 = dt * ud.coriolis_strength
-    strat = mem.mpv.HydroState_n.get_dSdy(mem.elem, mem.node)
-    Y = mem.sol.rhoY / mem.sol.rho
-    nu = -(dt**2) * (g / Msq) * strat * Y
-    
-    # Get vector components
-    VecU = getattr(Vec, attrs[0])
-    VecV = getattr(Vec, attrs[1])
-    VecW = getattr(Vec, attrs[2])
-
-    U,V,W = mem.cache.get_velocity_array_views(VecU.shape)
-    
-    apply_coriolis_matrix_inplace(VecU, VecV, VecW, U,V,W,wh1, wh2, wv, nu, nonhydro)
-    
-    # Return coefficients
-    if get_coeffs:
-        h11, h12, _, h21, h22, h23, h31, h32, h33 = _compute_coriolis_coefficients(wh1, wh2, wv, nu, nonhydro)
-        return (h11.T, h22.T, h12.T, h21.T)
-    
-
-def divergence_nodes(rhs, elem, node, Sol, ud):
-    """Main divergence function - handles boundary conditions and calls JIT-compiled core."""
-    ndim = elem.ndim
-    
-    # Handle boundary conditions
-    if not hasattr(ud, "ATMOSPHERIC_EXTENSION"):
-        if (ud.bdry_type[1] == opts.BdryType.WALL or 
-            ud.bdry_type[1] == opts.BdryType.RAYLEIGH):
-            Sol.rhou[:, :2, ...] = 0.0
-            Sol.rhov[:, :2, ...] = 0.0
-            Sol.rhow[:, :2, ...] = 0.0
-            Sol.rhou[:, -2:, ...] = 0.0
-            Sol.rhov[:, -2:, ...] = 0.0
-            Sol.rhow[:, -2:, ...] = 0.0
-    
-    # Call appropriate JIT-compiled function
-    if ndim == 2:
-        rhs[:] = _momentum_pot_temp_divergence_2d_jit(
-            Sol.rho, Sol.rhou, Sol.rhov, Sol.rhoY,
-            elem.dx, elem.dy
-        )
-    else:
-        _momentum_pot_temp_divergence_3d_jit(
-            rhs, Sol.rho, Sol.rhou, Sol.rhov, Sol.rhow, Sol.rhoY,
-            elem.dx, elem.dy, elem.dz
-        )
-    
-    return rhs
-
-
-@njit(cache=True)
-def _momentum_pot_temp_divergence_2d_jit(rho, rhou, rhov, rhoY, dx, dy):
-    """
-    JIT-compiled 2D momentum-potential temperature divergence calculation.
-    Computes ∇·(ρu θ, ρv θ) where θ = ρY/ρ is the potential temperature.
-    """
-    # Calculate potential temperature θ = ρY / ρ
-    theta = rhoY / rho
-
-    # Compute momentum-potential temperature flux components
-    rhou_theta = rhou * theta  # x-momentum flux weighted by potential temperature
-    rhov_theta = rhov * theta  # y-momentum flux weighted by potential temperature
-    
-    # Use generic divergence operator
-    return operators.compute_divergence_2d(rhou_theta, rhov_theta, dx, dy)
-
-
-@njit(cache=True)
-def _momentum_pot_temp_divergence_3d_jit(rhs, rho, rhou, rhov, rhow, rhoY, dx, dy, dz):
-    """
-    JIT-compiled 3D momentum-potential temperature divergence calculation.
-    Computes ∇·(ρu θ, ρv θ, ρw θ) where θ = ρY/ρ is the potential temperature.
-    """
-    # Calculate potential temperature θ = ρY / ρ
-    theta = rhoY / rho
-
-    # Compute momentum-potential temperature flux components
-    rhou_theta = rhou * theta  # x-momentum flux weighted by potential temperature
-    rhov_theta = rhov * theta  # y-momentum flux weighted by potential temperature
-    rhow_theta = rhow * theta  # z-momentum flux weighted by potential temperature
-
-    # Use generic total divergence operator
-    total_div = operators.compute_divergence_3d_total(rhou_theta, rhov_theta, rhow_theta, dx, dy, dz)
-
-    # Assign to inner region
-    rhs[1:-1, 1:-1, 1:-1] = total_div
-    
diff --git a/src/pybella/flow_solver/physics/gas_dynamics/thermodynamics.py b/src/pybella/flow_solver/physics/thermodynamics.py
similarity index 100%
rename from src/pybella/flow_solver/physics/gas_dynamics/thermodynamics.py
rename to src/pybella/flow_solver/physics/thermodynamics.py
diff --git a/src/pybella/flow_solver/utils/boundary.py b/src/pybella/flow_solver/utils/boundary.py
deleted file mode 100644
index a2dccff7..00000000
--- a/src/pybella/flow_solver/utils/boundary.py
+++ /dev/null
@@ -1,683 +0,0 @@
-"""
-For more details on this module, refer to the write-up :ref:`boundary_handling`.
-"""
-
-import copy
-import numpy as np
-from ...utils import options as opts
-from ...utils import io
-
-
-def set_explicit_boundary_data(Sol, elem, ud, th, mpv, step=None):
-    """
-    In-place update of the ghost cells in :class:`management.variable.Vars` given the boundary conditions specified by :class:`inputs.user_data.UserDataInit`.
-
-    Parameters
-    ----------
-    Sol : :class:`management.variable.Vars`
-        Solution data container
-    elem : :class:`discretization.kgrid.ElemSpaceDiscr`
-        Cells grid
-    ud : :class:`inputs.user_data.UserDataInit`
-        Data container for the initial conditions
-    th : :class:`physics.gas_dynamics.thermodynamic.init`
-        Thermodynamic variables of the system
-    mpv : :class:`physics.low_mach.mpv.MPV`
-        Variables relating to the elliptic solver
-    step : int, optional
-        Current step
-
-    """
-    igs = elem.igs
-    ndim = elem.ndim
-
-    # if step parameter is not None, then we are in the advection directional Strang-splitting, where the array has already flipped, and we should only update the relevant boundaries, i.e. those in the direction of the current Strang-split-step.
-    if step == None:
-        dims = np.arange(ndim)
-    else:
-        dims = [ndim - 1]
-
-    for dim in dims:
-        if step is not None:
-            current_step = step
-        else:
-            current_step = dim
-        ghost_padding, idx = get_ghost_padding(ndim, dim, igs)
-
-        if ud.gravity_strength[current_step] == 0.0:
-            # Do this for the axes that do not have gravity.
-            # Periodic BC.
-            if ud.bdry_type[current_step] == opts.BdryType.PERIODIC:
-                set_boundary(Sol, ghost_padding, "wrap", idx, step=None)
-            # Wall BC.
-            elif ud.bdry_type[current_step] == opts.BdryType.WALL:
-                set_boundary(Sol, ghost_padding, "symmetric", idx, step=None)
-            elif ud.bdry_type[current_step] == opts.BdryType.RAYLEIGH:
-                assert 0, "Rayleigh boundary not defined on x-direction."
-                # set_boundary(Sol,((0,0),(0,2)),'constant',(slice(None,),slice(0,-2)),step=None)
-                # set_boundary(Sol,((0,0),(2,0)),'symmetric',(slice(None,),slice(2,None)),step=None)
-
-        else:
-            # get current axis that has gravity.
-            gravity_axis = dim
-
-            direction = -1.0
-            offset = 0
-
-            # get gravity strength specified in the user data file.
-            g = ud.gravity_strength[gravity_axis]
-
-            # for the number of ghost cells in the gravity axis...
-            for side in ghost_padding[gravity_axis]:
-                direction *= -1
-                # loop through each of these ghost cells.
-                for current_idx in np.arange(side)[::-1]:
-                    if step != None:
-                        y_axs = ndim - 1
-                    else:
-                        y_axs = 1
-                    nlast, nsource, nimage = get_gravity_padding(
-                        ndim, current_idx, direction, offset, elem, y_axs=y_axs
-                    )
-
-                    Y_last = Sol.rhoY[nlast] / Sol.rho[nlast]
-
-                    rhoYv_image = (
-                        -Sol.rhov[nsource] * Sol.rhoY[nsource] / Sol.rho[nsource]
-                    )
-
-                    S = 1.0 / ud.stratification(elem.y[nimage[y_axs]])
-
-                    if hasattr(ud, "ATMOSPHERIC_EXTENSION"):
-                        dpi = (
-                            mpv.HydroState.p20[nimage[y_axs]]
-                            - mpv.HydroState.p20[nlast[y_axs]]
-                        ) * ud.Msq
-                    else:
-                        dpi = (
-                            direction
-                            * (th.Gamma * g)
-                            * 0.5
-                            * elem.dy
-                            * (1.0 / Y_last + S)
-                        )
-
-                    rhoY = (
-                        ((Sol.rhoY[nlast] ** th.gm1) + dpi) ** th.gm1inv
-                        if ud.is_compressible == 1
-                        else mpv.HydroState.rhoY0[nimage[y_axs]]
-                    )
-
-                    rho = rhoY * S
-
-                    Y_source = Sol.rhoY[nsource] / Sol.rho[nsource]
-                    Y_image = rhoY / rho
-
-                    if hasattr(ud, "ATMOSPHERIC_EXTENSION"):
-                        if direction > 0:  # if bottom boundary
-                            v = Sol.rhov[nsource] * Y_source / Sol.rho[nsource] * rho
-                        else:  # if top boundary
-                            v = Sol.rhov[nsource] * Y_source
-
-                        Th_slc = rhoY / rho / Y_last
-
-                    else:
-                        v = rhoYv_image / rhoY
-                        Th_slc = 1.0
-
-                    u = Sol.rhou[nsource] / Sol.rho[nsource]
-                    w = Sol.rhow[nsource] / Sol.rho[nsource]
-                    X = Sol.rhoX[nsource] / Sol.rho[nsource]
-
-                    # p = rhoY**th.gamm
-
-                    # rhoY = mpv.HydroState.rhoY0[nimage[y_axs]]
-                    # Y = Sol.rhoY[nimage] / Sol.rho[nimage]
-                    # rho = mpv.HydroState.rho0[nimage[y_axs]]
-
-                    # direction == 1 is the bottom
-                    # if np.sign(direction) == 1:
-                    # v = -Sol.rhov[nsource] / Sol.rho[nsource]
-
-                    Sol.rho[nimage] = rho
-                    Sol.rhou[nimage] = rho * u * Th_slc
-                    # Sol.rhov[nimage] = 0.0#rho*v
-                    if hasattr(ud, "ATMOSPHERIC_EXTENSION"):
-                        Sol.rhov[nimage] = -v / Y_image
-                    else:
-                        Sol.rhov[nimage] = rho * v
-                    Sol.rhow[nimage] = rho * w * Th_slc
-                    Sol.rhoY[nimage] = rhoY
-                    Sol.rhoX[nimage] = rho * X
-
-                offset += 1
-
-
-def set_boundary(Sol, pads, btype, idx, step=None):
-    """
-    Called by the function :func:`inputs.boundary.set_explicit_boundary_data`. Pads in-place the ghost cells for a given boundary type.
-
-    Parameters
-    ----------
-    Sol : :class:`management.variable.Vars`
-        Solution data container.
-    pads : tuple
-        A tuple containing the number of ghost cells to pad at each end.
-    btype : string
-        The type of boundary condition to pad. Currently supports:
-            * `wrap` for periodic boundary conditions
-            * `symmetric` for wall boundary conditions
-            * `negative_symmetric` for wall boundary conditions, but with the signs flipped.
-    idx : tuple
-        A tuple containing the slice indices for the inner array, e.g. `(slice(2,-2),slice(2,-2))` for a 2D-array with 2 ghost cells for all edges.
-    step : int, optional
-        If we are in the advection routine with the flipped arrays according to the directional Strang-splitting, we want to pad the correct direction. `step=0`, pads the x-direction while `step=1` pads the y-direction.
-
-    """
-    Sol.rho[...] = np.pad(Sol.rho[idx], pads, btype)
-    # Sol.rhou[...] = np.pad(Sol.rhou[idx],pads,btype)
-    # Sol.rhov[...] = np.pad(Sol.rhov[idx],pads,btype)
-    # Sol.rhow[...] = np.pad(Sol.rhow[idx],pads,btype)
-
-    if btype == "symmetric":
-        # Sol.rhou[...] = np.pad(Sol.rhou[idx],pads,negative_symmetric)
-        Sol.rhov[...] = np.pad(Sol.rhov[idx], pads, negative_symmetric)
-        # Sol.rhow[...] = np.pad(Sol.rhow[idx],pads,negative_symmetric)
-        Sol.rho[...] = np.pad(Sol.rho[idx], pads, "symmetric")
-        Sol.rhou[...] = np.pad(Sol.rhou[idx], pads, "symmetric")
-    elif btype == "constant":
-        Sol.rho[...] = np.pad(Sol.rho[idx], pads, "symmetric")
-        Sol.rhou[...] = np.pad(Sol.rhou[idx], pads, "symmetric")
-        Sol.rhov[...] = np.pad(Sol.rhov[idx], pads, btype)
-        Sol.rhow[...] = np.pad(Sol.rhow[idx], pads, "symmetric")
-        btype = "symmetric"
-    else:
-        Sol.rhou[...] = np.pad(Sol.rhou[idx], pads, btype)
-        Sol.rhov[...] = np.pad(Sol.rhov[idx], pads, btype)
-        Sol.rhow[...] = np.pad(Sol.rhow[idx], pads, btype)
-
-    # if step == 0:
-    #     Sol.rhov[...] = np.pad(Sol.rhov[idx],pads,btype)
-    #     # Sol.rhou[...] = np.pad(Sol.rhou[idx],pads,btype)
-    #     Sol.rhow[...] = np.pad(Sol.rhow[idx],pads,btype)
-    #     if btype == 'symmetric':
-    #         # Sol.rhov[...] = np.pad(Sol.rhov[idx],pads,negative_symmetric)
-    #         Sol.rhou[...] = np.pad(Sol.rhou[idx],pads,negative_symmetric)
-    #         # Sol.rhow[...] = np.pad(Sol.rhow[idx],pads,negative_symmetric)
-    #     else:
-    #         Sol.rhov[...] = np.pad(Sol.rhov[idx],pads,btype)
-    #         Sol.rhou[...] = np.pad(Sol.rhou[idx],pads,btype)
-    #         Sol.rhow[...] = np.pad(Sol.rhow[idx],pads,btype)
-
-    # if step == 1:
-    #     Sol.rhou[...] = np.pad(Sol.rhou[idx],pads,btype)
-    #     Sol.rhow[...] = np.pad(Sol.rhow[idx],pads,btype)
-    #     if btype == 'symmetric':
-    #         # Sol.rhou[...] = np.pad(Sol.rhou[idx],pads,negative_symmetric)
-    #         Sol.rhov[...] = np.pad(Sol.rhov[idx],pads,negative_symmetric)
-    #         # Sol.rhow[...] = np.pad(Sol.rhow[idx],pads,negative_symmetric)
-    #     else:
-    #         Sol.rhou[...] = np.pad(Sol.rhou[idx],pads,btype)
-    #         Sol.rhov[...] = np.pad(Sol.rhov[idx],pads,btype)
-    #         Sol.rhow[...] = np.pad(Sol.rhow[idx],pads,btype)
-
-    # if step == 2:
-    #     Sol.rhou[...] = np.pad(Sol.rhou[idx],pads,btype)
-    #     Sol.rhov[...] = np.pad(Sol.rhov[idx],pads,btype)
-    #     if btype == 'symmetric':
-    #         # Sol.rhou[...] = np.pad(Sol.rhou[idx],pads,negative_symmetric)
-    #         # Sol.rhov[...] = np.pad(Sol.rhov[idx],pads,negative_symmetric)
-    #         Sol.rhow[...] = np.pad(Sol.rhow[idx],pads,negative_symmetric)
-    #     else:
-    #         Sol.rhou[...] = np.pad(Sol.rhou[idx],pads,btype)
-    #         Sol.rhov[...] = np.pad(Sol.rhov[idx],pads,btype)
-    #         Sol.rhow[...] = np.pad(Sol.rhow[idx],pads,btype)
-
-    Sol.rhoY[...] = np.pad(Sol.rhoY[idx], pads, btype)
-    Sol.rhoX[...] = np.pad(Sol.rhoX[idx], pads, btype)
-
-
-def negative_symmetric(vector, pad_width, iaxis, kwargs=None):
-    """
-    Taken from the reference:
-
-    Parameters
-    ----------
-    vector : ndarray
-        A rank 1 array already padded with zeros. Padded values are vector `[:iaxis_pad_width[0]] and vector[-iaxis_pad_width[1]:]`.
-    iaxis_pad_width : tuple
-        A 2-tuple of ints, `iaxis_pad_width[0]` represents the number of values padded at the beginning of vector where `iaxis_pad_width[1]` represents the number of values padded at the end of vector.
-    iaxis : int
-        The axis currently being calculated.
-    kwargs : dict
-        Any keyword arguments the function requires.
-
-    References
-    ----------
-    https://docs.scipy.org/doc/numpy/reference/generated/numpy.pad.html
-
-    """
-    if pad_width[1] > 0:
-        sign = -1
-        vector[: pad_width[0]] = sign * vector[pad_width[0] : 2 * pad_width[0]][::-1]
-        vector[-pad_width[1] :] = sign * vector[-2 * pad_width[1] : -pad_width[1]][::-1]
-        return vector
-    else:  # axis must have length > 0 for padding
-        return vector
-
-
-def get_gravity_padding(ndim, cur_idx, direction, offset, elem, y_axs=None):
-    """
-    Parameters
-    ----------
-    ndim : int
-        Number of dimensions.
-    cur_idx : int
-        The current index of the ghost cell in the gravity direction to be updated.
-    direction : int
-        Top of the domain, `direction=+1`, bottom of the domain, `direction=-1`.
-    offset : int
-        `offset=0`, index starts counting from 0,1.... `offset=1`, index starts counting from -1,-2,..., i.e. end-selection of the array.
-    elem : :class:`discretization.kgrid.ElemSpaceDiscr`
-        Cell grid.
-    y_axs : int, optional
-        `Default == None`. Specifies the direction of the gravity axis. If `None`, then direction is the the y-axis.
-
-    """
-    cur_i = np.copy(cur_idx)
-    cur_idx += offset * ((elem.icy - 1) - 2 * cur_idx)
-    gravity_padding = [slice(None)] * ndim
-    if y_axs == None:
-        # y_axs = ndim - 1
-        y_axs = 1
-
-    nlast = np.copy(gravity_padding)
-    nlast[y_axs] = int(cur_idx + direction)
-
-    nsource = np.copy(gravity_padding)
-    nsource[y_axs] = int(
-        offset * (elem.icy) + direction * (2 * elem.igy - (1 - offset) - cur_i)
-    )
-
-    nimage = np.copy(gravity_padding)
-    nimage[y_axs] = int(cur_idx)
-    return tuple(nlast), tuple(nsource), tuple(nimage)
-
-
-def set_ghostcells_p2(p, elem, ud):
-    igs = elem.igs
-
-    for dim in range(elem.ndim):
-        ghost_padding, idx = get_ghost_padding(elem.ndim, dim, igs)
-
-        if ud.bdry_type[dim] == opts.BdryType.PERIODIC:
-            p[...] = np.pad(p[idx], ghost_padding, "wrap")
-        else:  # WALL
-            p[...] = np.pad(p[idx], ghost_padding, "symmetric")
-
-
-def set_ghostnodes_p2(p, node, ud, igs=None):
-    if igs is None:
-        igs = node.igs
-    for dim in range(node.ndim):
-        ghost_padding, idx = get_ghost_padding(node.ndim, dim, igs)
-
-        if ud.bdry_type[dim] == opts.BdryType.PERIODIC:
-            p[...] = np.pad(p[idx], ghost_padding, periodic_plus_one)
-        else:  # ud.bdry_type[dim] == opts.BdryType.WALL:
-            p[...] = np.pad(p[idx], ghost_padding, "reflect")
-
-    # if periodic_plus_one
-    if node.iicy == 2:  # implying horizontal slices
-        pn = p[:, 2, :]
-        pn = np.expand_dims(pn, axis=1)
-        p[...] = np.repeat(pn, node.icy, axis=1)
-
-
-def get_ghost_padding(ndim, dim, igs):
-    """
-    For a given direction, return the number of ghost cells to pad the current direction, and the index slice of the inner array without the ghost cells.
-
-    Parameters
-    ----------
-    ndim : int
-        Number of dimensions for the problem.
-    dim : int
-        Current dimension to update
-    igs : list
-        A list of number of ghost cells in all dimensions, e.g. `[2,2,2]` for 2 ghost cells in the x, y, and z directions.
-
-    Returns
-    -------
-    tuple
-        Number of ghost cells in the current dimension at both edges.
-    tuple
-        Index slice of the inner domain of the array.
-
-    """
-    ghost_padding = [(0, 0)] * ndim
-    ghost_padding[dim] = (igs[dim], igs[dim])
-
-    padded_idx = np.empty((ndim), dtype=object)
-    for idim in range(ndim):
-        padded_idx[idim] = slice(igs[idim], -igs[idim])
-    padded_idx[dim] = slice(None)
-
-    inner_domain = [slice(None)] * ndim
-    inner_domain[dim] = slice(igs[dim], -igs[dim])
-
-    return tuple(ghost_padding), tuple(inner_domain)
-
-
-def periodic_plus_one(vector, pad_width, iaxis, kwargs=None):
-    """
-    Taken from the reference:
-
-    Parameters
-    ----------
-    vector : ndarray
-        A rank 1 array already padded with zeros. Padded values are vector `[:iaxis_pad_width[0]] and vector[-iaxis_pad_width[1]:]`.
-    iaxis_pad_width : tuple
-        A 2-tuple of ints, `iaxis_pad_width[0]` represents the number of values padded at the beginning of vector where `iaxis_pad_width[1]` represents the number of values padded at the end of vector.
-    iaxis : int
-        The axis currently being calculated.
-    kwargs : dict
-        Any keyword arguments the function requires.
-    References
-    ----------
-    https://docs.scipy.org/doc/numpy/reference/generated/numpy.pad.html
-
-    """
-    if all(pad_width) > 0:
-        vector[: pad_width[0] + 1], vector[-pad_width[1] - 1 :] = (
-            vector[-pad_width[1] - pad_width[1] - 1 : -pad_width[1]],
-            vector[pad_width[0] : pad_width[0] + pad_width[0] + 1].copy(),
-        )
-    return vector
-
-
-def get_tau_y(ud, elem, node, alpha):
-    tauc_y = np.zeros_like(elem.y)
-    taun_y = np.zeros_like(node.y)
-
-    # ud.bcy = elem.y[-ud.inbcy-2]
-    ud.bny = node.y[-ud.inbcy - 3]
-    # ud.bny = ud.bcy
-
-    # c1c = elem.y <= ud.bcy
-    # ccc = (elem.y[:-2] - ud.bcy) / (elem.y[:-2][-1] - ud.bcy)
-    # c2c = np.logical_and(ccc >= 0.0, ccc <= 0.5)
-    # c3c = np.logical_and(ccc > 0.5, ccc <= 1.0)
-
-    c1n = node.y <= ud.bny
-    ccn = (node.y[:-2] - ud.bny) / (node.y[:-2][-1] - ud.bny)
-    c2n = np.logical_and(ccn >= 0.0, ccn <= 0.5)
-    c3n = np.logical_and(ccn > 0.5, ccn <= 1.0)
-
-    # ccc and ccn can be reused below
-
-    # tauc_y[np.where(c1c)] = 0.0
-    # tauc_y[np.where(c2c)] = - alpha / 2.0 * (1.0 - np.cos( (elem.y[np.where(c2c)] - ud.bcy) / (elem.y[-1] - ud.bcy) * np.pi ))
-    # tauc_y[np.where(c3c)] = - alpha / 2.0 * (1.0 + ((elem.y[np.where(c3c)] - ud.bcy) / (elem.y[-1] - ud.bcy) - 0.5) * np.pi)
-
-    taun_y[np.where(c1n)] = 0.0
-    taun_y[np.where(c2n)] = (
-        -alpha
-        / 2.0
-        * (
-            1.0
-            - np.cos((node.y[np.where(c2n)] - ud.bny) / (node.y[-1] - ud.bny) * np.pi)
-        )
-    )
-    taun_y[np.where(c3n)] = (
-        -alpha
-        / 2.0
-        * (
-            1.0
-            + ((node.y[np.where(c3n)] - ud.bny) / (node.y[-1] - ud.bny) - 0.5) * np.pi
-        )
-    )
-
-    taun_y[-2:] = -np.abs(taun_y).max()
-    tauc_y[...] = np.interp(elem.y, node.y, taun_y)
-    # dd = 1.0
-    # tauc_y = dd * tauc_y / np.abs(tauc_y).max()
-    # taun_y = dd * taun_y / np.abs(taun_y).max()
-    return tauc_y, taun_y
-
-
-def get_bottom_tau_y(ud, elem, node, alpha, cutoff=0.5):
-    tauc_y = np.zeros_like(elem.y)
-    taun_y = np.zeros_like(node.y)
-
-    assert ud.ymax > cutoff, "rayleigh forcing boundary below minimum domain extent"
-    idx = (np.abs(elem.y - (ud.ymax - cutoff))).argmin()
-
-    ud.forcing_bny = node.y[idx]
-
-    c1n = node.y <= ud.forcing_bny
-    ccn = (node.y[:-3] - ud.forcing_bny) / (node.y[:-3][-1] - ud.forcing_bny)
-    c2n = np.logical_and(ccn >= 0.0, ccn <= 0.5)
-    c3n = np.logical_and(ccn > 0.5, ccn <= 1.0)
-
-    taun_y[np.where(c1n)] = 0.0
-    taun_y[np.where(c2n)] = (
-        -alpha
-        / 2.0
-        * (
-            1.0
-            - np.cos(
-                (node.y[np.where(c2n)] - ud.forcing_bny)
-                / (node.y[-1] - ud.forcing_bny)
-                * np.pi
-            )
-        )
-    )
-    taun_y[np.where(c3n)] = (
-        -alpha
-        / 2.0
-        * (
-            1.0
-            + (
-                (node.y[np.where(c3n)] - ud.forcing_bny) / (node.y[-1] - ud.forcing_bny)
-                - 0.5
-            )
-            * np.pi
-        )
-    )
-
-    taun_y[-3:] = -np.abs(taun_y).max()
-    taun_y[...] = taun_y[::-1]
-    tauc_y = np.interp(elem.y, node.y, taun_y)
-
-    dd = 1.0
-    tauc_y = dd * tauc_y / np.abs(tauc_y).max()
-    taun_y = dd * taun_y / np.abs(taun_y).max()
-
-    # tauc_y = tauc_y[2:-2]
-    # taun_y = taun_y[2:-2]
-
-    return tauc_y, taun_y
-
-
-def apply_rayleigh_forcing(
-    Sol,
-    mpv,
-    ud,
-    elem,
-    node,
-    t,
-    step,
-    dt,
-    th,
-    bdry,
-    half=True,
-    Sol_half_new=None,
-    mpv_half_new=None,
-):
-    """Apply Rayleigh forcing boundary condition (file or function based)."""
-    if not (hasattr(ud, "rayleigh_forcing") and ud.rayleigh_forcing):
-        return
-
-    t_offset = 0.5 * dt if half else dt
-
-    if ud.rayleigh_forcing_type == "file":
-        reader = io.read_input(ud.rayleigh_forcing_fn, ud.rayleigh_forcing_path)
-
-        if Sol_half_new is None or mpv_half_new is None:
-            Sol_half_new = copy.deepcopy(Sol)
-            mpv_half_new = copy.deepcopy(mpv)
-
-        time_tag = "%.3d_after_full_step" % step
-        reader.get_data(Sol_half_new, mpv_half_new, time_tag, half=half)
-
-        up = Sol_half_new.rhou / Sol_half_new.rho
-        vp = Sol_half_new.rhov / Sol_half_new.rho
-        Yp = Sol_half_new.rhoY / Sol_half_new.rho - mpv.HydroState.Y0.reshape(1, -1)
-        pi = mpv_half_new.p2_nodes
-
-        bdry.rayleigh_damping(Sol, mpv, ud, elem, node, [up, vp, Yp, pi, t + t_offset])
-
-    elif ud.rayleigh_forcing_type == "func":
-        s = 5.0e-3 + 1e-4 + 0e-5
-        ud.rf_bot.eigenfunction(t + t_offset, s)
-        up, vp, Yp, pi = ud.rf_bot.dehatter(th)
-
-        ud.rf_bot.eigenfunction(t + t_offset, s, grid="n")
-        _, _, _, pi_n = ud.rf_bot.dehatter(th, grid="n")
-
-        bdry.rayleigh_damping(
-            Sol, mpv, ud, elem, node, [up, vp, Yp, pi_n, t + t_offset]
-        )
-
-    bdry.set_explicit_boundary_data(Sol, elem, ud, th, mpv)
-
-
-def rayleigh_damping(Sol, mpv, ud, elem, node, forcing=None):
-    u = Sol.rhou / Sol.rho  # [elem.i2]
-    v = Sol.rhov / Sol.rho  # [elem.i2]
-    Y = Sol.rhoY / Sol.rho  # [elem.i2]
-    rho = Sol.rho  # [elem.i2]
-
-    if ud.bdry_type[1] == opts.BdryType.RAYLEIGH:
-        tcy, tny = ud.tcy, ud.tny
-    else:
-        tcy, tny = 0.0, 0.0
-
-    if forcing is not None:
-        tcy_f, tny_f = ud.forcing_tcy, ud.forcing_tny
-        tcy, tny = 0.0, 0.0
-
-        u_f, v_f, Y_f, pi_f, t = forcing
-
-        if ud.rayleigh_forcing_type == "file":
-            G = np.sqrt(9.0 / 40.0)
-            N = np.sqrt(ud.Nsq_ref)
-            C = ud.Cs * ud.u_ref
-            Gam = N * G / C
-            Om = ud.coriolis_strength[2] / 2.0 / ud.t_ref
-            # Om = 7.292 * 1e-5 / ud.t_ref
-            growth_rate = np.sqrt(Om * C * Gam)
-            mfac = np.exp(growth_rate * t * ud.t_ref)
-
-            # if np.all(ud.coriolis_strength) == 0.0:
-            # if ud.trad_forcing:
-            # mfac = 1.0
-        else:
-            mfac = 1.0
-
-        mpv.p2_nodes[...] += tny_f * (mpv.p2_nodes) + np.abs(tny_f) * mfac * pi_f
-        c_f = 1.0
-
-    else:
-        u_f, v_f, Y_f = 0.0, 0.0, 0.0
-        c_f = 0.0
-        tcy_f, tny_f = 0.0, 0.0
-        mfac = 0.0
-
-    # assuming 2D vertical slice - not dimension agnostic
-    u += tcy * (u - ud.u_wind_speed) + c_f * (
-        tcy_f * (u - ud.u_wind_speed) + np.abs(tcy_f) * mfac * u_f
-    )
-    v += tcy * (v - ud.v_wind_speed) + c_f * (
-        tcy_f * (v - ud.v_wind_speed) + np.abs(tcy_f) * mfac * v_f
-    )
-
-    Ybar = mpv.HydroState.Y0.reshape(1, -1)
-    Y += tcy * (Y - Ybar) + c_f * (tcy_f * (Y - Ybar) + np.abs(tcy_f) * mfac * Y_f)
-
-    Sol.rhou[...] = rho * u
-    Sol.rhov[...] = rho * v
-    Sol.rhoY[...] = rho * Y
-
-
-def check_flux_bcs(Lefts, Rights, elem, split_step, ud):
-    igx = elem.igx
-    igy = elem.igy
-
-    if split_step == 1:
-        if ud.bdry_type[split_step] == opts.BdryType.WALL:
-            left_inner = (slice(None), slice(igy, igy + 1))
-            left_ghost = (slice(None), slice(igy - 1, igy))
-
-            right_inner = (slice(None), slice(-igy - 1, -igy))
-            right_ghost = (slice(None), slice(-igy, -igy + 1))
-
-            rhou_wall = 0.0
-            # Lefts.rhou[left_ghost] = Rights.rhou[left_inner] = rhou_wall
-            Lefts.rhoY[left_ghost] = Rights.rhoY[left_inner] = Rights.rho[
-                left_inner
-            ] * ud.stratification(0.0)
-
-            Lefts.rho[left_ghost] = Rights.rho[left_inner]
-            Lefts.rhov[left_ghost] = Rights.rhov[left_inner]
-            Lefts.rhow[left_ghost] = Rights.rhow[left_inner]
-            Lefts.rhoX[left_ghost] = Rights.rhoX[left_inner]
-
-            Rights.rho[right_ghost] = Lefts.rho[right_inner]
-            Rights.rhou[right_ghost] = -1.0 * Lefts.rhou[right_inner]
-            Rights.rhov[right_ghost] = Lefts.rhov[right_inner]
-            Rights.rhow[right_ghost] = Lefts.rhow[right_inner]
-            Rights.rhoY[right_ghost] = Lefts.rhoY[right_inner]
-
-    else:
-        if ud.bdry_type[split_step] == opts.BdryType.WALL:
-            assert 0  # INCOMPLETE!!!
-            Lefts.rho[left_inner] = Rights.rho[:, igx - 2]
-            Lefts.rhou[left_inner] = -1.0 * Rights.rhou[:, igx - 2]
-            Lefts.rhov[left_inner] = Rights.rhov[:, igx - 2]
-            Lefts.rhow[left_inner] = Rights.rhow[:, igx - 2]
-            Lefts.rhoY[left_inner] = Rights.rhoY[:, igx - 2]
-
-            # print("#################### TRUE ########################")
-            Rights.rho[right_ghost] = Lefts.rho[:, -igx - 2]
-            Rights.rhou[right_ghost] = -1.0 * Lefts.rhou[:, -igx - 2]
-            Rights.rhov[right_ghost] = Lefts.rhov[:, -igx - 2]
-            Rights.rhow[right_ghost] = Lefts.rhow[:, -igx - 2]
-            Rights.rhoY[right_ghost] = Lefts.rhoY[:, -igx - 2]
-            # print(Rights.rhoY[right_ghost])
-
-
-def scale_wall_node_values(rhs, node, ud, factor=0.5):
-    """Scale values at wall boundary nodes by a given factor."""
-    ndim = node.ndim
-    igs = node.igs
-    
-    for dim in range(ndim):
-        # Check if this dimension has wall boundaries
-        is_wall = (
-            ud.bdry_type[dim] == opts.BdryType.WALL or 
-            ud.bdry_type[dim] == opts.BdryType.RAYLEIGH
-        )
-        
-        if is_wall:
-            # Create index for all dimensions
-            idx = [slice(igs[d], -igs[d]) for d in range(ndim)]
-            
-            # Scale first and last interior nodes in this dimension
-            for boundary_idx in [igs[dim], -igs[dim] - 1]:
-                idx[dim] = boundary_idx
-                rhs[tuple(idx)] *= factor
-                # rhs = rhs.at[tuple(idx)].multiply(factor)
-    
-    return rhs
\ No newline at end of file
diff --git a/src/pybella/flow_solver/physics/low_mach/__init__.py b/src/pybella/flow_solver/utils/boundary/__init__.py
similarity index 100%
rename from src/pybella/flow_solver/physics/low_mach/__init__.py
rename to src/pybella/flow_solver/utils/boundary/__init__.py
diff --git a/src/pybella/flow_solver/utils/boundary/cell_boundary.py b/src/pybella/flow_solver/utils/boundary/cell_boundary.py
new file mode 100644
index 00000000..3ca35c60
--- /dev/null
+++ b/src/pybella/flow_solver/utils/boundary/cell_boundary.py
@@ -0,0 +1,310 @@
+"""
+For more details on this module, refer to the write-up :ref:`boundary_handling`.
+"""
+
+import numpy as np
+from ....utils import options as opts
+from .common import get_ghost_padding
+
+
+class CellBoundaryHandler:
+    """Handles different types of boundary conditions for ghost cells."""
+
+    def __init__(self, mem, ud):
+        self.mem = mem
+        self.ud = ud
+        self.igs = mem.elem.igs
+        self.ndim = mem.elem.ndim
+
+    def apply_no_gravity_boundary(self, sol, current_step, ghost_padding, idx):
+        """Apply boundary conditions for axes without gravity."""
+        bdry_type = self.ud.bdry_type[current_step]
+
+        if bdry_type == opts.BdryType.PERIODIC:
+            _set_boundary(sol, ghost_padding, "wrap", idx)
+        elif bdry_type == opts.BdryType.WALL:
+            _set_boundary(sol, ghost_padding, "symmetric", idx)
+        elif bdry_type == opts.BdryType.RAYLEIGH:
+            raise AssertionError("Rayleigh boundary not defined on x-direction.")
+
+    def apply_gravity_boundary(self, sol, dim, ghost_padding, step):
+        """Apply boundary conditions for axes with gravity."""
+        gravity_axis = dim
+        g = self.ud.gravity_strength[gravity_axis]
+        direction = -1.0
+        offset = 0
+
+        for side in ghost_padding[gravity_axis]:
+            direction *= -1
+            self._process_ghost_cells_side(sol, side, dim, direction, offset, step, g)
+            offset += 1
+
+    def _process_ghost_cells_side(self, sol, side, dim, direction, offset, step, g):
+        """Process ghost cells for one side of the boundary."""
+        y_axs = self.ndim - 1 if step is not None else 1
+
+        for current_idx in np.arange(side)[::-1]:
+            indices = self._get_gravity_indices(current_idx, direction, offset, y_axs)
+            ghost_values = self._calculate_ghost_values(
+                sol, indices, direction, g, y_axs
+            )
+            self._assign_ghost_values(sol, indices["image"], ghost_values)
+
+    def _get_gravity_indices(self, current_idx, direction, offset, y_axs):
+        """Get the indices for last, source, and image cells."""
+        nlast, nsource, nimage = _get_gravity_padding(
+            self.ndim, current_idx, direction, offset, self.mem.elem, y_axs=y_axs
+        )
+        return {"last": nlast, "source": nsource, "image": nimage}
+
+    def _calculate_ghost_values(self, sol, indices, direction, g, y_axs):
+        """Calculate values for ghost cells with gravity."""
+        nlast, nsource, nimage = indices["last"], indices["source"], indices["image"]
+
+        # Calculate basic quantities
+        Y_last = sol.rhoY[nlast] / sol.rho[nlast]
+        Y_source = sol.rhoY[nsource] / sol.rho[nsource]
+
+        rhoYv_image = -sol.rhov[nsource] * sol.rhoY[nsource] / sol.rho[nsource]
+        S = 1.0 / self.ud.stratification(self.mem.elem.y[nimage[y_axs]])
+
+        # Calculate pressure difference
+        dpi = self._calculate_pressure_difference(
+            nlast, nimage, direction, g, Y_last, S, y_axs
+        )
+
+        # Calculate density and mass fraction
+        rho, rhoY = self._calculate_density_and_mass_fraction(
+            sol, nlast, nimage, dpi, S, y_axs
+        )
+        Y_image = rhoY / rho
+
+        # Calculate velocity components
+        velocities = self._calculate_velocities(
+            sol, nsource, rhoYv_image, rhoY, Y_source, Y_image, direction
+        )
+
+        return {
+            "rho": rho,
+            "rhoY": rhoY,
+            "u": sol.rhou[nsource] / sol.rho[nsource],
+            "v": velocities["v"],
+            "w": sol.rhow[nsource] / sol.rho[nsource],
+            "X": sol.rhoX[nsource] / sol.rho[nsource],
+            "Th_slc": velocities.get("Th_slc", 1.0),
+        }
+
+    def _calculate_pressure_difference(
+        self, nlast, nimage, direction, g, Y_last, S, y_axs
+    ):
+        """Calculate pressure difference for ghost cells."""
+        if hasattr(self.ud, "ATMOSPHERIC_EXTENSION"):
+            return (
+                self.mem.npf.HydroState.p20[nimage[y_axs]]
+                - self.mem.npf.HydroState.p20[nlast[y_axs]]
+            ) * self.ud.Msq
+        else:
+            return (
+                direction
+                * (self.mem.th.Gamma * g)
+                * 0.5
+                * self.mem.elem.dy
+                * (1.0 / Y_last + S)
+            )
+
+    def _calculate_density_and_mass_fraction(self, sol, nlast, nimage, dpi, S, y_axs):
+        """Calculate density and mass fraction for ghost cells."""
+        if self.ud.is_compressible == 1:
+            rhoY = ((sol.rhoY[nlast] ** self.mem.th.gm1) + dpi) ** self.mem.th.gm1inv
+        else:
+            rhoY = self.mem.npf.HydroState.rhoY0[nimage[y_axs]]
+
+        rho = rhoY * S
+        return rho, rhoY
+
+    def _calculate_velocities(
+        self, sol, nsource, rhoYv_image, rhoY, Y_source, Y_image, direction
+    ):
+        """Calculate velocity components for ghost cells."""
+        result = {}
+
+        if hasattr(self.ud, "ATMOSPHERIC_EXTENSION"):
+            if direction > 0:  # bottom boundary
+                result["v"] = (
+                    sol.rhov[nsource] * Y_source / sol.rho[nsource] * rhoY / Y_image
+                )
+            else:  # top boundary
+                result["v"] = sol.rhov[nsource] * Y_source
+            result["Th_slc"] = (
+                rhoY / (rhoY / Y_image) / (sol.rhoY[nsource] / sol.rho[nsource])
+            )
+        else:
+            result["v"] = rhoYv_image / rhoY
+            result["Th_slc"] = 1.0
+
+        return result
+
+    def _assign_ghost_values(self, sol, nimage, ghost_values):
+        """Assign calculated values to ghost cells."""
+        sol.rho[nimage] = ghost_values["rho"]
+        sol.rhou[nimage] = (
+            ghost_values["rho"] * ghost_values["u"] * ghost_values["Th_slc"]
+        )
+        sol.rhow[nimage] = (
+            ghost_values["rho"] * ghost_values["w"] * ghost_values["Th_slc"]
+        )
+        sol.rhoY[nimage] = ghost_values["rhoY"]
+        sol.rhoX[nimage] = ghost_values["rho"] * ghost_values["X"]
+
+        # Handle v-component differently for atmospheric extension
+        if hasattr(self.ud, "ATMOSPHERIC_EXTENSION"):
+            sol.rhov[nimage] = -ghost_values["v"] / (
+                ghost_values["rhoY"] / ghost_values["rho"]
+            )
+        else:
+            sol.rhov[nimage] = ghost_values["rho"] * ghost_values["v"]
+
+
+def set_ghost_cells(mem, ud, step=None, sol=None):
+    """
+    In-place update of the ghost cells in :class:`management.variable.Vars`
+    given the boundary conditions specified by :class:`inputs.user_data.UserDataInit`.
+
+    Parameters
+    ----------
+    mem : object
+        Memory container with sol, elem, th, and npf attributes
+    ud : :class:`inputs.user_data.UserDataInit`
+        Data container for the initial conditions
+    step : int, optional
+        Current step for advection directional Strang-splitting
+    sol : object, optional
+        Solution object, defaults to mem.sol
+    """
+    if sol is None:
+        sol = mem.sol
+
+    # this is inefficient but whatever for now.
+    handler = CellBoundaryHandler(mem, ud)
+    dims = _get_dimensions_to_process(handler.ndim, step)
+
+    for dim in dims:
+        current_step = step if step is not None else dim
+        ghost_padding, idx = get_ghost_padding(handler.ndim, dim, handler.igs)
+
+        if ud.gravity_strength[current_step] == 0.0:
+            handler.apply_no_gravity_boundary(sol, current_step, ghost_padding, idx)
+        else:
+            handler.apply_gravity_boundary(sol, dim, ghost_padding, step)
+
+
+def _get_dimensions_to_process(ndim, step):
+    """Determine which dimensions to process based on step parameter."""
+    if step is None:
+        return np.arange(ndim)
+    else:
+        return [ndim - 1]
+
+
+# Functional approach with helper functions
+def _pad_field(sol, field_name, idx, pads, mode):
+    """Helper function to pad a single field"""
+    if hasattr(sol, field_name):
+        field = getattr(sol, field_name)
+        if mode == "negative_symmetric":
+            field[...] = np.pad(field[idx], pads, _negative_symmetric)
+        else:
+            field[...] = np.pad(field[idx], pads, mode)
+
+
+def _set_boundary(sol, pads, btype, idx):
+    """
+    Functional approach to setting the boundary.
+    """
+
+    # Define field groupings for each boundary type
+    boundary_specs = {
+        "symmetric": [
+            (["rho", "rhou", "rhow", "rhoY", "rhoX"], "symmetric"),
+            (["rhov"], "negative_symmetric"),
+        ],
+        "constant": [
+            (["rho", "rhou", "rhow", "rhoY", "rhoX"], "symmetric"),
+            (["rhov"], "constant"),
+        ],
+        "wrap": [(["rho", "rhou", "rhov", "rhow", "rhoY", "rhoX"], "wrap")],
+    }
+
+    if btype not in boundary_specs:
+        raise ValueError(f"Unsupported boundary type: {btype}")
+
+    # Apply padding to each group of fields
+    for field_names, padding_mode in boundary_specs[btype]:
+        for field_name in field_names:
+            _pad_field(sol, field_name, idx, pads, padding_mode)
+
+
+def _negative_symmetric(vector, pad_width, iaxis, kwargs=None):
+    """
+    Taken from the reference:
+
+    Parameters
+    ----------
+    vector : ndarray
+        A rank 1 array already padded with zeros. Padded values are vector `[:iaxis_pad_width[0]] and vector[-iaxis_pad_width[1]:]`.
+    iaxis_pad_width : tuple
+        A 2-tuple of ints, `iaxis_pad_width[0]` represents the number of values padded at the beginning of vector where `iaxis_pad_width[1]` represents the number of values padded at the end of vector.
+    iaxis : int
+        The axis currently being calculated.
+    kwargs : dict
+        Any keyword arguments the function requires.
+
+    References
+    ----------
+    https://docs.scipy.org/doc/numpy/reference/generated/numpy.pad.html
+
+    """
+    if pad_width[1] > 0:
+        sign = -1
+        vector[: pad_width[0]] = sign * vector[pad_width[0] : 2 * pad_width[0]][::-1]
+        vector[-pad_width[1] :] = sign * vector[-2 * pad_width[1] : -pad_width[1]][::-1]
+        return vector
+    else:  # axis must have length > 0 for padding
+        return vector
+
+
+def _get_gravity_padding(ndim, cur_idx, direction, offset, elem, y_axs=None):
+    """
+    Parameters
+    ----------
+    ndim : int
+        Number of dimensions.
+    cur_idx : int
+        The current index of the ghost cell in the gravity direction to be updated.
+    direction : int
+        Top of the domain, `direction=+1`, bottom of the domain, `direction=-1`.
+    offset : int
+        `offset=0`, index starts counting from 0,1.... `offset=1`, index starts counting from -1,-2,..., i.e. end-selection of the array.
+    elem : :class:`discretization.kgrid.ElemSpaceDiscr`
+        Cell grid.
+    y_axs : int, optional
+        `Default == None`. Specifies the direction of the gravity axis. If `None`, then direction is the the y-axis.
+
+    """
+    cur_i = np.copy(cur_idx)
+    cur_idx += offset * ((elem.icy - 1) - 2 * cur_idx)
+    gravity_padding = [slice(None)] * ndim
+    if y_axs == None:
+        y_axs = 1
+
+    nlast = np.copy(gravity_padding)
+    nlast[y_axs] = int(cur_idx + direction)
+
+    nsource = np.copy(gravity_padding)
+    nsource[y_axs] = int(
+        offset * (elem.icy) + direction * (2 * elem.igy - (1 - offset) - cur_i)
+    )
+
+    nimage = np.copy(gravity_padding)
+    nimage[y_axs] = int(cur_idx)
+    return tuple(nlast), tuple(nsource), tuple(nimage)
diff --git a/src/pybella/flow_solver/utils/boundary/common.py b/src/pybella/flow_solver/utils/boundary/common.py
new file mode 100644
index 00000000..d8740f35
--- /dev/null
+++ b/src/pybella/flow_solver/utils/boundary/common.py
@@ -0,0 +1,63 @@
+import numpy as np
+
+from ....utils import options as opts
+
+
+def get_ghost_padding(ndim, dim, igs):
+    """
+    For a given direction, return the number of ghost cells to pad the current direction, and the index slice of the inner array without the ghost cells.
+
+    Parameters
+    ----------
+    ndim : int
+        Number of dimensions for the problem.
+    dim : int
+        Current dimension to update
+    igs : list
+        A list of number of ghost cells in all dimensions, e.g. `[2,2,2]` for 2 ghost cells in the x, y, and z directions.
+
+    Returns
+    -------
+    tuple
+        Number of ghost cells in the current dimension at both edges.
+    tuple
+        Index slice of the inner domain of the array.
+
+    """
+    ghost_padding = [(0, 0)] * ndim
+    ghost_padding[dim] = (igs[dim], igs[dim])
+
+    padded_idx = np.empty((ndim), dtype=object)
+    for idim in range(ndim):
+        padded_idx[idim] = slice(igs[idim], -igs[idim])
+    padded_idx[dim] = slice(None)
+
+    inner_domain = [slice(None)] * ndim
+    inner_domain[dim] = slice(igs[dim], -igs[dim])
+
+    return tuple(ghost_padding), tuple(inner_domain)
+
+
+def scale_wall_node_values(rhs, node, ud, factor=0.5):
+    """Scale values at wall boundary nodes by a given factor."""
+    ndim = node.ndim
+    igs = node.igs
+
+    for dim in range(ndim):
+        # Check if this dimension has wall boundaries
+        is_wall = (
+            ud.bdry_type[dim] == opts.BdryType.WALL
+            or ud.bdry_type[dim] == opts.BdryType.RAYLEIGH
+        )
+
+        if is_wall:
+            # Create index for all dimensions
+            idx = [slice(igs[d], -igs[d]) for d in range(ndim)]
+
+            # Scale first and last interior nodes in this dimension
+            for boundary_idx in [igs[dim], -igs[dim] - 1]:
+                idx[dim] = boundary_idx
+                rhs[tuple(idx)] *= factor
+                # rhs = rhs.at[tuple(idx)].multiply(factor)
+
+    return rhs
diff --git a/src/pybella/flow_solver/utils/boundary/node_boundary.py b/src/pybella/flow_solver/utils/boundary/node_boundary.py
new file mode 100644
index 00000000..f83a7288
--- /dev/null
+++ b/src/pybella/flow_solver/utils/boundary/node_boundary.py
@@ -0,0 +1,48 @@
+import numpy as np
+from ....utils import options as opts
+from .common import get_ghost_padding
+
+
+def set_ghost_nodes(p, node, ud, igs=None):
+    if igs is None:
+        igs = node.igs
+    for dim in range(node.ndim):
+        ghost_padding, idx = get_ghost_padding(node.ndim, dim, igs)
+
+        if ud.bdry_type[dim] == opts.BdryType.PERIODIC:
+            p[...] = np.pad(p[idx], ghost_padding, periodic_plus_one)
+        else:  # ud.bdry_type[dim] == opts.BdryType.WALL:
+            p[...] = np.pad(p[idx], ghost_padding, "reflect")
+
+    # if periodic_plus_one
+    if node.iicy == 2:  # implying horizontal slices
+        pn = p[:, 2, :]
+        pn = np.expand_dims(pn, axis=1)
+        p[...] = np.repeat(pn, node.icy, axis=1)
+
+
+def periodic_plus_one(vector, pad_width, iaxis, kwargs=None):
+    """
+    Taken from the reference:
+
+    Parameters
+    ----------
+    vector : ndarray
+        A rank 1 array already padded with zeros. Padded values are vector `[:iaxis_pad_width[0]] and vector[-iaxis_pad_width[1]:]`.
+    iaxis_pad_width : tuple
+        A 2-tuple of ints, `iaxis_pad_width[0]` represents the number of values padded at the beginning of vector where `iaxis_pad_width[1]` represents the number of values padded at the end of vector.
+    iaxis : int
+        The axis currently being calculated.
+    kwargs : dict
+        Any keyword arguments the function requires.
+    References
+    ----------
+    https://docs.scipy.org/doc/numpy/reference/generated/numpy.pad.html
+
+    """
+    if all(pad_width) > 0:
+        vector[: pad_width[0] + 1], vector[-pad_width[1] - 1 :] = (
+            vector[-pad_width[1] - pad_width[1] - 1 : -pad_width[1]],
+            vector[pad_width[0] : pad_width[0] + pad_width[0] + 1].copy(),
+        )
+    return vector
diff --git a/src/pybella/flow_solver/utils/boundary/rayleigh_boundary.py b/src/pybella/flow_solver/utils/boundary/rayleigh_boundary.py
new file mode 100644
index 00000000..3d18c5de
--- /dev/null
+++ b/src/pybella/flow_solver/utils/boundary/rayleigh_boundary.py
@@ -0,0 +1,191 @@
+import copy
+import numpy as np
+from ....utils import io
+from ....utils import options as opts
+from . import cell_boundary as bdry_c
+
+
+def get_tau_y(ud, elem, node, alpha):
+    tauc_y = np.zeros_like(elem.y)
+    taun_y = np.zeros_like(node.y)
+
+    ud.bny = node.y[-ud.inbcy - 3]
+
+    c1n = node.y <= ud.bny
+    ccn = (node.y[:-2] - ud.bny) / (node.y[:-2][-1] - ud.bny)
+    c2n = np.logical_and(ccn >= 0.0, ccn <= 0.5)
+    c3n = np.logical_and(ccn > 0.5, ccn <= 1.0)
+
+    taun_y[np.where(c1n)] = 0.0
+    taun_y[np.where(c2n)] = (
+        -alpha
+        / 2.0
+        * (
+            1.0
+            - np.cos((node.y[np.where(c2n)] - ud.bny) / (node.y[-1] - ud.bny) * np.pi)
+        )
+    )
+    taun_y[np.where(c3n)] = (
+        -alpha
+        / 2.0
+        * (
+            1.0
+            + ((node.y[np.where(c3n)] - ud.bny) / (node.y[-1] - ud.bny) - 0.5) * np.pi
+        )
+    )
+
+    taun_y[-2:] = -np.abs(taun_y).max()
+    tauc_y[...] = np.interp(elem.y, node.y, taun_y)
+
+    return tauc_y, taun_y
+
+
+def get_bottom_tau_y(ud, elem, node, alpha, cutoff=0.5):
+    tauc_y = np.zeros_like(elem.y)
+    taun_y = np.zeros_like(node.y)
+
+    assert ud.ymax > cutoff, "rayleigh forcing boundary below minimum domain extent"
+    idx = (np.abs(elem.y - (ud.ymax - cutoff))).argmin()
+
+    ud.forcing_bny = node.y[idx]
+
+    c1n = node.y <= ud.forcing_bny
+    ccn = (node.y[:-3] - ud.forcing_bny) / (node.y[:-3][-1] - ud.forcing_bny)
+    c2n = np.logical_and(ccn >= 0.0, ccn <= 0.5)
+    c3n = np.logical_and(ccn > 0.5, ccn <= 1.0)
+
+    taun_y[np.where(c1n)] = 0.0
+    taun_y[np.where(c2n)] = (
+        -alpha
+        / 2.0
+        * (
+            1.0
+            - np.cos(
+                (node.y[np.where(c2n)] - ud.forcing_bny)
+                / (node.y[-1] - ud.forcing_bny)
+                * np.pi
+            )
+        )
+    )
+    taun_y[np.where(c3n)] = (
+        -alpha
+        / 2.0
+        * (
+            1.0
+            + (
+                (node.y[np.where(c3n)] - ud.forcing_bny) / (node.y[-1] - ud.forcing_bny)
+                - 0.5
+            )
+            * np.pi
+        )
+    )
+
+    taun_y[-3:] = -np.abs(taun_y).max()
+    taun_y[...] = taun_y[::-1]
+    tauc_y = np.interp(elem.y, node.y, taun_y)
+
+    dd = 1.0
+    tauc_y = dd * tauc_y / np.abs(tauc_y).max()
+    taun_y = dd * taun_y / np.abs(taun_y).max()
+
+    return tauc_y, taun_y
+
+
+def apply_rayleigh_forcing(
+    mem,
+    ud,
+    dt,
+    half=True,
+    sol_half_new=None,
+    npf_half_new=None,
+):
+    """Apply Rayleigh forcing boundary condition (file or function based)."""
+    if not (hasattr(ud, "rayleigh_forcing") and ud.rayleigh_forcing):
+        return
+
+    t_offset = 0.5 * dt if half else dt
+
+    if ud.rayleigh_forcing_type == "file":
+        reader = io.read_input(ud.rayleigh_forcing_fn, ud.rayleigh_forcing_path)
+
+        if sol_half_new is None or npf_half_new is None:
+            sol_half_new = copy.deepcopy(mem.sol)
+            npf_half_new = copy.deepcopy(mem.npf)
+
+        time_tag = "%.3d_after_full_step" % mem.time.step
+        reader.get_data(sol_half_new, npf_half_new, time_tag, half=half)
+
+        up = sol_half_new.rhou / sol_half_new.rho
+        vp = sol_half_new.rhov / sol_half_new.rho
+        Yp = sol_half_new.rhoY / sol_half_new.rho - mem.npf.HydroState.Y0.reshape(1, -1)
+        pi = npf_half_new.p2_nodes
+
+        rayleigh_damping(mem.sol, mem.npf, ud, [up, vp, Yp, pi, mem.time.t + t_offset])
+
+    elif ud.rayleigh_forcing_type == "func":
+        s = 5.0e-3 + 1e-4 + 0e-5
+        ud.rf_bot.eigenfunction(mem.time.t + t_offset, s)
+        up, vp, Yp, pi = ud.rf_bot.dehatter(mem.th)
+
+        ud.rf_bot.eigenfunction(mem.time.t + t_offset, s, grid="n")
+        _, _, _, pi_n = ud.rf_bot.dehatter(mem.th, grid="n")
+
+        rayleigh_damping(
+            mem.sol, mem.npf, ud, [up, vp, Yp, pi_n, mem.time.t + t_offset]
+        )
+
+    bdry_c.set_ghost_cells(mem, ud)
+
+
+def rayleigh_damping(sol, npf, ud, forcing=None):
+    u = sol.rhou / sol.rho  # [elem.i2]
+    v = sol.rhov / sol.rho  # [elem.i2]
+    Y = sol.rhoY / sol.rho  # [elem.i2]
+    rho = sol.rho  # [elem.i2]
+
+    if ud.bdry_type[1] == opts.BdryType.RAYLEIGH:
+        tcy, tny = ud.tcy, ud.tny
+    else:
+        tcy, tny = 0.0, 0.0
+
+    if forcing is not None:
+        tcy_f, tny_f = ud.forcing_tcy, ud.forcing_tny
+        tcy, tny = 0.0, 0.0
+
+        u_f, v_f, Y_f, pi_f, t = forcing
+
+        if ud.rayleigh_forcing_type == "file":
+            G = np.sqrt(9.0 / 40.0)
+            N = np.sqrt(ud.Nsq_ref)
+            C = ud.Cs * ud.u_ref
+            Gam = N * G / C
+            Om = ud.coriolis_strength[2] / 2.0 / ud.t_ref
+            growth_rate = np.sqrt(Om * C * Gam)
+            mfac = np.exp(growth_rate * t * ud.t_ref)
+
+        else:
+            mfac = 1.0
+
+        npf.p2_nodes[...] += tny_f * (npf.p2_nodes) + np.abs(tny_f) * mfac * pi_f
+        c_f = 1.0
+
+    else:
+        u_f, v_f, Y_f = 0.0, 0.0, 0.0
+        c_f = 0.0
+        tcy_f, tny_f = 0.0, 0.0
+        mfac = 0.0
+
+    # assuming 2D vertical slice - not dimension agnostic
+    u += tcy * (u - ud.u_wind_speed) + c_f * (
+        tcy_f * (u - ud.u_wind_speed) + np.abs(tcy_f) * mfac * u_f
+    )
+    v += tcy * (v - ud.v_wind_speed) + c_f * (
+        tcy_f * (v - ud.v_wind_speed) + np.abs(tcy_f) * mfac * v_f
+    )
+
+    Ybar = npf.HydroState.Y0.reshape(1, -1)
+    Y += tcy * (Y - Ybar) + c_f * (tcy_f * (Y - Ybar) + np.abs(tcy_f) * mfac * Y_f)
+
+    sol.rhou[...] = rho * u
+    sol.rhov[...] = rho * v
+    sol.rhoY[...] = rho * Y
diff --git a/src/pybella/flow_solver/utils/cache.py b/src/pybella/flow_solver/utils/cache.py
new file mode 100644
index 00000000..b56a67ab
--- /dev/null
+++ b/src/pybella/flow_solver/utils/cache.py
@@ -0,0 +1,190 @@
+import numpy as np
+import logging
+
+from . import fields
+
+
+class Characters(object):
+    """
+    Data container for the slope and amplitude of the interpolation to the faces for the Riemann solver.
+
+    """
+
+    def __init__(self, size):
+        """
+        Parameters
+        ----------
+        size : tuple
+            Tuple containing the number of cells in the respective directions including ghost cells.
+
+        Attributes
+        ----------
+        u : ndarray(size)
+        v : ndarray(size)
+        w : ndarray(size)
+        Y : ndarray(size)
+        X : ndarray(size)
+        plus : ndarray(size)
+        minus : ndarray(size)
+        entro : ndarray(size)
+
+        """
+        self.u = np.zeros((size), dtype=np.float64)
+        self.v = np.zeros((size), dtype=np.float64)
+        self.w = np.zeros((size), dtype=np.float64)
+        self.X = np.zeros((size), dtype=np.float64)
+        self.Y = np.zeros((size), dtype=np.float64)
+
+        self.squeezer()
+
+    def squeezer(self):
+        """
+        Removes dimension of size 1. All arrays are initialised as 3D arrays, this function will remove the unnecessary dimensions.
+
+        """
+        for key, value in vars(self).items():
+            setattr(self, key, value.squeeze())
+
+
+class FlowSolverCache:
+    """Cache for flow solver specific computations."""
+
+    __slots__ = (
+        "_recovery_cache",
+        "_velocity_cache",
+        "_coriolis_cache",
+        "_flux_cache",
+    )
+
+    def __init__(self):
+        self._recovery_cache = {}
+        self._velocity_cache = {}
+        self._coriolis_cache = {}
+        self._flux_cache = {}
+
+    def get_recovery_objects(self, shape, ud):
+        """Get cached recovery objects or create new ones."""
+
+        cache_key = (tuple(shape), id(ud))
+        if cache_key not in self._recovery_cache:
+            logging.info("Cache: Creating new recovery objects with shape %s", shape)
+            self._recovery_cache[cache_key] = {
+                "Diffs": Characters(shape),
+                "Ampls": Characters(shape),
+                "Lefts": fields.CellSolField(shape),
+                "Rights": fields.CellSolField(shape),
+                "Slopes": Characters(shape),
+            }
+
+        cache_obj = self._recovery_cache[cache_key]
+
+        return cache_obj
+
+    def get_velocity_arrays(self, shape, dtype=np.float64):
+        """Get cached velocity arrays (U, V, W) or create new ones."""
+
+        cache_key = (tuple(shape), dtype)
+
+        if cache_key not in self._velocity_cache:
+            logging.info("Cache: Creating new velocity arrays with shape %s", shape)
+            self._velocity_cache[cache_key] = {
+                "U": np.zeros(shape, dtype=dtype),
+                "V": np.zeros(shape, dtype=dtype),
+                "W": np.zeros(shape, dtype=dtype),
+            }
+
+        cache_obj = self._velocity_cache[cache_key]
+
+        return cache_obj
+
+    def get_velocity_array_views(self, shape, dtype=np.float64):
+        """Get views of cached velocity arrays for in-place operations."""
+        cache_obj = self.get_velocity_arrays(shape, dtype)
+
+        return cache_obj["U"], cache_obj["V"], cache_obj["W"]
+
+    def get_coriolis_arrays(self, shape, dtype=np.float64):
+        """Get cached Coriolis arrays (h11, h12, h13, h21, h22, h23, h31, h32, h33) or create new ones."""
+
+        cache_key = (tuple(shape), dtype)
+
+        if cache_key not in self._coriolis_cache:
+            logging.info("Cache: Creating new Coriolis arrays with shape %s", shape)
+            self._coriolis_cache[cache_key] = {
+                "h11": np.zeros(shape, dtype=dtype),
+                "h12": np.zeros(shape, dtype=dtype),
+                "h13": np.zeros(shape, dtype=dtype),
+                "h21": np.zeros(shape, dtype=dtype),
+                "h22": np.zeros(shape, dtype=dtype),
+                "h23": np.zeros(shape, dtype=dtype),
+                "h31": np.zeros(shape, dtype=dtype),
+                "h32": np.zeros(shape, dtype=dtype),
+                "h33": np.zeros(shape, dtype=dtype),
+                "denom": np.zeros(shape, dtype=dtype),
+            }
+
+        cache_obj = self._coriolis_cache[cache_key]
+
+        return cache_obj
+
+    def get_coriolis_array_views(self, shape, dtype=np.float64):
+        """Get views of cached Coriolis arrays for in-place operations."""
+        cache_obj = self.get_coriolis_arrays(shape, dtype)
+
+        return (
+            cache_obj["h11"],
+            cache_obj["h12"],
+            cache_obj["h13"],
+            cache_obj["h21"],
+            cache_obj["h22"],
+            cache_obj["h23"],
+            cache_obj["h31"],
+            cache_obj["h32"],
+            cache_obj["h33"],
+            cache_obj["denom"],
+        )
+
+    def get_flux_containers(self, elem, dtype=np.float64):
+        """
+        Get cached flux containers for each direction (States objects).
+
+        Parameters
+        ----------
+        elem : Grid
+            Grid object with `ndim`, `sfx`, `sfy`, `sfz` attributes.
+        ud : UserDefinedSettings
+            Used for instantiating States; its ID is part of the cache key.
+
+        Returns
+        -------
+        List[States]
+            List of directional flux containers, one per spatial dimension.
+        """
+        ndim = elem.ndim
+        shape_key = (
+            tuple(elem.sfx),  # Use one representative shape
+            dtype,
+        )
+
+        if (ndim, shape_key) not in self._flux_cache:
+            logging.info(
+                "Cache: Creating new flux containers for ndim=%d, shape=%s",
+                ndim,
+                shape_key[0],
+            )
+            flux = [None] * ndim
+            flux[0] = fields.CellSolField(elem.sfx)
+            if ndim > 1:
+                flux[1] = fields.CellSolField(elem.sfy)
+            if ndim > 2:
+                flux[2] = fields.CellSolField(elem.sfz)
+            self._flux_cache[(ndim, shape_key)] = flux
+
+        return self._flux_cache[(ndim, shape_key)]
+
+    def clear_all(self):
+        """Clear all caches to free memory."""
+        self._recovery_cache.clear()
+        self._velocity_cache.clear()
+        self._coriolis_cache.clear()
+        self._flux_cache.clear()
diff --git a/src/pybella/flow_solver/utils/variable.py b/src/pybella/flow_solver/utils/fields.py
similarity index 58%
rename from src/pybella/flow_solver/utils/variable.py
rename to src/pybella/flow_solver/utils/fields.py
index 093dff1b..16a8fc8e 100644
--- a/src/pybella/flow_solver/utils/variable.py
+++ b/src/pybella/flow_solver/utils/fields.py
@@ -2,20 +2,19 @@
 import scipy as sp
 import logging
 
-class Vars(object):
+
+class CellSolField(object):
     """
     The data container for the solution state variables, i.e. `Sol`.
 
     """
 
-    def __init__(self, size, ud):
+    def __init__(self, size):
         """
         Parameters
         ----------
         size : tuple
             Tuple containing the number of cells in the respective directions including ghost cells, e.g. `(48,48,10)` has 48 cells in the x and y-directions, and 10 cells in the z-directions
-        ud : :class:`inputs.user_data.UserDataInit`
-            Data container for the initial conditions
 
         Attributes
         ----------
@@ -31,18 +30,21 @@ def __init__(self, size, ud):
         2. `rhoX` has to be extended by `ud.nspec` for moist process.
 
         """
+        # For eventual extension to support multiple species
+        nspec = 1
+
         self.rho = np.zeros((size))
         self.rhou = np.zeros((size))
         self.rhov = np.zeros((size))
         self.rhow = np.zeros((size))
         self.rhoY = np.zeros((size))
-        self.rhoX = np.zeros(([ud.nspec] + list(size)))
+        self.rhoX = np.zeros(([nspec] + list(size)))
 
         self.u = np.zeros((size))
         self.v = np.zeros((size))
         self.w = np.zeros((size))
         self.Y = np.zeros((size))
-        self.X = np.zeros(([ud.nspec] + list(size)))
+        self.X = np.zeros(([nspec] + list(size)))
         self.p = np.zeros((size))
 
         self.squeezer()
@@ -75,7 +77,7 @@ def primitives(self, th):
         p : ndarray(size_of_rhoY)
 
         """
-        with np.errstate(divide='ignore', invalid='ignore'):
+        with np.errstate(divide="ignore", invalid="ignore"):
             # Direct division without nonzero indexing
             # We know that when this method is called in recovery, we always have one column of zeroes in self.rho.
             self.u[...] = self.rhou / self.rho
@@ -83,7 +85,7 @@ def primitives(self, th):
             self.w[...] = self.rhow / self.rho
             self.Y[...] = self.rhoY / self.rho
             self.X[...] = self.rhoX / self.rho
-            self.p[...] = self.rhoY ** th.gamm
+            self.p[...] = self.rhoY**th.gamm
 
     def flip(self):
         """
@@ -115,13 +117,13 @@ def mod_bg_wind(self, ud, fac):
         self.rhow[...] = self.rhow + fac * w0 * self.rho
 
 
-class States(Vars):
+class States(CellSolField):
     """
     Data container for `Lefts` and `Rights` for the Riemann solver. Inherits the solution class :class:`management.variable.Vars`.
 
     """
 
-    def __init__(self, size, ud):
+    def __init__(self, size):
         """
         Parameters
         ----------
@@ -135,7 +137,6 @@ def __init__(self, size, ud):
         Many variables in this data container are no longer used and can be removed.
 
         """
-        super().__init__(size, ud)
 
         self.p0 = np.zeros((size))
         self.p20 = np.zeros((size))
@@ -157,133 +158,58 @@ def get_dSdy(self, elem, node):
         if not self.init_dSdy:
             logging.info("Computing dSdy")
             self.dSdy = sp.signal.convolve(self.S0, [1.0, -1.0], mode="valid") / node.dy
-            
+
             for dim in range(0, node.ndim, 2):
                 self.dSdy = np.expand_dims(self.dSdy, dim)
                 self.dSdy = np.repeat(self.dSdy, elem.sc[dim], axis=dim)
-            
+
             self.init_dSdy = True
-        
+
         return self.dSdy
 
     def get_S0c(self, elem):
         if not self.init_S0c:
             logging.info("Computing S0c")
             S0c_result = self.S0
-            
+
             for dim in range(0, elem.ndim, 2):
                 S0c_result = np.expand_dims(S0c_result, dim)
                 S0c_result = np.repeat(S0c_result, elem.sc[dim], axis=dim)
-            
+
             self.S0c = S0c_result
             self.init_S0c = True
-        
+
         return self.S0c
 
 
-class Characters(object):
-    """
-    Data container for the slope and amplitude of the interpolation to the faces for the Riemann solver.
+class NodePressureField(object):
+    def __init__(self, elem, node):
+        sc = elem.sc
+        sn = node.sc
 
-    """
+        self.p0 = 1.0
+        self.p00 = 1.0
 
-    def __init__(self, size):
-        """
-        Parameters
-        ----------
-        size : tuple
-            Tuple containing the number of cells in the respective directions including ghost cells.
+        self.p2_cells = np.zeros((sc))
+        self.dp2_cells = np.zeros((sc))
+        self.p2_nodes = np.zeros((sn))
+        self.p2_nodes0 = np.zeros((sn))
+        self.dp2_nodes = np.zeros((sn))
 
-        Attributes
-        ----------
-        u : ndarray(size)
-        v : ndarray(size)
-        w : ndarray(size)
-        Y : ndarray(size)
-        X : ndarray(size)
-        plus : ndarray(size)
-        minus : ndarray(size)
-        entro : ndarray(size)
+        self.u = np.zeros((sc))
+        self.v = np.zeros((sc))
+        self.w = np.zeros((sc))
 
-        """
-        self.u = np.zeros((size))
-        self.v = np.zeros((size))
-        self.w = np.zeros((size))
-        self.X = np.zeros((size))
-        self.Y = np.zeros((size))
+        self.rhs = np.zeros((node.isc))
+        self.wcenter = np.zeros((node.isc))
+        self.wplus = np.zeros(([elem.ndim] + list(sc)))
+
+        self.HydroState = States([sc[1]])
+        self.HydroState_n = States([sn[1]])
 
         self.squeezer()
 
     def squeezer(self):
-        """
-        Removes dimension of size 1. All arrays are initialised as 3D arrays, this function will remove the unnecessary dimensions.
-
-        """
         for key, value in vars(self).items():
-            setattr(self, key, value.squeeze())
-
-
-class FlowSolverCache:
-    """Cache for flow solver specific computations."""
-    
-    def __init__(self):
-        self._recovery_cache = {}
-        self._velocity_cache = {}
-    
-    def get_recovery_objects(self, shape, ud):
-        """Get cached recovery objects or create new ones."""
-        
-        cache_key = (tuple(shape), id(ud))
-        if cache_key not in self._recovery_cache:
-            logging.info("Cache: Creating new recovery objects with shape %s", shape)
-            self._recovery_cache[cache_key] = {
-                'Diffs': Characters(shape),
-                'Ampls': Characters(shape),
-                'Lefts': States(shape, ud),
-                'Rights': States(shape, ud),
-                'Slopes': Characters(shape),   
-            }
-        
-        # Reset objects if they have reset methods
-        cache_obj = self._recovery_cache[cache_key]
-        # for obj in cache_obj.values():
-        #     if hasattr(obj, 'zero'):
-        #         obj.zero()
-        
-        return cache_obj
-    
-    def get_velocity_arrays(self, shape, dtype=np.float64):
-        """Get cached velocity arrays (U, V, W) or create new ones."""
-        
-        cache_key = (tuple(shape), dtype)
-        
-        if cache_key not in self._velocity_cache:
-            logging.info("Cache: Creating new velocity arrays with shape %s", shape)
-            self._velocity_cache[cache_key] = {
-                'U': np.zeros(shape, dtype=dtype),
-                'V': np.zeros(shape, dtype=dtype),
-                'W': np.zeros(shape, dtype=dtype)
-            }
-        
-        # Clear arrays for reuse
-        cache_obj = self._velocity_cache[cache_key]
-        # for arr in cache_obj.values():
-        #     arr.fill(0.0)
-        
-        return cache_obj
-    
-    def get_velocity_array_views(self, shape, dtype=np.float64):
-        """Get views of cached velocity arrays for in-place operations."""
-        cache_obj = self.get_velocity_arrays(shape, dtype)
-        
-        return cache_obj['U'], cache_obj['V'], cache_obj['W']
-    
-    def clear_velocity_cache(self):
-        """Clear velocity cache to free memory."""
-        self._velocity_cache.clear()
-    
-    def clear_all(self):
-        """Clear all caches to free memory."""
-        self._recovery_cache.clear()
-        self._velocity_cache.clear()
-
+            if type(value) == np.ndarray:
+                setattr(self, key, value.squeeze())
diff --git a/src/pybella/flow_solver/utils/prepare.py b/src/pybella/flow_solver/utils/prepare.py
index 9178de84..3ab6f920 100644
--- a/src/pybella/flow_solver/utils/prepare.py
+++ b/src/pybella/flow_solver/utils/prepare.py
@@ -1,13 +1,11 @@
 import numpy as np
 
 from ...utils import user_data, io, data_structures
-
-from ..discretisation import grid as dis_grid
-from . import variable as var
-from . import boundary as bdry
 from ..physics import hydrostatics
-from ..physics.low_mach import mpv as lm_var
-from ..physics.gas_dynamics import thermodynamics as gd_thermodynamics
+from ..physics import thermodynamics as gd_thermodynamics
+from ..discretisation import grid as dis_grid
+from . import fields, cache
+from .boundary import cell_boundary as bdry_c
 
 # test module
 from ...tests import diagnostics as diag
@@ -41,25 +39,13 @@ def initialise():
 
     elem, node = dis_grid.grid_init(ud)
 
-    sol = var.Vars(elem.sc, ud)
-
-    # Move these to the FlowSolverCache
-    flux = np.empty((3), dtype=object)
-    flux[0] = var.States(elem.sfx, ud)
-    if elem.ndim > 1:
-        flux[1] = var.States(elem.sfy, ud)
-    if elem.ndim > 2:
-        flux[2] = var.States(elem.sfz, ud)
+    sol = fields.CellSolField(elem.sc)
 
     th = gd_thermodynamics.ThermodynamicalQuantities(ud)
-    mpv = lm_var.MPV(elem, node, ud)
+    npf = fields.NodePressureField(elem, node)
 
     io.init_logger(ud)
 
-    # handle radiative BC
-    if ud.bdry_type[1].value == "radiation":
-        ud.tcy, ud.tny = bdry.get_tau_y(ud, elem, node, 0.5)
-
     ##########################################################
     # Initialise test module
     ##########################################################
@@ -72,33 +58,20 @@ def initialise():
     # Populate data structures
     ##########################################################
 
-    # member_state = data_structures.MemberState(
-    #     elem=elem,
-    #     node=node,
-    #     Sol=Sol,
-    #     flux=flux,
-    #     mpv=mpv,
-    #     th=th,
-    # )
-
     ensemble_state = data_structures.EnsembleState()
 
-    sol = sol_init(sol, mpv, elem, node, th, ud)
+    sol = sol_init(sol, npf, elem, node, th, ud)
 
     # Initialise cache and add to simulation state
-    flow_cache = var.FlowSolverCache()
-
+    flow_cache = cache.FlowSolverCache()
 
     ensemble_state.update_member(
-        elem=elem,
-        node=node,
-        sol=sol,
-        flux=flux,
-        mpv=mpv,
-        th=th,
-        cache=flow_cache
+        elem=elem, node=node, sol=sol, npf=npf, th=th, cache=flow_cache
     )
 
+    for member in ensemble_state.members:
+        bdry_c.set_ghost_cells(member, ud)
+
     restart_params = data_structures.RestartParameters(
         ud_rewrite=ud_rewrite,
         dap_rewrite=dap_rewrite,
@@ -118,8 +91,6 @@ def initialise():
         interface_params=interface_params,
     )
 
-
-
     return sim_st
 
 
@@ -127,20 +98,20 @@ def overwrite_init_with_restart(sst):
     es = sst.ensemble_state
     rp = sst.restart_params
 
-    hydrostatics.state(es.mpv, es.elem, es.node, es.th, es.ud)
+    hydrostatics.state(es.npf, es.elem, es.node, es.th, es.ud)
     sst.ud.old_suffix = np.copy(sst.ud.output_suffix)
     sst.ud.old_suffix = "_ensemble=%i%s" % (sst.N, sst.ud.old_suffix)
-    Sol0, mpv0, touts = io.sim_restart(
+    Sol0, npf0, touts = io.sim_restart(
         rp.r_params[0],
         rp.r_params[1],
         es.elem,
         es.node,
         es.ud,
         es.Sol,
-        es.mpv,
+        es.npf,
         rp.r_params[2],
     )
-    sol_ens = [[Sol0, es.flux, mpv0, [-np.inf, sst.step]]]
+    sol_ens = [[Sol0, es.flux, npf0, [-np.inf, sst.step]]]
     # ud.tout = touts[1:]
     sst.ud.tout = [touts[-1]]
     sst.t = touts[0]
diff --git a/src/pybella/flow_solver/utils/solver_diagnostics.py b/src/pybella/flow_solver/utils/solver_diagnostics.py
index 22983dcd..889545e7 100644
--- a/src/pybella/flow_solver/utils/solver_diagnostics.py
+++ b/src/pybella/flow_solver/utils/solver_diagnostics.py
@@ -3,7 +3,7 @@
 
 
 def get_p_from_pressure_related_fields(mem, ud, psinc=False):
-    p2n = mem.mpv.p2_nodes
+    p2n = mem.npf.p2_nodes
     rhoY = mem.sol.rhoY
     dp2n = (p2n - p2n.mean()) * ud.Msq
 
diff --git a/src/pybella/inputs/rising_bubble.py b/src/pybella/inputs/rising_bubble.py
index 30e86cec..a23903e1 100644
--- a/src/pybella/inputs/rising_bubble.py
+++ b/src/pybella/inputs/rising_bubble.py
@@ -1,6 +1,5 @@
 import numpy as np
 from ..flow_solver.physics import hydrostatics
-from ..flow_solver.utils import boundary as bdry
 
 
 class UserData(object):
@@ -38,7 +37,7 @@ def __init__(self):
         # self.output_suffix += '_w=%i-%i' %(self.blending_weight*16.0,16.0-(self.blending_weight*16.0))
 
 
-def sol_init(Sol, mpv, elem, node, th, ud, seed=None):
+def sol_init(Sol, npf, elem, node, th, ud, seed=None):
     u0 = ud.u_wind_speed
     v0 = ud.v_wind_speed
     w0 = ud.w_wind_speed
@@ -50,7 +49,7 @@ def sol_init(Sol, mpv, elem, node, th, ud, seed=None):
     g = ud.gravity_strength[1]
     # print(ud.rho_ref)
 
-    hydrostatics.state(mpv, elem, node, th, ud)
+    hydrostatics.state(npf, elem, node, th, ud)
 
     x = elem.x
     y = elem.y
@@ -71,8 +70,8 @@ def sol_init(Sol, mpv, elem, node, th, ud, seed=None):
 
     r = np.sqrt((x) ** 2 + (y - y0) ** 2) / r0
 
-    p = np.repeat(mpv.HydroState.p0.reshape(1, -1), elem.icx, axis=0)
-    rhoY = np.repeat(mpv.HydroState.rhoY0.reshape(1, -1), elem.icx, axis=0)
+    p = np.repeat(npf.HydroState.p0.reshape(1, -1), elem.icx, axis=0)
+    rhoY = np.repeat(npf.HydroState.rhoY0.reshape(1, -1), elem.icx, axis=0)
 
     perturbation = (delth / 300.0) * (np.cos(0.5 * np.pi * r) ** 2)
     perturbation[np.where(r > 1.0)] = 0.0
@@ -89,10 +88,8 @@ def sol_init(Sol, mpv, elem, node, th, ud, seed=None):
     Sol.rhow[x_idx, y_idx] = rho * w
     Sol.rhoY[x_idx, y_idx] = rhoY
 
-    p = mpv.HydroState_n.p0[0]
-    rhoY = mpv.HydroState_n.rhoY0[0]
-    mpv.p2_nodes[...] = (p - mpv.HydroState_n.p0[0]) / rhoY / ud.Msq
-
-    bdry.set_explicit_boundary_data(Sol, elem, ud, th, mpv)
+    p = npf.HydroState_n.p0[0]
+    rhoY = npf.HydroState_n.rhoY0[0]
+    npf.p2_nodes[...] = (p - npf.HydroState_n.p0[0]) / rhoY / ud.Msq
 
     return Sol
diff --git a/src/pybella/interfaces/dynamics_blending/schemes.py b/src/pybella/interfaces/dynamics_blending/schemes.py
index 4904372c..3c907cf8 100644
--- a/src/pybella/interfaces/dynamics_blending/schemes.py
+++ b/src/pybella/interfaces/dynamics_blending/schemes.py
@@ -4,7 +4,7 @@
 import numpy as np
 from scipy import signal
 
-from ...flow_solver.physics.gas_dynamics import eos as gd_eos
+from ...flow_solver.physics import eos as gd_eos
 from ...utils import io
 
 
@@ -55,8 +55,8 @@ def update_sol(self, mem, ud, sgn, label=None, writer=None):
         if writer != None:
             writer.write_all(mem, str(label) + "_before_blending")
 
-        Sol = mem.sol
-        mpv = mem.mpv
+        sol = mem.sol
+        npf = mem.npf
         th = mem.th
 
         if sgn == "bef":
@@ -66,8 +66,8 @@ def update_sol(self, mem, ud, sgn, label=None, writer=None):
         else:
             assert 0, "sgn == bef or sgn == aft"
 
-        rho = np.copy(Sol.rho)
-        rhoY = np.copy(Sol.rhoY)
+        rho = np.copy(sol.rho)
+        rhoY = np.copy(sol.rhoY)
 
         Y = rhoY / rho
 
@@ -76,32 +76,32 @@ def update_sol(self, mem, ud, sgn, label=None, writer=None):
         elif ud.blending_mean == "1.0":
             rhoYc = (1.0 + sign * self.fac * self.dp2c) ** (th.gm1inv)
 
-        alpha = rhoYc / Sol.rhoY
+        alpha = rhoYc / sol.rhoY
 
         if ud.blending_conv == "rho":
             ### keep theta, convert rho
-            Sol.rho[...] = rho * alpha
-            Sol.rhoY[...] = Sol.rho * Y
+            sol.rho[...] = rho * alpha
+            sol.rhoY[...] = sol.rho * Y
 
-            rho_fac = Sol.rho / rho
-            Sol.rhou[...] *= rho_fac
-            Sol.rhov[...] *= rho_fac
-            Sol.rhow[...] *= rho_fac
-            Sol.rhoX[...] *= rho_fac
+            rho_fac = sol.rho / rho
+            sol.rhou[...] *= rho_fac
+            sol.rhov[...] *= rho_fac
+            sol.rhow[...] *= rho_fac
+            sol.rhoX[...] *= rho_fac
 
         elif ud.blending_conv == "theta":
             ### keep rho, convert theta
             Yc = Y * alpha
-            Sol.rhoY[...] = rho * Yc
-            Sol.rhoX[...] = rho * (1.0 / Yc - mpv.HydroState.S0.reshape(1, -1))
+            sol.rhoY[...] = rho * Yc
+            sol.rhoX[...] = rho * (1.0 / Yc - npf.HydroState.S0.reshape(1, -1))
         else:
             assert 0, "ud.blending_conv undefined."
 
         if writer != None:
             writer.write_all(mem, str(label) + "_after_blending")
 
-    def update_p2n(self, mpv):
-        mpv.p2_nodes = self.dp2n
+    def update_p2n(self, npf):
+        npf.p2_nodes = self.dp2n
 
 
 ######################################################
@@ -111,10 +111,10 @@ def update_p2n(self, mpv):
 
 def do_comp_to_psinc_conv(mem, bld, ud, label, writer):
     logging.info("Converting COMP to PSINC")
-    dp2n = mem.mpv.p2_nodes
+    dp2n = mem.npf.p2_nodes
     bld.convert_p2n(dp2n)
     bld.update_sol(mem, ud, "bef", label=label, writer=writer)
-    bld.update_p2n(mem.mpv)
+    bld.update_p2n(mem.npf)
 
     return mem
 
@@ -131,8 +131,8 @@ def do_psinc_to_comp_conv(
     from ...flow_solver.discretisation import time_update
 
     logging.info(f"Blending... step = {step}")
-    Sol_freeze = copy.deepcopy(mem.sol)
-    mpv_freeze = copy.deepcopy(mem.mpv)
+    sol_freeze = copy.deepcopy(mem.sol)
+    npf_freeze = copy.deepcopy(mem.npf)
 
     ret = time_update.do(
         mem,
@@ -145,8 +145,8 @@ def do_psinc_to_comp_conv(
 
     fac_old = ud.blending_weight
     fac_new = 1.0 - fac_old
-    dp2n_0 = fac_new * ret.mpv.p2_nodes_half + fac_old * mpv_freeze.p2_nodes_half
-    dp2n_1 = fac_new * ret.mpv.p2_nodes + fac_old * mpv_freeze.p2_nodes
+    dp2n_0 = fac_new * ret.npf.p2_nodes_half + fac_old * npf_freeze.p2_nodes_half
+    dp2n_1 = fac_new * ret.npf.p2_nodes + fac_old * npf_freeze.p2_nodes
 
     if ud.blending_type == "half":
         dp2n = dp2n_0
@@ -157,12 +157,12 @@ def do_psinc_to_comp_conv(
 
     if writer != None:
         writer.populate(
-            str(label) + "_after_full_step", "p2_start", mpv_freeze.p2_nodes
+            str(label) + "_after_full_step", "p2_start", npf_freeze.p2_nodes
         )
     if writer != None:
-        writer.populate(str(label) + "_after_full_step", "p2_end", ret.mpv.p2_nodes)
-    mem.Sol = Sol_freeze
-    mem.mpv = mpv_freeze
+        writer.populate(str(label) + "_after_full_step", "p2_end", ret.npf.p2_nodes)
+    mem.sol = sol_freeze
+    mem.npf = npf_freeze
 
     # elem, node, _, _, _, th, _ = mem
 
@@ -171,7 +171,7 @@ def do_psinc_to_comp_conv(
     logging.info("Converting PSINC to COMP")
     bld.convert_p2n(dp2n)
     bld.update_sol(mem, ud, "aft", label=label, writer=writer)
-    bld.update_p2n(mem.mpv)
+    bld.update_p2n(mem.npf)
 
     # mem.time.step -= 1
     # mem.time.window_step -= 1
@@ -184,16 +184,16 @@ def do_psinc_to_comp_conv(
 ######################################################
 
 
-def do_swe_to_lake_conv(Sol, mpv, elem, node, ud, th, writer, label, debug):
+def do_swe_to_lake_conv(sol, npf, elem, node, ud, th, writer, label, debug):
     logging.info("swe to lake conversion...")
 
-    H1 = Sol.rho[
+    H1 = sol.rho[
         :,
         2:-2:,
     ][:, 0, :]
     # setattr(ud,'mean_val',H1.mean())
 
-    H10 = mpv.p2_nodes[:, 2:-2, :].mean(axis=1)
+    H10 = npf.p2_nodes[:, 2:-2, :].mean(axis=1)
     H10 -= H10.mean()
 
     # define 2D kernel
@@ -209,34 +209,34 @@ def do_swe_to_lake_conv(Sol, mpv, elem, node, ud, th, writer, label, debug):
     H1 = np.repeat(H1, elem.icy, axis=1)
     setattr(ud, "mean_val", H1)
 
-    Sol.rhou[...] = Sol.rhou / Sol.rho * ud.mean_val
-    Sol.rhov[...] = Sol.rhov / Sol.rho * ud.mean_val
-    Sol.rhow[...] = Sol.rhow / Sol.rho * ud.mean_val
-    Sol.rhoY[...] = Sol.rhoY / Sol.rho * ud.mean_val
-    Sol.rho[...] = ud.mean_val
+    sol.rhou[...] = sol.rhou / sol.rho * ud.mean_val
+    sol.rhov[...] = sol.rhov / sol.rho * ud.mean_val
+    sol.rhow[...] = sol.rhow / sol.rho * ud.mean_val
+    sol.rhoY[...] = sol.rhoY / sol.rho * ud.mean_val
+    sol.rho[...] = ud.mean_val
 
-    # boundary.set_ghostnodes_p2(mpv.p2_nodes,node,ud)
+    # boundary.set_ghostnodes_p2(npf.p2_nodes,node,ud)
 
     if debug == True:
-        writer.write_all(Sol, mpv, elem, node, th, str(label) + "_after_swe_to_lake")
+        writer.write_all(sol, npf, elem, node, th, str(label) + "_after_swe_to_lake")
 
 
 def do_lake_to_swe_conv(
-    Sol, flux, mpv, elem, node, ud, th, writer, label, debug, step, window_step, t, dt
+    sol, flux, npf, elem, node, ud, th, writer, label, debug, step, window_step, t, dt
 ):
     from ...flow_solver.discretisation import time_update
 
     if debug == True:
-        writer.write_all(Sol, mpv, elem, node, th, str(label) + "_after_lake_time_step")
+        writer.write_all(sol, npf, elem, node, th, str(label) + "_after_lake_time_step")
 
-    Sol_freeze = copy.deepcopy(Sol)
-    mpv_freeze = copy.deepcopy(mpv)
+    sol_freeze = copy.deepcopy(sol)
+    npf_freeze = copy.deepcopy(npf)
 
     logging.info("doing lake-to-swe time-update...")
     ret = time_update.time_update(
-        Sol,
+        sol,
         flux,
-        mpv,
+        npf,
         t,
         t + dt,
         ud,
@@ -252,8 +252,8 @@ def do_lake_to_swe_conv(
     fac_old = ud.blending_weight
     fac_new = 1.0 - fac_old
 
-    dp2n_0 = fac_new * ret[2].p2_nodes_half + fac_old * mpv_freeze.p2_nodes_half
-    dp2n_1 = fac_new * ret[2].p2_nodes + fac_old * mpv_freeze.p2_nodes
+    dp2n_0 = fac_new * ret[2].p2_nodes_half + fac_old * npf_freeze.p2_nodes_half
+    dp2n_1 = fac_new * ret[2].p2_nodes + fac_old * npf_freeze.p2_nodes
 
     if ud.blending_type == "half":
         dp2n = dp2n_0
@@ -262,12 +262,12 @@ def do_lake_to_swe_conv(
     else:
         assert 0, "incorrect ud.blending_type"
 
-    Sol = copy.deepcopy(Sol_freeze)
-    mpv = copy.deepcopy(mpv_freeze)
+    sol = copy.deepcopy(sol_freeze)
+    npf = copy.deepcopy(npf_freeze)
 
-    mpv.p2_nodes[...] = dp2n
+    npf.p2_nodes[...] = dp2n
 
-    H10 = mpv.p2_nodes[:, 2:-2, :].mean(axis=1)
+    H10 = npf.p2_nodes[:, 2:-2, :].mean(axis=1)
     logging.info("lake to swe conversion...")
     H10 -= H10.mean()
 
@@ -285,70 +285,70 @@ def do_lake_to_swe_conv(
     H1 = np.repeat(H1, elem.icy, axis=1)
     H1 = ud.mean_val + ud.Msq * H1
 
-    Sol.rho[...] = H1
-    Sol.rhou[...] = Sol.rhou / ud.mean_val * Sol.rho
-    Sol.rhov[...] = Sol.rhov / ud.mean_val * Sol.rho
-    Sol.rhow[...] = Sol.rhow / ud.mean_val * Sol.rho
-    Sol.rhoY[...] = Sol.rhoY / ud.mean_val * Sol.rho
+    sol.rho[...] = H1
+    sol.rhou[...] = sol.rhou / ud.mean_val * sol.rho
+    sol.rhov[...] = sol.rhov / ud.mean_val * sol.rho
+    sol.rhow[...] = sol.rhow / ud.mean_val * sol.rho
+    sol.rhoY[...] = sol.rhoY / ud.mean_val * sol.rho
 
     if debug == True:
-        writer.write_all(Sol, mpv, elem, node, th, str(label) + "_after_lake_to_swe")
-    return Sol, mpv
+        writer.write_all(sol, npf, elem, node, th, str(label) + "_after_lake_to_swe")
+    return sol, npf
 
 
 ######################################################
 # Nonhydrostatic - Hydrostatic blending
 ######################################################
 def do_nonhydro_to_hydro_conv(
-    Sol, flux, mpv, bld, elem, node, th, ud, label, writer, step, window_step, t, dt
+    sol, flux, npf, bld, elem, node, th, ud, label, writer, step, window_step, t, dt
 ):
     logging.info("nonhydrostatic to hydrostatic conversion...")
-    # bld.convert_p2n(mpv.p2_nodes)
-    # bld.update_Sol(Sol,elem,node,th,ud,mpv,'bef',label=label,writer=writer)
-    # Sol.rhov = Sol.rhov_half
+    # bld.convert_p2n(npf.p2_nodes)
+    # bld.update_sol(sol,elem,node,th,ud,npf,'bef',label=label,writer=writer)
+    # sol.rhov = sol.rhov_half
 
-    # Sol_tmp = deepcopy(Sol)
+    # sol_tmp = deepcopy(sol)
     # flux_tmp = deepcopy(flux)
-    # mpv_tmp = deepcopy(mpv)
+    # npf_tmp = deepcopy(npf)
 
     # nonhydro to hydro blending incomplete.
-    # ret = data.time_update(Sol,flux,mpv, t, t+1*dt, ud, elem, node, [0,0], th, bld=None, writer=None, debug=False)
+    # ret = data.time_update(sol,flux,npf, t, t+1*dt, ud, elem, node, [0,0], th, bld=None, writer=None, debug=False)
 
-    # Sol = Sol_tmp
+    # sol = sol_tmp
     # flux = flux_tmp
-    # mpv = mpv_tmp
-    # Sol = ret[0]
+    # npf = npf_tmp
+    # sol = ret[0]
     # flux = ret[1]
-    # mpv = ret[2]
-    # Sol = deepcopy(ret[0])
-    # mpv = deepcopy(ret[2])
-    # Sol.rhov[...] = Sol.rhov_half
+    # npf = ret[2]
+    # sol = deepcopy(ret[0])
+    # npf = deepcopy(ret[2])
+    # sol.rhov[...] = sol.rhov_half
     # t += 0.5*dt
     # t += 1*dt
-    return Sol, mpv, t
+    return sol, npf, t
 
 
 def do_hydro_to_nonhydro_conv(
-    Sol, flux, mpv, bld, elem, node, th, ud, label, writer, step, window_step, t, dt
+    sol, flux, npf, bld, elem, node, th, ud, label, writer, step, window_step, t, dt
 ):
     logging.info("hydrostatic to nonhydrostatic conversion...")
     logging.info(f"Blending... step = {step}")
 
-    # Sol_tmp = deepcopy(Sol)
+    # sol_tmp = deepcopy(sol)
     # flux_tmp = deepcopy(flux)
-    # mpv_tmp = deepcopy(mpv)
+    # npf_tmp = deepcopy(npf)
 
-    # ret = data.time_update(Sol,flux,mpv, t, t+dt, ud, elem, node, [0,step-1], th, bld=None, writer=None, debug=False)
+    # ret = data.time_update(sol,flux,npf, t, t+dt, ud, elem, node, [0,step-1], th, bld=None, writer=None, debug=False)
 
-    # Sol = Sol_tmp
+    # sol = sol_tmp
     # flux = flux_tmp
-    # mpv = mpv_tmp
+    # npf = npf_tmp
 
     # retv_half = ret[0].rhov_half / ret[0].rho_half
     # retv_full = ret[0].rhov / ret[0].rho
 
-    # solv_half = Sol.rhov_half / Sol.rho_half
-    # solv_full = Sol.rhov / Sol.rho
+    # solv_half = sol.rhov_half / sol.rho_half
+    # solv_full = sol.rhov / sol.rho
 
     # fac_full = 0.5
     # fac_half = 1.0 - fac_full
@@ -369,19 +369,19 @@ def do_hydro_to_nonhydro_conv(
     # if writer != None: writer.populate(str(label)+'_after_full_step', 'ret_half', ret[0].rhov_half)
     # if writer != None: writer.populate(str(label)+'_after_full_step', 'ret_full', ret[0].rhov)
 
-    # if writer != None: writer.populate(str(label)+'_after_full_step', 'solv_half', Sol.rhov_half)
-    # if writer != None: writer.populate(str(label)+'_after_full_step', 'solv_full', Sol.rhov)
+    # if writer != None: writer.populate(str(label)+'_after_full_step', 'solv_half', sol.rhov_half)
+    # if writer != None: writer.populate(str(label)+'_after_full_step', 'solv_full', sol.rhov)
 
-    # Sol.rhov = Sol.rho * (fac_full * solv_full + fac_half * retv_half)
+    # sol.rhov = sol.rho * (fac_full * solv_full + fac_half * retv_half)
     # if writer != None: writer.populate(str(label)+'_after_full_step', 'p2_end', ret[2].p2_nodes)
 
-    # fac_mpv_half = 0.5
-    # fac_mpv_full = 1.0 - fac_mpv_half
-    # mpv.p2_nodes = fac_mpv_half * mpv.p2_nodes + fac_mpv_full * ret[2].p2_nodes
+    # fac_npf_half = 0.5
+    # fac_npf_full = 1.0 - fac_npf_half
+    # npf.p2_nodes = fac_npf_half * npf.p2_nodes + fac_npf_full * ret[2].p2_nodes
     # dp2n = ret[2].p2_nodes_half
     # bld.convert_p2n(dp2n)
-    # bld.update_Sol(Sol,elem,node,th,ud,mpv,'aft',label=label,writer=writer)
-    # bld.update_p2n(Sol,mpv,node,th,ud)
+    # bld.update_sol(sol,elem,node,th,ud,npf,'aft',label=label,writer=writer)
+    # bld.update_p2n(sol,npf,node,th,ud)
     #
 
     ###############################
@@ -394,23 +394,23 @@ def do_hydro_to_nonhydro_conv(
     #     )
 
     # writer.write_all(mem, str(label) + "_half_full")
-    # writer.populate(str(label) + "_ic", "pwchi", Sol.pwchi)
+    # writer.populate(str(label) + "_ic", "pwchi", sol.pwchi)
 
     # if test_hydrob == False:
-    #     Sol = copy.deepcopy(Sol_half_old)
-    #     # mpv = copy.deepcopy(mpv_half_old)
+    #     sol = copy.deepcopy(sol_half_old)
+    #     # npf = copy.deepcopy(npf_half_old)
 
     #     logging.info(termcolor.colored("test_hydrob == False", "red"))
     #     writer.write_all(mem, str(label) + "_quarter")
 
-    #     writer.populate(str(label) + "_quarter", "pwchi", Sol.pwchi)
+    #     writer.populate(str(label) + "_quarter", "pwchi", sol.pwchi)
 
     #     logging.info("quarter dt = %.8f" % (dt * 0.5))
 
     #     ret = do(
-    #         Sol_half_old,
+    #         sol_half_old,
     #         flux_half_old,
-    #         mpv_half_old,
+    #         npf_half_old,
     #         dt - 0.5 * dt,
     #         dt + 0.5 * dt,
     #         ud,
@@ -423,26 +423,26 @@ def do_hydro_to_nonhydro_conv(
     #         debug=False,
     #     )
 
-    #     Sol_tu = copy.deepcopy(ret[0])
-    #     # mpv_tu = copy.deepcopy(ret[2])
-    #     Sol.rho[...] = Sol_tu.rho_half
-    #     Sol.rhou[...] = Sol_tu.rhou_half
-    #     Sol.rhov[...] = Sol_tu.rhov_half
-    #     Sol.rhow[...] = Sol_tu.rhow_half
-    #     Sol.rhoX[...] = Sol_tu.rhoX_half
-    #     Sol.rhoY[...] = Sol_tu.rhoY_half
-    #     Sol.pwchi[...] = Sol_tu.pwchi
+    #     sol_tu = copy.deepcopy(ret[0])
+    #     # npf_tu = copy.deepcopy(ret[2])
+    #     sol.rho[...] = sol_tu.rho_half
+    #     sol.rhou[...] = sol_tu.rhou_half
+    #     sol.rhov[...] = sol_tu.rhov_half
+    #     sol.rhow[...] = sol_tu.rhow_half
+    #     sol.rhoX[...] = sol_tu.rhoX_half
+    #     sol.rhoY[...] = sol_tu.rhoY_half
+    #     sol.pwchi[...] = sol_tu.pwchi
 
-    #     # mpv.p2_nodes[...] = mpv_tu.p2_nodes_half
+    #     # npf.p2_nodes[...] = npf_tu.p2_nodes_half
 
     #     writer.write_all(mem, str(label) + "_half")
 
-    #     writer.populate(str(label) + "_half", "pwchi", Sol.pwchi)
+    #     writer.populate(str(label) + "_half", "pwchi", sol.pwchi)
 
     #     ret = do(
-    #         Sol,
+    #         sol,
     #         flux,
-    #         mpv,
+    #         npf,
     #         dt,
     #         2.0 * dt,
     #         ud,
@@ -455,25 +455,25 @@ def do_hydro_to_nonhydro_conv(
     #         debug=False,
     #     )
 
-    #     Sol = copy.deepcopy(ret[0])
+    #     sol = copy.deepcopy(ret[0])
     #     flux = copy.deepcopy(ret[1])
-    #     mpv = copy.deepcopy(ret[2])
+    #     npf = copy.deepcopy(ret[2])
 
     # if test_hydrob == True:
-    #     Sol = copy.deepcopy(Sol_half_old)
-    #     # mpv = copy.deepcopy(mpv_half_old)
+    #     sol = copy.deepcopy(sol_half_old)
+    #     # npf = copy.deepcopy(npf_half_old)
 
     #     logging.info(termcolor.colored("test_hydrob == False", "red"))
     #     writer.write_all(mem, str(label) + "_quarter")
 
-    #     # writer.populate(str(label)+'_quarter', 'pwchi', Sol.pwchi)
+    #     # writer.populate(str(label)+'_quarter', 'pwchi', sol.pwchi)
 
     #     logging.info("quarter dt = %.8f" % (dt * 0.5))
 
     #     ret = do(
-    #         Sol_half_old,
+    #         sol_half_old,
     #         flux_half_old,
-    #         mpv_half_old,
+    #         npf_half_old,
     #         dt - 0.5 * dt,
     #         dt + 0.5 * dt,
     #         ud,
@@ -486,26 +486,26 @@ def do_hydro_to_nonhydro_conv(
     #         debug=False,
     #     )
 
-    #     Sol_tu = copy.deepcopy(ret[0])
-    #     # mpv_tu = copy.deepcopy(ret[2])
-    #     Sol.rho[...] = Sol_tu.rho_half
-    #     Sol.rhou[...] = Sol_tu.rhou_half
-    #     Sol.rhov[...] = Sol_tu.rhov_half
-    #     Sol.rhow[...] = Sol_tu.rhow_half
-    #     Sol.rhoX[...] = Sol_tu.rhoX_half
-    #     Sol.rhoY[...] = Sol_tu.rhoY_half
-    #     Sol.pwchi[...] = Sol_tu.pwchi
+    #     sol_tu = copy.deepcopy(ret[0])
+    #     # npf_tu = copy.deepcopy(ret[2])
+    #     sol.rho[...] = sol_tu.rho_half
+    #     sol.rhou[...] = sol_tu.rhou_half
+    #     sol.rhov[...] = sol_tu.rhov_half
+    #     sol.rhow[...] = sol_tu.rhow_half
+    #     sol.rhoX[...] = sol_tu.rhoX_half
+    #     sol.rhoY[...] = sol_tu.rhoY_half
+    #     sol.pwchi[...] = sol_tu.pwchi
 
-    #     # mpv.p2_nodes[...] = mpv_tu.p2_nodes_half
+    #     # npf.p2_nodes[...] = npf_tu.p2_nodes_half
 
-    #     # writer.write_all(Sol,mpv,elem,node,th,str(label)+'_half')
+    #     # writer.write_all(sol,npf,elem,node,th,str(label)+'_half')
 
-    #     # writer.populate(str(label)+'_half', 'pwchi', Sol.pwchi)
+    #     # writer.populate(str(label)+'_half', 'pwchi', sol.pwchi)
 
     #     ret = do(
-    #         Sol,
+    #         sol,
     #         flux,
-    #         mpv,
+    #         npf,
     #         dt,
     #         2.0 * dt,
     #         ud,
@@ -518,11 +518,11 @@ def do_hydro_to_nonhydro_conv(
     #         debug=False,
     #     )
 
-    #     Sol = copy.deepcopy(ret[0])
+    #     sol = copy.deepcopy(ret[0])
     #     flux = copy.deepcopy(ret[1])
-    #     mpv = copy.deepcopy(ret[2])
-    #     # writer.write_all(Sol,mpv,elem,node,th,str(label)+'_half')
-    #     # writer.populate(str(label)+'_half', 'pwchi', Sol.pwchi)
+    #     npf = copy.deepcopy(ret[2])
+    #     # writer.write_all(sol,npf,elem,node,th,str(label)+'_half')
+    #     # writer.populate(str(label)+'_half', 'pwchi', sol.pwchi)
 
     #     logging.info(termcolor.colored("test_hydrob == True", "red"))
 
@@ -531,7 +531,7 @@ def do_hydro_to_nonhydro_conv(
     # if c2:
     # ud.is_nonhydrostatic = 1
 
-    return Sol, mpv
+    return sol, npf
 
 
 ######################################################
@@ -554,7 +554,7 @@ def blending_before_timestep(
     # Blending : Do full regime to limit regime conversion
     ######################################################
     # do unpacking
-    elem, node, Sol, flux, mpv, th, _, _ = mem
+    elem, node, sol, npf, th, _, _ = mem
 
     # these make sure that we are the correct window step
     if bld is not None and window_step == 0:
@@ -562,7 +562,7 @@ def blending_before_timestep(
         if (bld.bb or bld.cb) and ud.blending_conv is not None:
             # these distinguish between SWE and Euler blending
             if ud.blending_conv == "swe":
-                do_swe_to_lake_conv(Sol, mpv, elem, node, ud, th, writer, label, debug)
+                do_swe_to_lake_conv(sol, npf, elem, node, ud, th, writer, label, debug)
                 swe_to_lake = True
             else:
                 mem = do_comp_to_psinc_conv(mem, bld, ud, label, writer)
@@ -605,10 +605,10 @@ def blending_before_timestep(
                 ud.compressibility = 0.0
                 mem = do_comp_to_psinc_conv(mem, bld, ud, label, writer)
             elif bld.hydro_init > 0:
-                Sol, mpv, t = do_nonhydro_to_hydro_conv(
-                    Sol,
+                sol, npf, t = do_nonhydro_to_hydro_conv(
+                    sol,
                     flux,
-                    mpv,
+                    npf,
                     bld,
                     elem,
                     node,
@@ -624,7 +624,7 @@ def blending_before_timestep(
                 ud.is_nonhydrostatic = 0
                 ud.nonhydrostasy = 0.0
         else:
-            do_swe_to_lake_conv(Sol, mpv, elem, node, ud, th, writer, label, debug)
+            do_swe_to_lake_conv(sol, npf, elem, node, ud, th, writer, label, debug)
             swe_to_lake = True
             ud.is_compressible = 0
             ud.compressibility = 0.0
@@ -652,10 +652,10 @@ def blending_before_timestep(
         ud.initial_blending == True and step == ud.no_of_hy_initial and bld is not None
     ):
         if ud.blending_conv != "swe":
-            Sol, mpv = do_hydro_to_nonhydro_conv(
-                Sol,
+            sol, npf = do_hydro_to_nonhydro_conv(
+                sol,
                 flux,
-                mpv,
+                npf,
                 bld,
                 elem,
                 node,
@@ -676,13 +676,12 @@ def blending_before_timestep(
         ud.is_nonhydrostatic = gd_eos.is_nonhydrostatic(ud, window_step)
         ud.nonhydrostasy = gd_eos.nonhydrostasy(ud, t, window_step)
 
-    return swe_to_lake, Sol, mpv, t
+    return swe_to_lake, sol, npf, t
 
 
 def blending_after_timestep(
-    Sol,
-    flux,
-    mpv,
+    sol,
+    npf,
     bld,
     elem,
     node,
@@ -716,10 +715,10 @@ def blending_after_timestep(
     ):
         tmp_CFL = np.copy(ud.CFL)
         ud.CFL = 0.8
-        Sol, mpv = do_lake_to_swe_conv(
-            Sol,
+        sol, npf = do_lake_to_swe_conv(
+            sol,
             flux,
-            mpv,
+            npf,
             elem,
             node,
             ud,
@@ -736,7 +735,7 @@ def blending_after_timestep(
         ud.is_compressible = 1
         ud.compressibility = 1.0
 
-    return Sol, mpv
+    return sol, npf
 
 
 def prepare_blending(
@@ -756,7 +755,7 @@ def prepare_blending(
     if check_and_apply_initial_hydrostatic_conversion(step, ud, bld):
         ud.is_nonhydrostatic = 0
 
-    swe_to_lake, Sol, mpv, t = blending_before_timestep(
+    swe_to_lake, sol, npf, t = blending_before_timestep(
         mem,
         ud,
         bld,
@@ -770,7 +769,7 @@ def prepare_blending(
         debug,
     )
 
-    return swe_to_lake, Sol, mpv, t
+    return swe_to_lake, sol, npf, t
 
 
 def check_and_apply_initial_hydrostatic_conversion(step, ud, bld):
diff --git a/src/pybella/tests/diagnostics.py b/src/pybella/tests/diagnostics.py
index e7ab3c3a..16d91e67 100644
--- a/src/pybella/tests/diagnostics.py
+++ b/src/pybella/tests/diagnostics.py
@@ -28,10 +28,17 @@ def update_targets(self):
             dump_name = tp.name.replace("target", "test")
             self.arr_dump[dump_name] = {}
 
+            rho = self.__get_ens(
+                tc, tp, "rho", time_increment=self.time_increment, summed=False
+            )
+
             for attribute in tp.attributes:
                 arr = self.__get_ens(
                     tc, tp, attribute, time_increment=self.time_increment, summed=False
                 )
+
+                if attribute != "p2_nodes" and attribute != "rho":
+                    arr = arr / rho
                 self.arr_dump[dump_name][attribute] = float(arr.sum())
 
                 if self.plot:
@@ -79,7 +86,7 @@ def test_do(self, mem, ud):
                             time_increment=self.time_increment,
                             summed=False,
                         )
-                        setattr(mem.mpv, attribute, data)
+                        setattr(mem.npf, attribute, data)
                         ref_data = self.__get_ens(
                             tc,
                             tp,
@@ -87,7 +94,7 @@ def test_do(self, mem, ud):
                             time_increment=self.time_increment,
                             summed=False,
                         )
-                    setattr(ref_mem.mpv, attribute, ref_data)
+                    setattr(ref_mem.npf, attribute, ref_data)
             except Exception as e:
                 raise AssertionError(
                     f"test {self.current_run} has no target for comparison: {e}"
@@ -182,7 +189,7 @@ def __plot_comparison(self, mem, ref_mem, ud):
     @staticmethod
     def __get_sol_for_comparison(mem, ud, attribute):
         Sol = mem.sol
-        mpv = mem.mpv
+        npf = mem.npf
         if attribute != "p2_nodes":
             test_sol = np.copy(getattr(Sol, attribute).T)
             if attribute != "rho":
@@ -190,11 +197,11 @@ def __get_sol_for_comparison(mem, ud, attribute):
                 test_sol /= rho
 
                 # if attribute == 'rhoY':
-                #     test_sol -= mpv.HydroState.Y0[:,np.newaxis]
+                #     test_sol -= npf.HydroState.Y0[:,np.newaxis]
 
         else:
-            # test_sol = mpv.p2_nodes.T * ud.Msq
-            # test_sol -= mpv.HydroState_n.pi0[:,np.newaxis]
+            # test_sol = npf.p2_nodes.T * ud.Msq
+            # test_sol -= npf.HydroState_n.pi0[:,np.newaxis]
             test_sol = get_p_from_pressure_related_fields(mem, ud).T
             # pass
 
diff --git a/src/pybella/tests/test_blending_warm_bubble.py b/src/pybella/tests/test_blending_warm_bubble.py
index 104da5c9..697f75ea 100644
--- a/src/pybella/tests/test_blending_warm_bubble.py
+++ b/src/pybella/tests/test_blending_warm_bubble.py
@@ -1,6 +1,5 @@
 import numpy as np
 from ..flow_solver.physics import hydrostatics
-from ..flow_solver.utils import boundary as bdry
 
 from ..utils.data_structures import DiagnosticState
 
@@ -71,7 +70,7 @@ def __init__(self):
         self.autogen_fn = False
 
 
-def sol_init(Sol, mpv, elem, node, th, ud, seed=None):
+def sol_init(Sol, npf, elem, node, th, ud, seed=None):
     u0 = ud.u_wind_speed
     v0 = ud.v_wind_speed
     w0 = ud.w_wind_speed
@@ -80,7 +79,7 @@ def sol_init(Sol, mpv, elem, node, th, ud, seed=None):
     y0 = 0.2
     r0 = 0.2
 
-    hydrostatics.integrated_state(mpv, elem, node, th, ud)
+    hydrostatics.integrated_state(npf, elem, node, th, ud)
 
     x = elem.x
     y = elem.y
@@ -89,8 +88,8 @@ def sol_init(Sol, mpv, elem, node, th, ud, seed=None):
 
     r = np.sqrt((x) ** 2 + (y - y0) ** 2) / r0
 
-    p = np.repeat(mpv.HydroState.p0.reshape(1, -1), elem.icx, axis=0)
-    rhoY = mpv.HydroState.rhoY0[np.newaxis, :]
+    p = np.repeat(npf.HydroState.p0.reshape(1, -1), elem.icx, axis=0)
+    rhoY = npf.HydroState.rhoY0[np.newaxis, :]
 
     perturbation = (delth / 300.0) * (np.cos(0.5 * np.pi * r) ** 2)
     perturbation[np.where(r > 1.0)] = 0.0
@@ -107,10 +106,8 @@ def sol_init(Sol, mpv, elem, node, th, ud, seed=None):
     Sol.rhow[x_idx, y_idx] = rho * w
     Sol.rhoY[x_idx, y_idx] = rhoY
 
-    p = mpv.HydroState_n.p0
-    rhoY = mpv.HydroState_n.rhoY0
-    mpv.p2_nodes[...] = (p - mpv.HydroState_n.p0) / rhoY / ud.Msq
-
-    bdry.set_explicit_boundary_data(Sol, elem, ud, th, mpv)
+    p = npf.HydroState_n.p0
+    rhoY = npf.HydroState_n.rhoY0
+    npf.p2_nodes[...] = (p - npf.HydroState_n.p0) / rhoY / ud.Msq
 
     return Sol
diff --git a/src/pybella/tests/test_internal_long_wave.py b/src/pybella/tests/test_internal_long_wave.py
index 5510d348..29d8322d 100644
--- a/src/pybella/tests/test_internal_long_wave.py
+++ b/src/pybella/tests/test_internal_long_wave.py
@@ -2,7 +2,7 @@
 
 from ..utils import options as opts
 
-from ..flow_solver.utils import boundary as bdry, variable as var
+from ..flow_solver.utils import fields
 from ..flow_solver.physics import hydrostatics
 
 from ..utils.data_structures import DiagnosticState
@@ -126,7 +126,7 @@ def rhoe_method(rho, u, v, w, p, ud, th):
         return p * gm1inv + 0.5 * Msq * rho * (u * u + v * v + w * w)
 
 
-def sol_init(Sol, mpv, elem, node, th, ud, seeds=None):
+def sol_init(Sol, npf, elem, node, th, ud, seeds=None):
     u0 = ud.u_wind_speed
     v0 = ud.v_wind_speed
     w0 = ud.w_wind_speed
@@ -135,10 +135,10 @@ def sol_init(Sol, mpv, elem, node, th, ud, seeds=None):
     xc = 0.0
     a = ud.scale_factor * 5.0e3 / ud.h_ref
 
-    hydrostatics.analytical_state(mpv, elem, node, th, ud)
+    hydrostatics.analytical_state(npf, elem, node, th, ud)
 
-    HySt = var.States(node.sc, ud)
-    HyStn = var.States(node.sc, ud)
+    HySt = fields.States(node.sc)
+    HyStn = fields.States(node.sc)
 
     x = elem.x.reshape(-1, 1)
     y = elem.y.reshape(1, -1)
@@ -167,8 +167,8 @@ def sol_init(Sol, mpv, elem, node, th, ud, seeds=None):
         p = HySt.p0[:, y_idx][c_idx]
         rhoY = HySt.rhoY0[:, y_idx][c_idx]
     else:
-        p = mpv.HydroState.p0[y_idx]
-        rhoY = mpv.HydroState.rhoY0[y_idx]
+        p = npf.HydroState.p0[y_idx]
+        rhoY = npf.HydroState.rhoY0[y_idx]
 
     rho = rhoY / Y[:, y_idx]
     Sol.rho[x_idx, y_idx] = rho
@@ -177,23 +177,21 @@ def sol_init(Sol, mpv, elem, node, th, ud, seeds=None):
     Sol.rhow[x_idx, y_idx] = rho * w
     Sol.rhoY[x_idx, y_idx] = rhoY
 
-    mpv.p2_cells[x_idx, y_idx] = HySt.p20[x_idx, y_idx][c_idx]
+    npf.p2_cells[x_idx, y_idx] = HySt.p20[x_idx, y_idx][c_idx]
 
     Sol.rhoX[x_idx, y_idx] = Sol.rho[x_idx, y_idx] * (
-        1.0 / Y[:, y_idx] - mpv.HydroState.S0[y_idx]
+        1.0 / Y[:, y_idx] - npf.HydroState.S0[y_idx]
     )
 
-    mpv.p2_nodes[:, elem.igy : -elem.igy] = HyStn.p20[:, elem.igy : -elem.igy]
+    npf.p2_nodes[:, elem.igy : -elem.igy] = HyStn.p20[:, elem.igy : -elem.igy]
 
-    hydrostatics.initial_pressure(Sol, mpv, elem, node, ud, th)
+    hydrostatics.initial_pressure(Sol, npf, elem, node, ud, th)
 
     ud.nonhydrostasy = 1.0 if ud.is_nonhydrostatic == 1 else 0.0
     ud.compressibility = 1.0 if ud.is_compressible == 1 else 0.0
 
     if "imbal" in ud.aux:
-        mpv.p2_nodes[...] = 0.0
-
-    bdry.set_explicit_boundary_data(Sol, elem, ud, th, mpv)
+        npf.p2_nodes[...] = 0.0
 
     return Sol
 
diff --git a/src/pybella/tests/test_lamb_wave.py b/src/pybella/tests/test_lamb_wave.py
index d474213d..f8c7eea2 100644
--- a/src/pybella/tests/test_lamb_wave.py
+++ b/src/pybella/tests/test_lamb_wave.py
@@ -1,13 +1,11 @@
 import numpy as np
 
 from ..utils import options as opts
+from ..utils.data_structures import DiagnosticState
 
-from ..flow_solver.utils import boundary as bdry
-
+from ..flow_solver.utils.boundary import rayleigh_boundary as bdry_r
 from ..flow_solver.physics import hydrostatics
 
-from ..utils.data_structures import DiagnosticState
-
 
 class UserData(object):
 
@@ -75,8 +73,6 @@ def __init__(self):
         self.max_iterations = 10000
 
         self.tout = [360.0]
-        # self.tout = np.arange(0,361,1.0)
-        # self.tout = np.append(self.tout, [720.0])
         self.stepmax = 301
         self.output_timesteps = True
 
@@ -229,13 +225,13 @@ def dehatter(self, th, grid="c"):
             return up.T, vp.T, Yp.T, pi_p.T
 
 
-def sol_init(Sol, mpv, elem, node, th, ud, seeds=None):
+def sol_init(Sol, npf, elem, node, th, ud, seeds=None):
     if hasattr(ud, "rayleigh_bdry_switch"):
         if ud.rayleigh_bdry_switch:
             ud.bdry_type[1] = opts.BdryType.RAYLEIGH
 
     if ud.bdry_type[1] == opts.BdryType.RAYLEIGH:
-        ud.tcy, ud.tny = bdry.get_tau_y(ud, elem, node, 0.5)
+        ud.tcy, ud.tny = bdry_r.get_tau_y(ud, elem, node, 0.5)
 
     A0 = 1.0e-1 / ud.u_ref
     Msq = ud.Msq
@@ -258,13 +254,13 @@ def sol_init(Sol, mpv, elem, node, th, ud, seeds=None):
     ud.stratification = ud.stratification(dy)
 
     # Use hydrostatically balanced background
-    hydrostatics.analytical_state(mpv, elem, node, th, ud)
-    rhobar = mpv.HydroState.rho0.reshape(1, -1)
-    Ybar = mpv.HydroState.Y0.reshape(1, -1)
-    pibar = mpv.HydroState.p20.reshape(1, -1) * ud.Msq
+    hydrostatics.analytical_state(npf, elem, node, th, ud)
+    rhobar = npf.HydroState.rho0.reshape(1, -1)
+    Ybar = npf.HydroState.Y0.reshape(1, -1)
+    pibar = npf.HydroState.p20.reshape(1, -1) * ud.Msq
 
-    rhobar_n = mpv.HydroState_n.rho0.reshape(1, -1)
-    Ybar_n = mpv.HydroState_n.Y0.reshape(1, -1)
+    rhobar_n = npf.HydroState_n.rho0.reshape(1, -1)
+    Ybar_n = npf.HydroState_n.Y0.reshape(1, -1)
 
     ##################################################
     # dimensionless Brunt-Väisälä frequency
@@ -305,16 +301,14 @@ def sol_init(Sol, mpv, elem, node, th, ud, seeds=None):
     Sol.rhow[...] = rho * w
     Sol.rhoY[...] = rho * Y
     Sol.rhoX[...] = 0.0
-    mpv.p2_cells[...] = pi_p
+    npf.p2_cells[...] = pi_p
 
     ###################################################
     # initialise nodal pi
     ud.rf_bot.eigenfunction(0, 1, grid="n")
     _, _, _, pi_n = ud.rf_bot.dehatter(th, grid="n")
 
-    mpv.p2_nodes[...] = pi_n
-
-    bdry.set_explicit_boundary_data(Sol, elem, ud, th, mpv)
+    npf.p2_nodes[...] = pi_n
 
     if hasattr(ud, "mixed_run"):
         if ud.mixed_run:
diff --git a/src/pybella/tests/test_travelling_vortex.py b/src/pybella/tests/test_travelling_vortex.py
index 08b86ebb..a8513384 100644
--- a/src/pybella/tests/test_travelling_vortex.py
+++ b/src/pybella/tests/test_travelling_vortex.py
@@ -1,10 +1,11 @@
 import numpy as np
 
 from ..utils import options as opts
-from ..flow_solver.utils import boundary as bdry
+from ..flow_solver.utils.boundary import node_boundary as bdry_n
 from ..flow_solver.physics import hydrostatics
-from ..flow_solver.physics.low_mach import second_projection as lm_sp
-from ..flow_solver.utils import variable as var
+from ..flow_solver.numerics import implicit_euler
+from ..flow_solver.utils import cache
+
 
 from ..utils.data_structures import DiagnosticState
 
@@ -93,7 +94,7 @@ def rhoe_function(self, rho, u, v, w, p, ud, th):
         return p * gm1inv + 0.5 * Msq * rho * (u**2 + v**2 + w**2)
 
 
-def sol_init(Sol, mpv, elem, node, th, ud, seed=None):
+def sol_init(Sol, npf, elem, node, th, ud, seed=None):
     u0 = ud.u_wind_speed
     v0 = ud.v_wind_speed
     w0 = 0.0
@@ -133,7 +134,7 @@ def sol_init(Sol, mpv, elem, node, th, ud, seed=None):
     igxn = node.igx
     igyn = node.igy
 
-    hydrostatics.integrated_state(mpv, elem, node, th, ud)
+    hydrostatics.integrated_state(npf, elem, node, th, ud)
 
     coe = np.zeros((25))
     coe[0] = 1.0 / 24.0
@@ -194,8 +195,8 @@ def sol_init(Sol, mpv, elem, node, th, ud, seed=None):
     u = u0 + uth * (-(ys - yccs) / r)
     v = v0 + uth * (+(xs - xccs) / r)
     w = w0
-    p_hydro = mpv.HydroState.p0[igy:-igy]
-    rhoY = mpv.HydroState.rhoY0[igy:-igy]
+    p_hydro = npf.HydroState.p0[igy:-igy]
+    rhoY = npf.HydroState.rhoY0[igy:-igy]
 
     rho = np.zeros_like(r)
     rho[...] += (rho0 + del_rho * (1.0 - (r / R0) ** 2) ** 6) * (r < R0)
@@ -243,12 +244,10 @@ def sol_init(Sol, mpv, elem, node, th, ud, seed=None):
         # Sol.rhoe[:,igy:-igy] = ud.rhoe(rho,u,v,w,p_hydro,ud,th)
         Sol.rhoY[:, igy:-igy] = rhoY
 
-    mpv.p2_cells[:, igy:-igy] = (
-        th.Gamma * fac**2 * np.divide(p2c, mpv.HydroState.rhoY0[igy:-igy])
+    npf.p2_cells[:, igy:-igy] = (
+        th.Gamma * fac**2 * np.divide(p2c, npf.HydroState.rhoY0[igy:-igy])
     )
 
-    bdry.set_ghostcells_p2(mpv.p2_cells, elem, ud)
-
     xs = node.x[igxn:-igxn].reshape(-1, 1)
     ys = node.y[igyn:-igyn].reshape(1, -1)
     xccs = np.zeros_like(xs)
@@ -263,32 +262,30 @@ def sol_init(Sol, mpv, elem, node, th, ud, seed=None):
     r = np.sqrt((xs - xccs) ** 2 + (ys - yccs) ** 2)
 
     for ip in range(25):
-        mpv.p2_nodes[igxn:-igxn, igyn:-igyn] += (
+        npf.p2_nodes[igxn:-igxn, igyn:-igyn] += (
             alpha * coe[ip] * ((r / R0) ** (12 + ip) - 1.0) * rotdir**2
         )
     for ip in range(13):
-        mpv.p2_nodes[igxn:-igxn, igyn:-igyn] += (
+        npf.p2_nodes[igxn:-igxn, igyn:-igyn] += (
             alpha_const * const_coe[ip] * ((r / R0) ** (12 + ip) - 1.0) * rotdir**2
         )
 
-    mpv.p2_nodes[igxn:-igxn, igyn:-igyn] *= r / R0 < 1.0
+    npf.p2_nodes[igxn:-igxn, igyn:-igyn] *= r / R0 < 1.0
 
-    mpv.p2_nodes[igxn:-igxn, igyn:-igyn] = (
+    npf.p2_nodes[igxn:-igxn, igyn:-igyn] = (
         th.Gamma
         * fac**2
         * np.divide(
-            mpv.p2_nodes[igxn:-igxn, igyn:-igyn], mpv.HydroState.rhoY0[igyn : -igyn + 1]
+            npf.p2_nodes[igxn:-igxn, igyn:-igyn], npf.HydroState.rhoY0[igyn : -igyn + 1]
         )
     )
 
     ud.nonhydrostasy = float(ud.is_nonhydrostatic)
     ud.compressibility = float(ud.is_compressible)
 
-    bdry.set_explicit_boundary_data(Sol, elem, ud, th, mpv)
-
     if "imbal" in ud.aux:
         Sol.rhoY[...] = 1.0
-        mpv.p2_nodes[...] = 0.0
+        npf.p2_nodes[...] = 0.0
 
     if ud.initial_projection == True:
         is_compressible = np.copy(ud.is_compressible)
@@ -296,28 +293,28 @@ def sol_init(Sol, mpv, elem, node, th, ud, seed=None):
         ud.is_compressible = 0
         ud.compressibility = 0.0
 
-        p2aux = np.copy(mpv.p2_nodes)
+        p2aux = np.copy(npf.p2_nodes)
 
         Sol.rhou -= u0 * Sol.rho
         Sol.rhov -= v0 * Sol.rho
 
         mem = obj()
         mem.sol = Sol
-        mem.mpv = mpv
+        mem.npf = npf
         mem.elem = elem
         mem.node = node
         mem.th = th
         mem.time = obj()
         mem.time.t = ud.dtfixed
         mem.time.step = 0
-        mem.cache = var.FlowSolverCache()
+        mem.cache = cache.FlowSolverCache()
 
-        lm_sp.euler_backward_non_advective_impl_part(
-            Sol, mpv, elem, node, ud, th, 0.0, ud.dtfixed, mem
+        implicit_euler.do_implicit_part(
+            mem, ud, ud.dtfixed, writer=None, label="initial_projection"
         )
 
-        mpv.p2_nodes[...] = p2aux
-        mpv.dp2_nodes[...] = 0.0
+        npf.p2_nodes[...] = p2aux
+        npf.dp2_nodes[...] = 0.0
 
         Sol.rhou += u0 * Sol.rho
         Sol.rhov += v0 * Sol.rho
@@ -333,4 +330,4 @@ def T_from_p_rho(p, rho):
 
 
 class obj(object):
-    pass
\ No newline at end of file
+    pass
diff --git a/src/pybella/tests/test_unstable_lamb.py b/src/pybella/tests/test_unstable_lamb.py
index 54dfb078..8605e330 100644
--- a/src/pybella/tests/test_unstable_lamb.py
+++ b/src/pybella/tests/test_unstable_lamb.py
@@ -4,7 +4,7 @@
 
 import numpy as np
 from ..flow_solver.physics import hydrostatics
-from ..flow_solver.utils import boundary as bdry
+from ..flow_solver.utils.boundary import rayleigh_boundary as bdry_r
 from ..utils import options as opts
 
 from ..utils.data_structures import DiagnosticState
@@ -263,16 +263,16 @@ def dehatter(self, th, grid="c"):
             return up.T, vp.T, Yp.T, pi_p.T
 
 
-def sol_init(Sol, mpv, elem, node, th, ud, seeds=None):
+def sol_init(Sol, npf, elem, node, th, ud, seeds=None):
     if hasattr(ud, "rayleigh_bdry_switch"):
         if ud.rayleigh_bdry_switch:
             ud.bdry_type[1] = opts.BdryType.RAYLEIGH
 
     if ud.bdry_type[1] == opts.BdryType.RAYLEIGH:
-        ud.tcy, ud.tny = bdry.get_tau_y(ud, elem, node, 0.5)
+        ud.tcy, ud.tny = bdry_r.get_tau_y(ud, elem, node, 0.5)
 
     if ud.rayleigh_forcing:
-        ud.forcing_tcy, ud.forcing_tny = bdry.get_bottom_tau_y(
+        ud.forcing_tcy, ud.forcing_tny = bdry_r.get_bottom_tau_y(
             ud, elem, node, 0.2, cutoff=0.3
         )
 
@@ -297,13 +297,13 @@ def sol_init(Sol, mpv, elem, node, th, ud, seeds=None):
     ud.stratification = ud.stratification(dy)
 
     # Use hydrostatically balanced background
-    hydrostatics.analytical_state(mpv, elem, node, th, ud)
-    rhobar = mpv.HydroState.rho0.reshape(1, -1)
-    Ybar = mpv.HydroState.Y0.reshape(1, -1)
-    pibar = mpv.HydroState.p20.reshape(1, -1) * ud.Msq
+    hydrostatics.analytical_state(npf, elem, node, th, ud)
+    rhobar = npf.HydroState.rho0.reshape(1, -1)
+    Ybar = npf.HydroState.Y0.reshape(1, -1)
+    pibar = npf.HydroState.p20.reshape(1, -1) * ud.Msq
 
-    rhobar_n = mpv.HydroState_n.rho0.reshape(1, -1)
-    Ybar_n = mpv.HydroState_n.Y0.reshape(1, -1)
+    rhobar_n = npf.HydroState_n.rho0.reshape(1, -1)
+    Ybar_n = npf.HydroState_n.Y0.reshape(1, -1)
 
     ##################################################
     # dimensionless Brunt-Väisälä frequency
@@ -345,16 +345,14 @@ def sol_init(Sol, mpv, elem, node, th, ud, seeds=None):
     Sol.rhow[...] = rho * w
     Sol.rhoY[...] = rho * Y
     Sol.rhoX[...] = 0.0
-    mpv.p2_cells[...] = pi_p
+    npf.p2_cells[...] = pi_p
 
     ###################################################
     # initialise nodal pi
     ud.rf_bot.eigenfunction(0, 1, grid="n")
     _, _, _, pi_n = ud.rf_bot.dehatter(th, grid="n")
 
-    mpv.p2_nodes[...] = pi_n
-
-    bdry.set_explicit_boundary_data(Sol, elem, ud, th, mpv)
+    npf.p2_nodes[...] = pi_n
 
     if hasattr(ud, "mixed_run"):
         if ud.mixed_run:
diff --git a/src/pybella/utils/data_structures.py b/src/pybella/utils/data_structures.py
index e00b9f0a..6b9fae8a 100644
--- a/src/pybella/utils/data_structures.py
+++ b/src/pybella/utils/data_structures.py
@@ -2,9 +2,9 @@
 from dataclasses import dataclass, field, fields
 
 from ..flow_solver.discretisation.grid import Grid
-from ..flow_solver.utils.variable import Vars, FlowSolverCache
-from ..flow_solver.physics.low_mach.mpv import MPV
-from ..flow_solver.physics.gas_dynamics.thermodynamics import ThermodynamicalQuantities
+from ..flow_solver.utils.fields import CellSolField, NodePressureField, States
+from ..flow_solver.utils.cache import FlowSolverCache
+from ..flow_solver.physics.thermodynamics import ThermodynamicalQuantities
 
 
 @dataclass
@@ -18,9 +18,8 @@ class IntegrationTime:
 class ModelState:
     elem: Grid
     node: Grid
-    sol: Vars
-    flux: List[Vars]
-    mpv: MPV
+    sol: CellSolField
+    npf: NodePressureField
     th: ThermodynamicalQuantities
     cache: FlowSolverCache = field(default_factory=FlowSolverCache)
     time: IntegrationTime = field(init=False)
@@ -68,15 +67,14 @@ def update_member(
         self,
         elem: Grid,
         node: Grid,
-        sol: Vars,
-        mpv: MPV,
-        flux: List[Vars],
+        sol: CellSolField,
+        npf: NodePressureField,
         th: ThermodynamicalQuantities,
-        cache: Optional[FlowSolverCache] = None
+        cache: Optional[FlowSolverCache] = None,
     ):
         if cache is None:
             cache = FlowSolverCache()
-        new_state = ModelState(elem, node, sol, flux, mpv, th, cache)
+        new_state = ModelState(elem, node, sol, npf, th, cache)
         self.members.append(new_state)
 
     def set_members(self, members: List[ModelState]):
diff --git a/src/pybella/utils/io.py b/src/pybella/utils/io.py
index 68cdeba7..c8960d50 100644
--- a/src/pybella/utils/io.py
+++ b/src/pybella/utils/io.py
@@ -162,13 +162,13 @@ def io_create_file(self, paths, restart):
 
     def write_all(self, model_state, name):
         """
-        At a given time, write output from `Sol` and `mpv` to the HDF5 file.
+        At a given time, write output from `Sol` and `npf` to the HDF5 file.
 
         Parameters
         ----------
         Sol : :class:`management.variable.Vars`
             Solution data container
-        mpv : :class:`physics.low_mach.mpv.MPV`
+        npf : :class:`physics.low_mach.npf.MPV`
             Variables relating to the elliptic solver
         elem : :class:`discretization.kgrid.ElemSpaceDiscr`
             Cells grid
@@ -182,7 +182,7 @@ def write_all(self, model_state, name):
         """
 
         Sol = model_state.sol
-        mpv = model_state.mpv
+        npf = model_state.npf
 
         logging.info("writing hdf output..." + name)
         # rho
@@ -196,7 +196,7 @@ def write_all(self, model_state, name):
         self.populate(name, "rhow", Sol.rhow)
         self.populate(name, "rhoX", Sol.rhoX)
 
-        self.populate(name, "p2_nodes", mpv.p2_nodes)
+        self.populate(name, "p2_nodes", npf.p2_nodes)
 
         # vorticity in (x,z)
         # self.populate(name,'vortz', self.vortz(Sol,elem,node))
@@ -357,11 +357,11 @@ def vorty(self, Sol, elem, node):
         vortz[1:-1, :, 1:-1] = tmp
         return vortz
 
-    def dpress_dim(self, mpv, ud, th):
-        p0 = th.Gamma * ud.Msq * mpv.p2_cells
+    def dpress_dim(self, npf, ud, th):
+        p0 = th.Gamma * ud.Msq * npf.p2_cells
         p = np.power(p0, th.Gammainv, dtype=np.complex)
         p = p.real
-        return (p - mpv.HydroState.p0[0, :]) * self.ud.p_ref
+        return (p - npf.HydroState.p0[0, :]) * self.ud.p_ref
 
     def populate(self, name, path, data, options=None):
         """
@@ -476,7 +476,7 @@ def __init__(self, fn, path):
         self.fn = fn
         self.path = path
 
-    def get_data(self, Sol, mpv, time_tag, half=False):
+    def get_data(self, Sol, npf, time_tag, half=False):
         file = h5py.File(self.path + "/" + self.fn, "r")
 
         if half:
@@ -490,7 +490,7 @@ def get_data(self, Sol, mpv, time_tag, half=False):
         Sol.rhow[...] = file["rhow" + half_tag]["rhow" + half_tag + "_" + time_tag][:]
         Sol.rhoY[...] = file["rhoY" + half_tag]["rhoY" + half_tag + "_" + time_tag][:]
 
-        mpv.p2_nodes[...] = file["p2_nodes" + half_tag][
+        npf.p2_nodes[...] = file["p2_nodes" + half_tag][
             "p2_nodes" + half_tag + "_" + time_tag
         ][:]
 
@@ -603,7 +603,7 @@ def get_args():
     return N, UserData, sol_init, rstrt, ud, dap, params
 
 
-def sim_restart(path, name, elem, node, ud, Sol, mpv, restart_touts):
+def sim_restart(path, name, elem, node, ud, Sol, npf, restart_touts):
     """
     Function to restart simulation from a saved file. Dataset has to be structured in the same way as the output format of this file.
 
@@ -616,7 +616,7 @@ def sim_restart(path, name, elem, node, ud, Sol, mpv, restart_touts):
     file = h5py.File(str(path), "r")
 
     Sol_data = ["rho", "rhou", "rhov", "rhow", "rhoX", "rhoY"]
-    mpv_data = ["p2_nodes"]
+    npf_data = ["p2_nodes"]
 
     for data in Sol_data:
         value = file[data][data + name][:]
@@ -628,14 +628,14 @@ def sim_restart(path, name, elem, node, ud, Sol, mpv, restart_touts):
         else:
             assert 0, "Sol attribute mismatch"
 
-    for data in mpv_data:
+    for data in npf_data:
         value = file[data][data + name][:]
-        if hasattr(mpv, data):
-            shp = getattr(mpv, data).shape
-            setattr(mpv, data, value)
-            assert getattr(mpv, data).shape == shp
+        if hasattr(npf, data):
+            shp = getattr(npf, data).shape
+            setattr(npf, data, value)
+            assert getattr(npf, data).shape == shp
         else:
-            assert 0, "mpv attribute mismatch"
+            assert 0, "npf attribute mismatch"
 
     t = restart_touts
 
@@ -648,7 +648,7 @@ def sim_restart(path, name, elem, node, ud, Sol, mpv, restart_touts):
     )
 
     file.close()
-    return Sol, mpv, t
+    return Sol, npf, t
 
 
 def fn_gen(ud, dap, N):
diff --git a/src/pybella/utils/operators.py b/src/pybella/utils/operators.py
deleted file mode 100644
index 37e9a0a3..00000000
--- a/src/pybella/utils/operators.py
+++ /dev/null
@@ -1,650 +0,0 @@
-import numpy as np
-import scipy as sp
-from numba import njit
-from functools import lru_cache
-
-@lru_cache(maxsize=2)
-def get_flux_convolution_kernels(ndim):
-    """Create convolution kernels for advective flux computation.
-    
-    Parameters
-    ----------
-    ndim : int
-        Number of dimensions (2 or 3)
-        
-    Returns
-    -------
-    dict
-        Dictionary containing kernels for each direction
-        
-    Notes
-    -----
-    Results are cached since kernels don't change during computation.
-    """
-    if ndim == 2:
-        kernel_u = np.array([[0.5, 1.0, 0.5], [0.5, 1.0, 0.5]])
-        return {
-            'u': kernel_u,
-            'v': kernel_u.T
-        }
-    elif ndim == 3:
-        kernel_u = np.array([
-            [[1, 2, 1], [2, 4, 2], [1, 2, 1]], 
-            [[1, 2, 1], [2, 4, 2], [1, 2, 1]]
-        ])
-        return {
-            'u': kernel_u,
-            'v': np.swapaxes(kernel_u, 1, 0),
-            'w': np.swapaxes(kernel_u, 2, 0)
-        }
-    else:
-        raise ValueError(f"Unsupported dimension: {ndim}")
-
-
-@lru_cache(maxsize=4)
-def get_averaging_kernel(ndim, width=3, normalize=True):
-    """
-    Create a generic averaging kernel for arbitrary dimensions.
-
-    Parameters
-    ----------
-    ndim : int
-        Number of dimensions (e.g., 2 or 3)
-    width : int, default=3
-        Size of the kernel along each axis (can be even or odd)
-    normalize : bool, default=True
-        Whether to normalize the kernel to sum to 1
-
-    Returns
-    -------
-    np.ndarray
-        Averaging kernel of shape (width,) * ndim
-
-    Notes
-    -----
-    - Odd widths result in centered kernels.
-    - Even widths are useful for staggered/grid-face averaging.
-    """
-    shape = (width,) * ndim
-    kernel = np.ones(shape, dtype=np.float64)
-
-    if normalize:
-        kernel /= kernel.size
-
-    return kernel
-
-@njit(cache=True)
-def _numba_convolve_2d(data, kernel):
-    """Numba-compiled 2D convolution for better performance."""
-    data_h, data_w = data.shape
-    kernel_h, kernel_w = kernel.shape
-    
-    result_h = data_h - kernel_h + 1
-    result_w = data_w - kernel_w + 1
-    result = np.zeros((result_h, result_w))
-    
-    for i in range(result_h):
-        for j in range(result_w):
-            for ki in range(kernel_h):
-                for kj in range(kernel_w):
-                    result[i, j] += data[i + ki, j + kj] * kernel[ki, kj]
-    
-    return result
-
-
-@njit(cache=True)
-def _numba_convolve_3d(data, kernel):
-    """Numba-compiled 3D convolution for better performance."""
-    data_d, data_h, data_w = data.shape
-    kernel_d, kernel_h, kernel_w = kernel.shape
-    
-    result_d = data_d - kernel_d + 1
-    result_h = data_h - kernel_h + 1
-    result_w = data_w - kernel_w + 1
-    result = np.zeros((result_d, result_h, result_w))
-    
-    for i in range(result_d):
-        for j in range(result_h):
-            for k in range(result_w):
-                for ki in range(kernel_d):
-                    for kj in range(kernel_h):
-                        for kk in range(kernel_w):
-                            result[i, j, k] += data[i + ki, j + kj, k + kk] * kernel[ki, kj, kk]
-    
-    return result
-
-
-def apply_convolution_kernel(data, kernel, normalize=True, axis_swap=None, use_numba=True):
-    """Apply convolution kernel with optional normalization and axis swapping.
-    
-    Parameters
-    ----------
-    data : np.ndarray
-        Input data array
-    kernel : np.ndarray
-        Convolution kernel
-    normalize : bool, default=True
-        Whether to normalize by kernel sum
-    axis_swap : tuple or None, default=None
-        Tuple of (from_axis, to_axis) for np.moveaxis
-    use_numba : bool, default=True
-        Whether to use Numba-compiled convolution (faster for repeated calls)
-        
-    Returns
-    -------
-    np.ndarray
-        Convolved result
-        
-    Notes
-    -----
-    For large arrays or single calls, scipy.signal.fftconvolve might be faster.
-    For repeated calls on smaller arrays, Numba convolution is typically faster.
-    """
-    if use_numba and data.ndim in (2, 3):
-        if data.ndim == 2:
-            result = _numba_convolve_2d(data, kernel)
-        else:  # 3D
-            result = _numba_convolve_3d(data, kernel)
-    else:
-        # Fallback to scipy for other dimensions or when requested
-        result = sp.signal.fftconvolve(data, kernel, mode="valid")
-    
-    if normalize:
-        result = result / kernel.sum()
-    
-    if axis_swap is not None:
-        result = np.moveaxis(result, axis_swap[0], axis_swap[1])
-    
-    return result
-
-
-# Configuration for directional convolutions
-DIRECTION_CONFIG = {
-    2: {
-        'u': {'axis_swap': (0, -1)},
-        'v': {'axis_swap': None}
-    },
-    3: {
-        'u': {'axis_swap': (0, -1)},
-        'v': {'axis_swap': (-1, 0)},
-        'w': {'axis_swap': None}
-    }
-}
-
-def apply_directional_convolution(data, kernel, direction, ndim, normalize=True, use_numba=True):
-    """Apply convolution kernel for a specific direction with appropriate axis swapping.
-    
-    Parameters
-    ----------
-    data : np.ndarray
-        Input data array
-    kernel : np.ndarray
-        Convolution kernel for the direction
-    direction : str
-        Direction ('u', 'v', or 'w')
-    ndim : int
-        Number of dimensions (2 or 3)
-    normalize : bool, default=True
-        Whether to normalize by kernel sum
-    use_numba : bool, default=True
-        Whether to use Numba-compiled convolution
-        
-    Returns
-    -------
-    np.ndarray
-        Convolved result with appropriate axis swapping
-    """
-    if direction not in DIRECTION_CONFIG[ndim]:
-        raise ValueError(f"Direction '{direction}' not supported for {ndim}D")
-    
-    config = DIRECTION_CONFIG[ndim][direction]
-    return apply_convolution_kernel(
-        data, kernel, 
-        normalize=normalize, 
-        axis_swap=config['axis_swap'], 
-        use_numba=use_numba
-    )
-
-
-@njit(cache=True)
-def compute_divergence_2d(u_field, v_field, dx, dy):
-    """
-    Compute 2D divergence: ∇·F = ∂u/∂x + ∂v/∂y
-    
-    Parameters
-    ----------
-    u_field : np.ndarray
-        Field component in x-direction
-    v_field : np.ndarray  
-        Field component in y-direction
-    dx : float
-        Grid spacing in x-direction
-    dy : float
-        Grid spacing in y-direction
-        
-    Returns
-    -------
-    np.ndarray
-        Divergence field averaged to cell centers
-    """
-    # X-direction: ∂u/∂x
-    div_x = finite_difference_1d(u_field, dx, axis=0)
-    # Average to y-cell centers
-    div_x = 0.5 * (div_x[:, :-1] + div_x[:, 1:])
-    
-    # Y-direction: ∂v/∂y  
-    div_y = finite_difference_1d(v_field, dy, axis=1)
-    # Average to x-cell centers
-    div_y = 0.5 * (div_y[:-1, :] + div_y[1:, :])
-    
-    return div_x + div_y
-
-
-@njit(cache=True)
-def compute_divergence_3d(u_field, v_field, w_field, dx, dy, dz):
-    """
-    Compute 3D divergence: ∇·F = ∂u/∂x + ∂v/∂y + ∂w/∂z
-    
-    Parameters
-    ----------
-    u_field : np.ndarray
-        Field component in x-direction
-    v_field : np.ndarray
-        Field component in y-direction  
-    w_field : np.ndarray
-        Field component in z-direction
-    dx : float
-        Grid spacing in x-direction
-    dy : float
-        Grid spacing in y-direction
-    dz : float
-        Grid spacing in z-direction
-        
-    Returns
-    -------
-    tuple
-        (div_x, div_y, div_z) - Individual divergence components
-    """
-    # X-direction: ∂u/∂x
-    div_x = finite_difference_1d(u_field, dx, axis=0)
-    # Average to y-cell centers, then to z-faces
-    div_x = 0.5 * (div_x[:, :-1, :] + div_x[:, 1:, :])
-    div_x = -0.5 * (div_x[:, :, :-1] + div_x[:, :, 1:])  # Note: negative from original
-    
-    # Y-direction: ∂v/∂y
-    div_y = finite_difference_1d(v_field, dy, axis=1)
-    # Average to x-cell centers, then to z-faces
-    div_y = 0.5 * (div_y[:-1, :, :] + div_y[1:, :, :])
-    div_y = 0.5 * (div_y[:, :, :-1] + div_y[:, :, 1:])
-    
-    # Z-direction: ∂w/∂z
-    div_z = finite_difference_1d(w_field, dz, axis=2)
-    # Average to cell centers
-    div_z = 0.5 * (div_z[:-1, :, :] + div_z[1:, :, :])
-    div_z = 0.5 * (div_z[:, :-1, :] + div_z[:, 1:, :])
-    
-    return div_x, div_y, div_z
-
-
-@njit(cache=True)
-def compute_divergence_3d_total(u_field, v_field, w_field, dx, dy, dz):
-    """
-    Compute total 3D divergence: ∇·F = ∂u/∂x + ∂v/∂y + ∂w/∂z
-    
-    Parameters
-    ----------
-    u_field : np.ndarray
-        Field component in x-direction
-    v_field : np.ndarray
-        Field component in y-direction  
-    w_field : np.ndarray
-        Field component in z-direction
-    dx : float
-        Grid spacing in x-direction
-    dy : float
-        Grid spacing in y-direction
-    dz : float
-        Grid spacing in z-direction
-        
-    Returns
-    -------
-    np.ndarray
-        Total divergence field
-    """
-    div_x, div_y, div_z = compute_divergence_3d(u_field, v_field, w_field, dx, dy, dz)
-    return div_x + div_y + div_z
-
-
-@njit(cache=True)
-def finite_difference_1d(field, spacing, axis=0):
-    """
-    Compute 1D finite difference along specified axis.
-    
-    Parameters
-    ----------
-    field : np.ndarray
-        Input field
-    spacing : float
-        Grid spacing
-    axis : int, default=0
-        Axis along which to compute difference
-        
-    Returns
-    -------
-    np.ndarray
-        Finite difference result
-    """
-    if field.ndim == 2:
-        if axis == 0:
-            return (field[1:, :] - field[:-1, :]) / spacing
-        elif axis == 1:
-            return (field[:, 1:] - field[:, :-1]) / spacing
-        else:
-            raise ValueError("axis must be 0 or 1 for 2D arrays")
-    elif field.ndim == 3:
-        if axis == 0:
-            return (field[1:, :, :] - field[:-1, :, :]) / spacing
-        elif axis == 1:
-            return (field[:, 1:, :] - field[:, :-1, :]) / spacing
-        elif axis == 2:
-            return (field[:, :, 1:] - field[:, :, :-1]) / spacing
-        else:
-            raise ValueError("axis must be 0, 1, or 2 for 3D arrays")
-    else:
-        raise ValueError("field must be 2D or 3D array")
-    
-# @njit
-def average_to_centers_2d(field, axis):
-    """
-    Average field values to cell centers along specified axis.
-    
-    Parameters
-    ----------
-    field : np.ndarray
-        Input field (2D)
-    axis : int
-        Axis along which to average (0 or 1)
-        
-    Returns
-    -------
-    np.ndarray
-        Averaged field
-    """
-    if axis == 0:
-        return 0.5 * (field[:-1, :] + field[1:, :])
-    elif axis == 1:
-        return 0.5 * (field[:, :-1] + field[:, 1:])
-    else:
-        raise ValueError("axis must be 0 or 1 for 2D arrays")
-
-
-# @njit
-def average_to_centers_3d(field, axis):
-    """
-    Average field values to cell centers along specified axis.
-    
-    Parameters
-    ----------
-    field : np.ndarray
-        Input field (3D)
-    axis : int
-        Axis along which to average (0, 1, or 2)
-        
-    Returns
-    -------
-    np.ndarray
-        Averaged field
-    """
-    if axis == 0:
-        return 0.5 * (field[:-1, :, :] + field[1:, :, :])
-    elif axis == 1:
-        return 0.5 * (field[:, :-1, :] + field[:, 1:, :])
-    elif axis == 2:
-        return 0.5 * (field[:, :, :-1] + field[:, :, 1:])
-    else:
-        raise ValueError("axis must be 0, 1, or 2 for 3D arrays")
-
-
-@njit(cache=True)
-def compute_gradient_2d(field, dx, dy):
-    """
-    Compute 2D gradient: ∇φ = (∂φ/∂x, ∂φ/∂y)
-    
-    Parameters
-    ----------
-    field : np.ndarray
-        Scalar field
-    dx : float
-        Grid spacing in x-direction
-    dy : float
-        Grid spacing in y-direction
-        
-    Returns
-    -------
-    tuple
-        (grad_x, grad_y) - Gradient components
-    """
-    grad_x = finite_difference_1d(field, dx, axis=0)
-    grad_y = finite_difference_1d(field, dy, axis=1)
-    
-    return grad_x, grad_y
-
-
-@njit(cache=True)
-def compute_gradient_3d(field, dx, dy, dz):
-    """
-    Compute 3D gradient: ∇φ = (∂φ/∂x, ∂φ/∂y, ∂φ/∂z)
-    
-    Parameters
-    ----------
-    field : np.ndarray
-        Scalar field
-    dx : float
-        Grid spacing in x-direction
-    dy : float
-        Grid spacing in y-direction
-    dz : float
-        Grid spacing in z-direction
-        
-    Returns
-    -------
-    tuple
-        (grad_x, grad_y, grad_z) - Gradient components
-    """
-    grad_x = finite_difference_1d(field, dx, axis=0)
-    grad_y = finite_difference_1d(field, dy, axis=1)
-    grad_z = finite_difference_1d(field, dz, axis=2)
-    
-    return grad_x, grad_y, grad_z
-
-
-#######
-# Compute gradient at nodes
-#######
-
-@njit(cache=True)
-def _compute_grad_nodes_2d(p, dx, dy):
-    """Compute 2D gradient at nodes using corner averaging."""
-    # Pre-computed signs for each corner
-    signs_x = np.array([-1.0, -1.0, +1.0, +1.0])
-    signs_y = np.array([-1.0, +1.0, -1.0, +1.0])
-    
-    # Initialize gradient components
-    Dpx = np.zeros((p.shape[0] - 1, p.shape[1] - 1))
-    Dpy = np.zeros((p.shape[0] - 1, p.shape[1] - 1))
-    
-    # Corner contributions
-    # Bottom-left
-    Dpx += signs_x[0] * p[0:-1, 0:-1]
-    Dpy += signs_y[0] * p[0:-1, 0:-1]
-    
-    # Bottom-right
-    Dpx += signs_x[1] * p[0:-1, 1:]
-    Dpy += signs_y[1] * p[0:-1, 1:]
-    
-    # Top-left
-    Dpx += signs_x[2] * p[1:, 0:-1]
-    Dpy += signs_y[2] * p[1:, 0:-1]
-    
-    # Top-right
-    Dpx += signs_x[3] * p[1:, 1:]
-    Dpy += signs_y[3] * p[1:, 1:]
-    
-    # Apply scaling factors
-    scale_factor = 0.5 ** (2 - 1)  # 0.5^(ndim-1)
-    Dpx *= scale_factor / dx
-    Dpy *= scale_factor / dy
-    
-    return Dpx, Dpy
-
-@njit(cache=True)
-def _compute_grad_nodes_3d(p, dx, dy, dz):
-    """Compute 3D gradient at nodes using corner averaging."""
-    # Pre-computed signs for each corner
-    signs_x = np.array([-1.0, -1.0, -1.0, -1.0, +1.0, +1.0, +1.0, +1.0])
-    signs_y = np.array([-1.0, -1.0, +1.0, +1.0, -1.0, -1.0, +1.0, +1.0])
-    signs_z = np.array([-1.0, +1.0, -1.0, +1.0, -1.0, +1.0, -1.0, +1.0])
-    
-    # Initialize gradient components
-    Dpx = np.zeros((p.shape[0] - 1, p.shape[1] - 1, p.shape[2] - 1))
-    Dpy = np.zeros((p.shape[0] - 1, p.shape[1] - 1, p.shape[2] - 1))
-    Dpz = np.zeros((p.shape[0] - 1, p.shape[1] - 1, p.shape[2] - 1))
-    
-    # Corner contributions (8 corners for 3D)
-    # Bottom-left-back
-    Dpx += signs_x[0] * p[0:-1, 0:-1, 0:-1]
-    Dpy += signs_y[0] * p[0:-1, 0:-1, 0:-1]
-    Dpz += signs_z[0] * p[0:-1, 0:-1, 0:-1]
-    
-    # Bottom-left-front
-    Dpx += signs_x[1] * p[0:-1, 0:-1, 1:]
-    Dpy += signs_y[1] * p[0:-1, 0:-1, 1:]
-    Dpz += signs_z[1] * p[0:-1, 0:-1, 1:]
-    
-    # Bottom-right-back
-    Dpx += signs_x[2] * p[0:-1, 1:, 0:-1]
-    Dpy += signs_y[2] * p[0:-1, 1:, 0:-1]
-    Dpz += signs_z[2] * p[0:-1, 1:, 0:-1]
-    
-    # Bottom-right-front
-    Dpx += signs_x[3] * p[0:-1, 1:, 1:]
-    Dpy += signs_y[3] * p[0:-1, 1:, 1:]
-    Dpz += signs_z[3] * p[0:-1, 1:, 1:]
-    
-    # Top-left-back
-    Dpx += signs_x[4] * p[1:, 0:-1, 0:-1]
-    Dpy += signs_y[4] * p[1:, 0:-1, 0:-1]
-    Dpz += signs_z[4] * p[1:, 0:-1, 0:-1]
-    
-    # Top-left-front
-    Dpx += signs_x[5] * p[1:, 0:-1, 1:]
-    Dpy += signs_y[5] * p[1:, 0:-1, 1:]
-    Dpz += signs_z[5] * p[1:, 0:-1, 1:]
-    
-    # Top-right-back
-    Dpx += signs_x[6] * p[1:, 1:, 0:-1]
-    Dpy += signs_y[6] * p[1:, 1:, 0:-1]
-    Dpz += signs_z[6] * p[1:, 1:, 0:-1]
-    
-    # Top-right-front
-    Dpx += signs_x[7] * p[1:, 1:, 1:]
-    Dpy += signs_y[7] * p[1:, 1:, 1:]
-    Dpz += signs_z[7] * p[1:, 1:, 1:]
-    
-    # Apply scaling factors
-    scale_factor = 0.5 ** (3 - 1)  # 0.5^(ndim-1)
-    Dpx *= scale_factor / dx
-    Dpy *= scale_factor / dy
-    Dpz *= scale_factor / dz
-    
-    return Dpx, Dpy, Dpz
-
-@njit(cache=True)
-def compute_gradient_nodes_2d(p, dx, dy):
-    """
-    Compute gradient at nodes using finite difference averaging.
-    
-    Parameters
-    ----------
-    p : np.ndarray
-        Scalar field (2D)
-    dx : float
-        Grid spacing in x-direction
-    dy : float
-        Grid spacing in y-direction
-        
-    Returns
-    -------
-    tuple
-        (grad_x, grad_y) - Gradient components at nodes
-        
-    Notes
-    -----
-    The gradient is computed at nodes by averaging contributions from
-    all neighboring cells. Output arrays have shape (nx-1, ny-1).
-    """
-    return _compute_grad_nodes_2d(p, dx, dy)
-
-@njit(cache=True)
-def compute_gradient_nodes_3d(p, dx, dy, dz):
-    """
-    Compute gradient at nodes using finite difference averaging.
-    
-    Parameters
-    ----------
-    p : np.ndarray
-        Scalar field (3D)
-    dx : float
-        Grid spacing in x-direction
-    dy : float
-        Grid spacing in y-direction
-    dz : float
-        Grid spacing in z-direction
-        
-    Returns
-    -------
-    tuple
-        (grad_x, grad_y, grad_z) - Gradient components at nodes
-        
-    Notes
-    -----
-    The gradient is computed at nodes by averaging contributions from
-    all neighboring cells. Output arrays have shape (nx-1, ny-1, nz-1).
-    """
-    return _compute_grad_nodes_3d(p, dx, dy, dz)
-
-def compute_gradient_nodes(p, ndim, dxy):
-    """
-    Compute gradient at nodes using finite difference averaging.
-    
-    Parameters
-    ----------
-    p : np.ndarray
-        Scalar field
-    ndim : int
-        Number of dimensions (2 or 3)
-    dxy : tuple
-        Grid spacings (dx, dy, dz)
-        
-    Returns
-    -------
-    tuple
-        Gradient components at nodes. For 2D: (grad_x, grad_y, zeros)
-        For 3D: (grad_x, grad_y, grad_z)
-        
-    Notes
-    -----
-    This is the main interface function that dispatches to the appropriate
-    dimension-specific implementation. Always returns 3 components for
-    consistency, with the z-component being zero for 2D cases.
-    """
-    dx, dy, dz = dxy
-    
-    if ndim == 2:
-        grad_x, grad_y = compute_gradient_nodes_2d(p, dx, dy)
-        grad_z = np.zeros_like(grad_x)
-        return grad_x, grad_y, grad_z
-    elif ndim == 3:
-        return compute_gradient_nodes_3d(p, dx, dy, dz)
-    else:
-        raise ValueError(f"Unsupported dimension: {ndim}")
\ No newline at end of file
diff --git a/src/pybella/utils/operators/__init__.py b/src/pybella/utils/operators/__init__.py
new file mode 100644
index 00000000..e69de29b
diff --git a/src/pybella/utils/operators/convolution.py b/src/pybella/utils/operators/convolution.py
new file mode 100644
index 00000000..f343bd3a
--- /dev/null
+++ b/src/pybella/utils/operators/convolution.py
@@ -0,0 +1,208 @@
+import numpy as np
+import numba as nb
+import scipy as sp
+import functools
+
+# Configuration for directional convolutions
+DIRECTION_CONFIG = {
+    2: {"u": {"axis_swap": (0, -1)}, "v": {"axis_swap": None}},
+    3: {
+        "u": {"axis_swap": (0, -1)},
+        "v": {"axis_swap": (-1, 0)},
+        "w": {"axis_swap": None},
+    },
+}
+
+
+@functools.lru_cache(maxsize=2)
+def get_flux_kernels(ndim):
+    """Create convolution kernels for advective flux computation.
+
+    Parameters
+    ----------
+    ndim : int
+        Number of dimensions (2 or 3)
+
+    Returns
+    -------
+    dict
+        Dictionary containing kernels for each direction
+
+    Notes
+    -----
+    Results are cached since kernels don't change during computation.
+    """
+    if ndim == 2:
+        kernel_u = np.array([[0.5, 1.0, 0.5], [0.5, 1.0, 0.5]])
+        return {"u": kernel_u, "v": kernel_u.T}
+    elif ndim == 3:
+        kernel_u = np.array(
+            [[[1, 2, 1], [2, 4, 2], [1, 2, 1]], [[1, 2, 1], [2, 4, 2], [1, 2, 1]]]
+        )
+        return {
+            "u": kernel_u,
+            "v": np.swapaxes(kernel_u, 1, 0),
+            "w": np.swapaxes(kernel_u, 2, 0),
+        }
+    else:
+        raise ValueError(f"Unsupported dimension: {ndim}")
+
+
+@functools.lru_cache(maxsize=4)
+def get_averaging_kernel(ndim, width=3, normalize=True):
+    """
+    Create a generic averaging kernel for arbitrary dimensions.
+
+    Parameters
+    ----------
+    ndim : int
+        Number of dimensions (e.g., 2 or 3)
+    width : int, default=3
+        Size of the kernel along each axis (can be even or odd)
+    normalize : bool, default=True
+        Whether to normalize the kernel to sum to 1
+
+    Returns
+    -------
+    np.ndarray
+        Averaging kernel of shape (width,) * ndim
+
+    Notes
+    -----
+    - Odd widths result in centered kernels.
+    - Even widths are useful for staggered/grid-face averaging.
+    """
+    shape = (width,) * ndim
+    kernel = np.ones(shape, dtype=np.float64)
+
+    if normalize:
+        kernel /= kernel.size
+
+    return kernel
+
+
+@nb.njit(cache=True)
+def _convolve_2d(data, kernel):
+    """Numba-compiled 2D convolution for better performance."""
+    data_h, data_w = data.shape
+    kernel_h, kernel_w = kernel.shape
+
+    result_h = data_h - kernel_h + 1
+    result_w = data_w - kernel_w + 1
+    result = np.zeros((result_h, result_w))
+
+    for i in range(result_h):
+        for j in range(result_w):
+            for ki in range(kernel_h):
+                for kj in range(kernel_w):
+                    result[i, j] += data[i + ki, j + kj] * kernel[ki, kj]
+
+    return result
+
+
+@nb.njit(cache=True)
+def _convolve_3d(data, kernel):
+    """Numba-compiled 3D convolution for better performance."""
+    data_d, data_h, data_w = data.shape
+    kernel_d, kernel_h, kernel_w = kernel.shape
+
+    result_d = data_d - kernel_d + 1
+    result_h = data_h - kernel_h + 1
+    result_w = data_w - kernel_w + 1
+    result = np.zeros((result_d, result_h, result_w))
+
+    for i in range(result_d):
+        for j in range(result_h):
+            for k in range(result_w):
+                for ki in range(kernel_d):
+                    for kj in range(kernel_h):
+                        for kk in range(kernel_w):
+                            result[i, j, k] += (
+                                data[i + ki, j + kj, k + kk] * kernel[ki, kj, kk]
+                            )
+
+    return result
+
+
+def apply_convolution_kernel(
+    data, kernel, normalize=True, axis_swap=None, use_numba=True
+):
+    """Apply convolution kernel with optional normalization and axis swapping.
+
+    Parameters
+    ----------
+    data : np.ndarray
+        Input data array
+    kernel : np.ndarray
+        Convolution kernel
+    normalize : bool, default=True
+        Whether to normalize by kernel sum
+    axis_swap : tuple or None, default=None
+        Tuple of (from_axis, to_axis) for np.moveaxis
+    use_numba : bool, default=True
+        Whether to use Numba-compiled convolution (faster for repeated calls)
+
+    Returns
+    -------
+    np.ndarray
+        Convolved result
+
+    Notes
+    -----
+    For large arrays or single calls, scipy.signal.fftconvolve might be faster.
+    For repeated calls on smaller arrays, Numba convolution is typically faster.
+    """
+    if use_numba and data.ndim in (2, 3):
+        if data.ndim == 2:
+            result = _convolve_2d(data, kernel)
+        else:  # 3D
+            result = _convolve_3d(data, kernel)
+    else:
+        # Fallback to scipy for other dimensions or when requested
+        result = sp.signal.fftconvolve(data, kernel, mode="valid")
+
+    if normalize:
+        result = result / kernel.sum()
+
+    if axis_swap is not None:
+        result = np.moveaxis(result, axis_swap[0], axis_swap[1])
+
+    return result
+
+
+def apply_directional_convolution(
+    data, kernel, direction, ndim, normalize=True, use_numba=True
+):
+    """Apply convolution kernel for a specific direction with appropriate axis swapping.
+
+    Parameters
+    ----------
+    data : np.ndarray
+        Input data array
+    kernel : np.ndarray
+        Convolution kernel for the direction
+    direction : str
+        Direction ('u', 'v', or 'w')
+    ndim : int
+        Number of dimensions (2 or 3)
+    normalize : bool, default=True
+        Whether to normalize by kernel sum
+    use_numba : bool, default=True
+        Whether to use Numba-compiled convolution
+
+    Returns
+    -------
+    np.ndarray
+        Convolved result with appropriate axis swapping
+    """
+    if direction not in DIRECTION_CONFIG[ndim]:
+        raise ValueError(f"Direction '{direction}' not supported for {ndim}D")
+
+    config = DIRECTION_CONFIG[ndim][direction]
+    return apply_convolution_kernel(
+        data,
+        kernel,
+        normalize=normalize,
+        axis_swap=config["axis_swap"],
+        use_numba=use_numba,
+    )
diff --git a/src/pybella/utils/operators/divergence.py b/src/pybella/utils/operators/divergence.py
new file mode 100644
index 00000000..3e8af161
--- /dev/null
+++ b/src/pybella/utils/operators/divergence.py
@@ -0,0 +1,188 @@
+import numba as nb
+from .. import options as opts
+from . import finite_difference
+
+
+@nb.njit(cache=True)
+def compute_2d(u_field, v_field, dx, dy):
+    """
+    Compute 2D divergence: ∇·F = ∂u/∂x + ∂v/∂y
+
+    Parameters
+    ----------
+    u_field : np.ndarray
+        Field component in x-direction
+    v_field : np.ndarray
+        Field component in y-direction
+    dx : float
+        Grid spacing in x-direction
+    dy : float
+        Grid spacing in y-direction
+
+    Returns
+    -------
+    np.ndarray
+        Divergence field averaged to cell centers
+    """
+    # X-direction: ∂u/∂x
+    div_x = finite_difference.do_1d(u_field, dx, axis=0)
+    # Average to y-cell centers
+    div_x = 0.5 * (div_x[:, :-1] + div_x[:, 1:])
+
+    # Y-direction: ∂v/∂y
+    div_y = finite_difference.do_1d(v_field, dy, axis=1)
+    # Average to x-cell centers
+    div_y = 0.5 * (div_y[:-1, :] + div_y[1:, :])
+
+    return div_x + div_y
+
+
+@nb.njit(cache=True)
+def compute_3d_components(u_field, v_field, w_field, dx, dy, dz):
+    """
+    Compute 3D divergence: ∇·F = ∂u/∂x + ∂v/∂y + ∂w/∂z
+
+    Parameters
+    ----------
+    u_field : np.ndarray
+        Field component in x-direction
+    v_field : np.ndarray
+        Field component in y-direction
+    w_field : np.ndarray
+        Field component in z-direction
+    dx : float
+        Grid spacing in x-direction
+    dy : float
+        Grid spacing in y-direction
+    dz : float
+        Grid spacing in z-direction
+
+    Returns
+    -------
+    tuple
+        (div_x, div_y, div_z) - Individual divergence components
+    """
+    # X-direction: ∂u/∂x
+    div_x = finite_difference.do_1d(u_field, dx, axis=0)
+    # Average to y-cell centers, then to z-faces
+    div_x = 0.5 * (div_x[:, :-1, :] + div_x[:, 1:, :])
+    div_x = -0.5 * (div_x[:, :, :-1] + div_x[:, :, 1:])  # Note: negative from original
+
+    # Y-direction: ∂v/∂y
+    div_y = finite_difference.do_1d(v_field, dy, axis=1)
+    # Average to x-cell centers, then to z-faces
+    div_y = 0.5 * (div_y[:-1, :, :] + div_y[1:, :, :])
+    div_y = 0.5 * (div_y[:, :, :-1] + div_y[:, :, 1:])
+
+    # Z-direction: ∂w/∂z
+    div_z = finite_difference.do_1d(w_field, dz, axis=2)
+    # Average to cell centers
+    div_z = 0.5 * (div_z[:-1, :, :] + div_z[1:, :, :])
+    div_z = 0.5 * (div_z[:, :-1, :] + div_z[:, 1:, :])
+
+    return div_x, div_y, div_z
+
+
+@nb.njit(cache=True)
+def compute_3d_sum(u_field, v_field, w_field, dx, dy, dz):
+    """
+    Compute total 3D divergence: ∇·F = ∂u/∂x + ∂v/∂y + ∂w/∂z
+
+    Parameters
+    ----------
+    u_field : np.ndarray
+        Field component in x-direction
+    v_field : np.ndarray
+        Field component in y-direction
+    w_field : np.ndarray
+        Field component in z-direction
+    dx : float
+        Grid spacing in x-direction
+    dy : float
+        Grid spacing in y-direction
+    dz : float
+        Grid spacing in z-direction
+
+    Returns
+    -------
+    np.ndarray
+        Total divergence field
+    """
+    div_x, div_y, div_z = compute_3d_components(u_field, v_field, w_field, dx, dy, dz)
+    return div_x + div_y + div_z
+
+
+def compute_at_nodes(rhs, elem, sol, ud):
+    """Main divergence function - handles boundary conditions and calls JIT-compiled core."""
+    ndim = elem.ndim
+
+    # Handle boundary conditions
+    if not hasattr(ud, "ATMOSPHERIC_EXTENSION"):
+        if (
+            ud.bdry_type[1] == opts.BdryType.WALL
+            or ud.bdry_type[1] == opts.BdryType.RAYLEIGH
+        ):
+            sol.rhou[:, :2, ...] = 0.0
+            sol.rhov[:, :2, ...] = 0.0
+            sol.rhow[:, :2, ...] = 0.0
+            sol.rhou[:, -2:, ...] = 0.0
+            sol.rhov[:, -2:, ...] = 0.0
+            sol.rhow[:, -2:, ...] = 0.0
+
+    # Call appropriate JIT-compiled function
+    if ndim == 2:
+        rhs[:] = _momentum_pot_temp_divergence_2d_jit(
+            sol.rho, sol.rhou, sol.rhov, sol.rhoY, elem.dx, elem.dy
+        )
+    else:
+        _momentum_pot_temp_divergence_3d_jit(
+            rhs,
+            sol.rho,
+            sol.rhou,
+            sol.rhov,
+            sol.rhow,
+            sol.rhoY,
+            elem.dx,
+            elem.dy,
+            elem.dz,
+        )
+
+    return rhs
+
+
+@nb.njit(cache=True)
+def _momentum_pot_temp_divergence_2d_jit(rho, rhou, rhov, rhoY, dx, dy):
+    """
+    JIT-compiled 2D momentum-potential temperature divergence calculation.
+    Computes ∇·(ρu θ, ρv θ) where θ = ρY/ρ is the potential temperature.
+    """
+    # Calculate potential temperature θ = ρY / ρ
+    theta = rhoY / rho
+
+    # Compute momentum-potential temperature flux components
+    rhou_theta = rhou * theta  # x-momentum flux weighted by potential temperature
+    rhov_theta = rhov * theta  # y-momentum flux weighted by potential temperature
+
+    # Use generic divergence operator
+    return compute_2d(rhou_theta, rhov_theta, dx, dy)
+
+
+@nb.njit(cache=True)
+def _momentum_pot_temp_divergence_3d_jit(rhs, rho, rhou, rhov, rhow, rhoY, dx, dy, dz):
+    """
+    JIT-compiled 3D momentum-potential temperature divergence calculation.
+    Computes ∇·(ρu θ, ρv θ, ρw θ) where θ = ρY/ρ is the potential temperature.
+    """
+    # Calculate potential temperature θ = ρY / ρ
+    theta = rhoY / rho
+
+    # Compute momentum-potential temperature flux components
+    rhou_theta = rhou * theta  # x-momentum flux weighted by potential temperature
+    rhov_theta = rhov * theta  # y-momentum flux weighted by potential temperature
+    rhow_theta = rhow * theta  # z-momentum flux weighted by potential temperature
+
+    # Use generic total divergence operator
+    total_div = compute_3d_sum(rhou_theta, rhov_theta, rhow_theta, dx, dy, dz)
+
+    # Assign to inner region
+    rhs[1:-1, 1:-1, 1:-1] = total_div
diff --git a/src/pybella/utils/operators/finite_difference.py b/src/pybella/utils/operators/finite_difference.py
new file mode 100644
index 00000000..6460c550
--- /dev/null
+++ b/src/pybella/utils/operators/finite_difference.py
@@ -0,0 +1,40 @@
+import numba as nb
+
+
+@nb.njit(cache=True)
+def do_1d(field, spacing, axis=0):
+    """
+    Compute 1D finite difference along specified axis.
+
+    Parameters
+    ----------
+    field : np.ndarray
+        Input field
+    spacing : float
+        Grid spacing
+    axis : int, default=0
+        Axis along which to compute difference
+
+    Returns
+    -------
+    np.ndarray
+        Finite difference result
+    """
+    if field.ndim == 2:
+        if axis == 0:
+            return (field[1:, :] - field[:-1, :]) / spacing
+        elif axis == 1:
+            return (field[:, 1:] - field[:, :-1]) / spacing
+        else:
+            raise ValueError("axis must be 0 or 1 for 2D arrays")
+    elif field.ndim == 3:
+        if axis == 0:
+            return (field[1:, :, :] - field[:-1, :, :]) / spacing
+        elif axis == 1:
+            return (field[:, 1:, :] - field[:, :-1, :]) / spacing
+        elif axis == 2:
+            return (field[:, :, 1:] - field[:, :, :-1]) / spacing
+        else:
+            raise ValueError("axis must be 0, 1, or 2 for 3D arrays")
+    else:
+        raise ValueError("field must be 2D or 3D array")
diff --git a/src/pybella/utils/operators/gradient.py b/src/pybella/utils/operators/gradient.py
new file mode 100644
index 00000000..a6606d3d
--- /dev/null
+++ b/src/pybella/utils/operators/gradient.py
@@ -0,0 +1,253 @@
+import numpy as np
+import numba as nb
+from . import finite_difference
+
+
+@nb.njit(cache=True)
+def compute_gradient_2d(field, dx, dy):
+    """
+    Compute 2D gradient: ∇φ = (∂φ/∂x, ∂φ/∂y)
+
+    Parameters
+    ----------
+    field : np.ndarray
+        Scalar field
+    dx : float
+        Grid spacing in x-direction
+    dy : float
+        Grid spacing in y-direction
+
+    Returns
+    -------
+    tuple
+        (grad_x, grad_y) - Gradient components
+    """
+    grad_x = finite_difference.do_1d(field, dx, axis=0)
+    grad_y = finite_difference.do_1d(field, dy, axis=1)
+
+    return grad_x, grad_y
+
+
+@nb.njit(cache=True)
+def compute_gradient_3d(field, dx, dy, dz):
+    """
+    Compute 3D gradient: ∇φ = (∂φ/∂x, ∂φ/∂y, ∂φ/∂z)
+
+    Parameters
+    ----------
+    field : np.ndarray
+        Scalar field
+    dx : float
+        Grid spacing in x-direction
+    dy : float
+        Grid spacing in y-direction
+    dz : float
+        Grid spacing in z-direction
+
+    Returns
+    -------
+    tuple
+        (grad_x, grad_y, grad_z) - Gradient components
+    """
+    grad_x = finite_difference.do_1d(field, dx, axis=0)
+    grad_y = finite_difference.do_1d(field, dy, axis=1)
+    grad_z = finite_difference.do_1d(field, dz, axis=2)
+
+    return grad_x, grad_y, grad_z
+
+
+#######
+# Compute gradient at nodes
+#######
+
+
+@nb.njit(cache=True)
+def _compute_grad_nodes_2d(p, dx, dy):
+    """Compute 2D gradient at nodes using corner averaging."""
+    # Pre-computed signs for each corner
+    signs_x = np.array([-1.0, -1.0, +1.0, +1.0])
+    signs_y = np.array([-1.0, +1.0, -1.0, +1.0])
+
+    # Initialize gradient components
+    Dpx = np.zeros((p.shape[0] - 1, p.shape[1] - 1))
+    Dpy = np.zeros((p.shape[0] - 1, p.shape[1] - 1))
+
+    # Corner contributions
+    # Bottom-left
+    Dpx += signs_x[0] * p[0:-1, 0:-1]
+    Dpy += signs_y[0] * p[0:-1, 0:-1]
+
+    # Bottom-right
+    Dpx += signs_x[1] * p[0:-1, 1:]
+    Dpy += signs_y[1] * p[0:-1, 1:]
+
+    # Top-left
+    Dpx += signs_x[2] * p[1:, 0:-1]
+    Dpy += signs_y[2] * p[1:, 0:-1]
+
+    # Top-right
+    Dpx += signs_x[3] * p[1:, 1:]
+    Dpy += signs_y[3] * p[1:, 1:]
+
+    # Apply scaling factors
+    scale_factor = 0.5 ** (2 - 1)  # 0.5^(ndim-1)
+    Dpx *= scale_factor / dx
+    Dpy *= scale_factor / dy
+
+    return Dpx, Dpy
+
+
+@nb.njit(cache=True)
+def _compute_grad_nodes_3d(p, dx, dy, dz):
+    """Compute 3D gradient at nodes using corner averaging."""
+    # Pre-computed signs for each corner
+    signs_x = np.array([-1.0, -1.0, -1.0, -1.0, +1.0, +1.0, +1.0, +1.0])
+    signs_y = np.array([-1.0, -1.0, +1.0, +1.0, -1.0, -1.0, +1.0, +1.0])
+    signs_z = np.array([-1.0, +1.0, -1.0, +1.0, -1.0, +1.0, -1.0, +1.0])
+
+    # Initialize gradient components
+    Dpx = np.zeros((p.shape[0] - 1, p.shape[1] - 1, p.shape[2] - 1))
+    Dpy = np.zeros((p.shape[0] - 1, p.shape[1] - 1, p.shape[2] - 1))
+    Dpz = np.zeros((p.shape[0] - 1, p.shape[1] - 1, p.shape[2] - 1))
+
+    # Corner contributions (8 corners for 3D)
+    # Bottom-left-back
+    Dpx += signs_x[0] * p[0:-1, 0:-1, 0:-1]
+    Dpy += signs_y[0] * p[0:-1, 0:-1, 0:-1]
+    Dpz += signs_z[0] * p[0:-1, 0:-1, 0:-1]
+
+    # Bottom-left-front
+    Dpx += signs_x[1] * p[0:-1, 0:-1, 1:]
+    Dpy += signs_y[1] * p[0:-1, 0:-1, 1:]
+    Dpz += signs_z[1] * p[0:-1, 0:-1, 1:]
+
+    # Bottom-right-back
+    Dpx += signs_x[2] * p[0:-1, 1:, 0:-1]
+    Dpy += signs_y[2] * p[0:-1, 1:, 0:-1]
+    Dpz += signs_z[2] * p[0:-1, 1:, 0:-1]
+
+    # Bottom-right-front
+    Dpx += signs_x[3] * p[0:-1, 1:, 1:]
+    Dpy += signs_y[3] * p[0:-1, 1:, 1:]
+    Dpz += signs_z[3] * p[0:-1, 1:, 1:]
+
+    # Top-left-back
+    Dpx += signs_x[4] * p[1:, 0:-1, 0:-1]
+    Dpy += signs_y[4] * p[1:, 0:-1, 0:-1]
+    Dpz += signs_z[4] * p[1:, 0:-1, 0:-1]
+
+    # Top-left-front
+    Dpx += signs_x[5] * p[1:, 0:-1, 1:]
+    Dpy += signs_y[5] * p[1:, 0:-1, 1:]
+    Dpz += signs_z[5] * p[1:, 0:-1, 1:]
+
+    # Top-right-back
+    Dpx += signs_x[6] * p[1:, 1:, 0:-1]
+    Dpy += signs_y[6] * p[1:, 1:, 0:-1]
+    Dpz += signs_z[6] * p[1:, 1:, 0:-1]
+
+    # Top-right-front
+    Dpx += signs_x[7] * p[1:, 1:, 1:]
+    Dpy += signs_y[7] * p[1:, 1:, 1:]
+    Dpz += signs_z[7] * p[1:, 1:, 1:]
+
+    # Apply scaling factors
+    scale_factor = 0.5 ** (3 - 1)  # 0.5^(ndim-1)
+    Dpx *= scale_factor / dx
+    Dpy *= scale_factor / dy
+    Dpz *= scale_factor / dz
+
+    return Dpx, Dpy, Dpz
+
+
+@nb.njit(cache=True)
+def compute_gradient_nodes_2d(p, dx, dy):
+    """
+    Compute gradient at nodes using finite difference averaging.
+
+    Parameters
+    ----------
+    p : np.ndarray
+        Scalar field (2D)
+    dx : float
+        Grid spacing in x-direction
+    dy : float
+        Grid spacing in y-direction
+
+    Returns
+    -------
+    tuple
+        (grad_x, grad_y) - Gradient components at nodes
+
+    Notes
+    -----
+    The gradient is computed at nodes by averaging contributions from
+    all neighboring cells. Output arrays have shape (nx-1, ny-1).
+    """
+    return _compute_grad_nodes_2d(p, dx, dy)
+
+
+@nb.njit(cache=True)
+def compute_gradient_nodes_3d(p, dx, dy, dz):
+    """
+    Compute gradient at nodes using finite difference averaging.
+
+    Parameters
+    ----------
+    p : np.ndarray
+        Scalar field (3D)
+    dx : float
+        Grid spacing in x-direction
+    dy : float
+        Grid spacing in y-direction
+    dz : float
+        Grid spacing in z-direction
+
+    Returns
+    -------
+    tuple
+        (grad_x, grad_y, grad_z) - Gradient components at nodes
+
+    Notes
+    -----
+    The gradient is computed at nodes by averaging contributions from
+    all neighboring cells. Output arrays have shape (nx-1, ny-1, nz-1).
+    """
+    return _compute_grad_nodes_3d(p, dx, dy, dz)
+
+
+def compute_at_nodes(p, ndim, dxy):
+    """
+    Compute gradient at nodes using finite difference averaging.
+
+    Parameters
+    ----------
+    p : np.ndarray
+        Scalar field
+    ndim : int
+        Number of dimensions (2 or 3)
+    dxy : tuple
+        Grid spacings (dx, dy, dz)
+
+    Returns
+    -------
+    tuple
+        Gradient components at nodes. For 2D: (grad_x, grad_y, zeros)
+        For 3D: (grad_x, grad_y, grad_z)
+
+    Notes
+    -----
+    This is the main interface function that dispatches to the appropriate
+    dimension-specific implementation. Always returns 3 components for
+    consistency, with the z-component being zero for 2D cases.
+    """
+    dx, dy, dz = dxy
+
+    if ndim == 2:
+        grad_x, grad_y = compute_gradient_nodes_2d(p, dx, dy)
+        grad_z = np.zeros_like(grad_x)
+        return grad_x, grad_y, grad_z
+    elif ndim == 3:
+        return compute_gradient_nodes_3d(p, dx, dy, dz)
+    else:
+        raise ValueError(f"Unsupported dimension: {ndim}")
diff --git a/src/pybella/utils/operators/laplacian/__init__.py b/src/pybella/utils/operators/laplacian/__init__.py
new file mode 100644
index 00000000..e69de29b
diff --git a/src/pybella/utils/operators/laplacian/lap2D_manual.py b/src/pybella/utils/operators/laplacian/lap2D_manual.py
new file mode 100644
index 00000000..a17d4d4b
--- /dev/null
+++ b/src/pybella/utils/operators/laplacian/lap2D_manual.py
@@ -0,0 +1,249 @@
+import numpy as np
+import numba as nb
+from ... import options as opts
+
+
+def get_linop(npf, node, coriolis, diag_inv, ud):
+    dx = node.dx
+    dy = node.dy
+
+    if hasattr(ud, "ATMOSPHERIC_EXTENSION") and ud.ATMOSPHERIC_EXTENSION:
+        y_atmosphere = True
+    else:
+        y_atmosphere = False
+
+    ###################
+    x_wall = ud.bdry_type[0] == opts.BdryType.WALL
+    y_wall = ud.bdry_type[1] == opts.BdryType.WALL
+
+    cor_slc = (slice(1, -1), slice(1, -1))
+    coeff_slc = (slice(1, -1), slice(1, -1))
+
+    # Coefficient extraction
+    hplusx = np.ravel(npf.wplus[0][coeff_slc], order="F")
+    hplusy = np.ravel(npf.wplus[1][coeff_slc], order="F")
+    hcenter = np.ravel(npf.wcenter[node.i1], order="F")
+
+    # Coriolis terms
+    cxx = np.ravel(coriolis[0][cor_slc], order="C")
+    cyy = np.ravel(coriolis[1][cor_slc], order="C")
+    cxy = np.ravel(coriolis[2][cor_slc], order="C")
+    cyx = np.ravel(coriolis[3][cor_slc], order="C")
+
+    # Diagonal inverse
+    dinv = np.ravel(diag_inv[node.i1], order="F")
+
+    # Pack as tuples
+    coeffs = (hplusx, hplusy, hcenter)
+    coriolis = (cxx, cyy, cxy, cyx)
+
+    return lambda p: lap2D_gather(
+        p,
+        node.iicx,
+        node.iicy,
+        coeffs,
+        dx,
+        dy,
+        x_wall,
+        y_wall,
+        y_atmosphere,
+        dinv,
+        coriolis,
+    )
+
+
+@nb.njit(cache=True)
+def lap2D_gather(
+    p, iicxn, iicyn, coeffs, dx, dy, x_wall, y_wall, y_atmosphere, diag_inv, coriolis
+):
+    ngnc = (iicxn) * (iicyn)
+    lap = np.zeros((ngnc))
+    cnt_x = 0
+    cnt_y = 0
+
+    oodx = 1.0 / dx
+    oody = 1.0 / dy
+    cxx, cyy, cxy, cyx = coriolis
+
+    hplusx, hplusy, hcenter = coeffs
+
+    for idx in range(iicxn * iicyn):
+        nr_row = idx // iicxn
+        col_idx = idx - (nr_row * iicxn)
+
+        ne_row_idx = nr_row * (iicxn + 1)
+        ne_col_idx = col_idx
+        ne_idx = ne_row_idx + ne_col_idx
+
+        ne_topleft = ne_idx
+        ne_topright = ne_idx + 1
+        ne_botleft = ne_idx + (iicxn + 1)
+        ne_botright = ne_idx + (iicxn + 1) + 1
+
+        # get indices of the 9pt stencil
+        topleft_idx = idx - iicxn - 1
+        midleft_idx = idx - 1
+        botleft_idx = idx + iicxn - 1
+
+        topmid_idx = idx - iicxn
+        midmid_idx = idx
+        botmid_idx = idx + iicxn
+
+        topright_idx = idx - iicxn + 1
+        midright_idx = idx + 1
+        botright_idx = idx + iicxn + 1
+
+        if cnt_x == 0:
+            topleft_idx += iicxn - 1
+            midleft_idx += iicxn - 1
+            botleft_idx += iicxn - 1
+
+        if cnt_x == (iicxn - 1):
+            topright_idx -= iicxn - 1
+            midright_idx -= iicxn - 1
+            botright_idx -= iicxn - 1
+
+        val = 0
+
+        if cnt_y == 0:
+            if y_atmosphere:
+                topleft_idx += 2 * (iicxn - val)
+                topmid_idx += 2 * (iicxn - val)
+                topright_idx += 2 * (iicxn - val)
+            else:
+                topleft_idx += (iicxn) * (iicyn - 1)
+                topmid_idx += (iicxn) * (iicyn - 1)
+                topright_idx += (iicxn) * (iicyn - 1)
+
+        if cnt_y == (iicyn - 1):
+            if y_atmosphere:
+                botleft_idx -= 2 * (iicxn - val)
+                botmid_idx -= 2 * (iicxn - val)
+                botright_idx -= 2 * (iicxn - val)
+            else:
+                botleft_idx -= (iicxn) * (iicyn - 1)
+                botmid_idx -= (iicxn) * (iicyn - 1)
+                botright_idx -= (iicxn) * (iicyn - 1)
+
+        topleft = p[topleft_idx]
+        midleft = p[midleft_idx]
+        botleft = p[botleft_idx]
+
+        topmid = p[topmid_idx]
+        midmid = p[midmid_idx]
+        botmid = p[botmid_idx]
+
+        topright = p[topright_idx]
+        midright = p[midright_idx]
+        botright = p[botright_idx]
+
+        hplusx_topleft = hplusx[ne_topleft]
+        hplusx_botleft = hplusx[ne_botleft]
+        hplusy_topleft = hplusy[ne_topleft]
+        hplusy_botleft = hplusy[ne_botleft]
+
+        hplusx_topright = hplusx[ne_topright]
+        hplusx_botright = hplusx[ne_botright]
+        hplusy_topright = hplusy[ne_topright]
+        hplusy_botright = hplusy[ne_botright]
+
+        cxx_tl = cxx[ne_topleft]
+        cxx_tr = cxx[ne_topright]
+        cxx_bl = cxx[ne_botleft]
+        cxx_br = cxx[ne_botright]
+
+        cxy_tl = cxy[ne_topleft]
+        cxy_tr = cxy[ne_topright]
+        cxy_bl = cxy[ne_botleft]
+        cxy_br = cxy[ne_botright]
+
+        cyx_tl = cyx[ne_topleft]
+        cyx_tr = cyx[ne_topright]
+        cyx_bl = cyx[ne_botleft]
+        cyx_br = cyx[ne_botright]
+
+        cyy_tl = cyy[ne_topleft]
+        cyy_tr = cyy[ne_topright]
+        cyy_bl = cyy[ne_botleft]
+        cyy_br = cyy[ne_botright]
+
+        if x_wall and (cnt_x == 0):
+            hplusx_topleft = 0.0
+            hplusy_topleft = 0.0
+            hplusx_botleft = 0.0
+            hplusy_botleft = 0.0
+
+        if x_wall and (cnt_x == (iicxn - 1)):
+            hplusx_topright = 0.0
+            hplusy_topright = 0.0
+            hplusx_botright = 0.0
+            hplusy_botright = 0.0
+
+        if y_wall and (cnt_y == 0):
+            if y_atmosphere:
+                pass
+            else:
+                hplusx_topleft = 0.0
+                hplusy_topleft = 0.0
+                hplusx_topright = 0.0
+                hplusy_topright = 0.0
+
+        if y_wall and (cnt_y == (iicyn - 1)):
+            if y_atmosphere:
+                pass
+            else:
+                hplusx_botleft = 0.0
+                hplusy_botleft = 0.0
+                hplusx_botright = 0.0
+                hplusy_botright = 0.0
+
+        Dx_tl = 0.5 * (topmid - topleft + midmid - midleft) * hplusx_topleft
+        Dx_tr = 0.5 * (topright - topmid + midright - midmid) * hplusx_topright
+        Dx_bl = 0.5 * (botmid - botleft + midmid - midleft) * hplusx_botleft
+        Dx_br = 0.5 * (botright - botmid + midright - midmid) * hplusx_botright
+
+        Dy_tl = 0.5 * (midmid - topmid + midleft - topleft) * hplusy_topleft
+        Dy_tr = 0.5 * (midright - topright + midmid - topmid) * hplusy_topright
+        Dy_bl = 0.5 * (botmid - midmid + botleft - midleft) * hplusy_botleft
+        Dy_br = 0.5 * (botright - midright + botmid - midmid) * hplusy_botright
+
+        fac = 1.0
+        Dxx = (
+            0.5
+            * (cxx_tr * Dx_tr - cxx_tl * Dx_tl + cxx_br * Dx_br - cxx_bl * Dx_bl)
+            * oodx
+            * oodx
+            * fac
+        )
+        Dyy = (
+            0.5
+            * (cyy_br * Dy_br - cyy_tr * Dy_tr + cyy_bl * Dy_bl - cyy_tl * Dy_tl)
+            * oody
+            * oody
+            * fac
+        )
+        Dyx = (
+            0.5
+            * (cxy_br * Dy_br - cxy_bl * Dy_bl + cxy_tr * Dy_tr - cxy_tl * Dy_tl)
+            * oody
+            * oodx
+            * fac
+        )
+        Dxy = (
+            0.5
+            * (cyx_br * Dx_br - cyx_tr * Dx_tr + cyx_bl * Dx_bl - cyx_tl * Dx_tl)
+            * oodx
+            * oody
+            * fac
+        )
+
+        lap[idx] = Dxx + Dyy + Dyx + Dxy + hcenter[idx] * p[idx]
+
+        lap[idx] *= diag_inv[idx]
+
+        cnt_x += 1
+        if cnt_x % iicxn == 0:
+            cnt_y += 1
+            cnt_x = 0
+
+    return lap
diff --git a/src/pybella/utils/operators/laplacian/lap2D_numba.py b/src/pybella/utils/operators/laplacian/lap2D_numba.py
new file mode 100644
index 00000000..314f152d
--- /dev/null
+++ b/src/pybella/utils/operators/laplacian/lap2D_numba.py
@@ -0,0 +1,203 @@
+import numpy as np
+import numba as nb
+from ... import options as opts
+
+
+def get_linop(npf, node, coriolis, diag_inv, ud):
+    dx = node.dx
+    dy = node.dy
+
+    hplusx = npf.wplus[0]
+    hplusy = npf.wplus[1]
+    hcenter = npf.wcenter
+
+    coeffs = [hplusx.T, hplusy.T, hcenter.T]
+
+    shp = node.iisc
+
+    dummy_p = np.zeros((node.isc[1], node.isc[0]))
+
+    if hasattr(ud, "ATMOSPHERIC_EXTENSION") and ud.ATMOSPHERIC_EXTENSION:
+        boundary_handler = periodic_x_wall_y
+    else:
+        boundary_handler = periodic
+
+        x_wall = (
+            ud.bdry_type[0] == opts.BdryType.WALL
+            or ud.bdry_type[0] == opts.BdryType.RAYLEIGH
+        )
+        y_wall = (
+            ud.bdry_type[1] == opts.BdryType.WALL
+            or ud.bdry_type[1] == opts.BdryType.RAYLEIGH
+        )
+
+        if x_wall:
+            coeffs[0], coeffs[1] = apply_x_wall_boundary_coeffs(coeffs[0], coeffs[1])
+        if y_wall:
+            coeffs[0], coeffs[1] = apply_y_wall_boundary_coeffs(coeffs[0], coeffs[1])
+
+    return lambda p: lap2D_generic(
+        p, dummy_p, dx, dy, coeffs, diag_inv.T, coriolis, shp, boundary_handler
+    )
+
+
+@nb.njit(cache=True)
+def lap2D_generic(p, dp, dx, dy, coeffs, diag_inv, coriolis, shp, boundary_handler):
+    p = p.reshape(shp[1], shp[0])
+    dp[1:-1, 1:-1] = p
+
+    dp[...] = boundary_handler(dp)
+    dp[...] = kernel_9pt(
+        dp,
+        dx,
+        dy,
+        coeffs[0],
+        coeffs[1],
+        coeffs[2],
+        diag_inv,
+        coriolis[0],
+        coriolis[1],
+        coriolis[2],
+        coriolis[3],
+    )
+
+    return dp[1:-1, 1:-1].ravel()
+
+
+@nb.njit(cache=True)
+def periodic_x_wall_y(arr):
+    # periodic padding
+    arr[:, 0] = arr[:, -3]
+    arr[:, -1] = arr[:, 2]
+
+    # wall padding
+    arr[0, :] = arr[2, :]
+    arr[-1, :] = arr[-3, :]
+
+    return arr
+
+
+@nb.njit(cache=True)
+def periodic(arr):
+    """Apply periodic boundary conditions"""
+    arr[:, 0] = arr[:, -3]
+    arr[:, -1] = arr[:, 2]
+    arr[0, :] = arr[-3, :]
+    arr[-1, :] = arr[2, :]
+
+    return arr
+
+
+@nb.njit(cache=True)
+def apply_x_wall_boundary_coeffs(hpx, hpy):
+    """Apply wall boundary conditions by modifying coefficients"""
+    hpx[:, 0] = 0.0
+    hpy[:, 0] = 0.0
+    hpx[:, -1] = 0.0
+    hpy[:, -1] = 0.0
+    hpx[:, 1] = 0.0
+    hpy[:, 1] = 0.0
+    hpx[:, -2] = 0.0
+    hpy[:, -2] = 0.0
+
+    return hpx, hpy
+
+
+@nb.njit(cache=True)
+def apply_y_wall_boundary_coeffs(hpx, hpy):
+    """Apply wall boundary conditions by modifying coefficients"""
+    hpx[0, :] = 0.0
+    hpy[0, :] = 0.0
+    hpx[-1, :] = 0.0
+    hpy[-1, :] = 0.0
+    hpx[1, :] = 0.0
+    hpy[1, :] = 0.0
+    hpx[-2, :] = 0.0
+    hpy[-2, :] = 0.0
+
+    return hpx, hpy
+
+
+@nb.stencil
+def kernel_9pt(a, dx, dy, hpx, hpy, hpc, diag_inv, cxx, cyy, cxy, cyx):
+    oodx = 1.0 / dx
+    oody = 1.0 / dy
+
+    topleft = a[1, -1]
+    topmid = a[1, 0]
+    topright = a[1, 1]
+
+    midleft = a[0, -1]
+    midmid = a[0, 0]
+    midright = a[0, 1]
+
+    botleft = a[-1, -1]
+    botmid = a[-1, 0]
+    botright = a[-1, 1]
+
+    hpx_bl = hpx[0, 0]
+    hpx_br = hpx[0, 1]
+    hpx_tl = hpx[1, 0]
+    hpx_tr = hpx[1, 1]
+
+    hpy_bl = hpy[0, 0]
+    hpy_br = hpy[0, 1]
+    hpy_tl = hpy[1, 0]
+    hpy_tr = hpy[1, 1]
+
+    cxx_bl = cxx[0, 0]
+    cxx_br = cxx[0, 1]
+    cxx_tl = cxx[1, 0]
+    cxx_tr = cxx[1, 1]
+
+    cyy_bl = cyy[0, 0]
+    cyy_br = cyy[0, 1]
+    cyy_tl = cyy[1, 0]
+    cyy_tr = cyy[1, 1]
+
+    cxy_bl = cxy[0, 0]
+    cxy_br = cxy[0, 1]
+    cxy_tl = cxy[1, 0]
+    cxy_tr = cxy[1, 1]
+
+    cyx_bl = cyx[0, 0]
+    cyx_br = cyx[0, 1]
+    cyx_tl = cyx[1, 0]
+    cyx_tr = cyx[1, 1]
+
+    Dx_tl = 0.5 * (topmid - topleft + midmid - midleft) * hpx_tl
+    Dx_tr = 0.5 * (topright - topmid + midright - midmid) * hpx_tr
+    Dx_bl = 0.5 * (botmid - botleft + midmid - midleft) * hpx_bl
+    Dx_br = 0.5 * (botright - botmid + midright - midmid) * hpx_br
+
+    Dy_tl = 0.5 * (topmid - midmid + topleft - midleft) * hpy_tl
+    Dy_tr = 0.5 * (topright - midright + topmid - midmid) * hpy_tr
+    Dy_bl = 0.5 * (midmid - botmid + midleft - botleft) * hpy_bl
+    Dy_br = 0.5 * (midright - botright + midmid - botmid) * hpy_br
+
+    Dxx = (
+        0.5
+        * (cxx_tr * Dx_tr - cxx_tl * Dx_tl + cxx_br * Dx_br - cxx_bl * Dx_bl)
+        * oodx
+        * oodx
+    )
+    Dyy = (
+        0.5
+        * (cyy_tr * Dy_tr - cyy_br * Dy_br + cyy_tl * Dy_tl - cyy_bl * Dy_bl)
+        * oody
+        * oody
+    )
+    Dyx = (
+        0.5
+        * (cxy_br * Dy_br - cxy_bl * Dy_bl + cxy_tr * Dy_tr - cxy_tl * Dy_tl)
+        * oody
+        * oodx
+    )
+    Dxy = (
+        0.5
+        * (cyx_tr * Dx_tr - cyx_br * Dx_br + cyx_tl * Dx_tl - cyx_bl * Dx_bl)
+        * oodx
+        * oody
+    )
+
+    return ((Dxx + Dyy + Dyx + Dxy) + hpc[0, 0] * a[0, 0]) * diag_inv[0, 0]
diff --git a/src/pybella/utils/operators/laplacian/lap3D.py b/src/pybella/utils/operators/laplacian/lap3D.py
new file mode 100644
index 00000000..5cd492f0
--- /dev/null
+++ b/src/pybella/utils/operators/laplacian/lap3D.py
@@ -0,0 +1,258 @@
+import numba as nb
+
+
+def get_linop(elem, node, npf, ud, diag_inv, dt):
+    oodxyz = node.dxyz
+    oodxyz = 1.0 / (oodxyz**2)
+    oodx2, oody2, oodz2 = oodxyz[0], oodxyz[1], oodxyz[2]
+    odx, odz = 1.0 / node.dx, 1.0 / node.dz
+
+    i0 = (slice(0, -1), slice(0, -1), slice(0, -1))
+    i1 = (slice(1, -1), slice(1, -1), slice(1, -1))
+    i2 = (slice(2, -2), slice(2, -2), slice(2, -2))
+
+    ndim = elem.ndim
+    periodicity = np.empty(ndim, dtype="int")
+    for dim in range(ndim):
+        periodicity[dim] = ud.bdry_type[dim] == opts.BdryType.PERIODIC
+
+    hplusx = npf.wplus[0][i0][i1]
+    hplusy = npf.wplus[1][i0][i1]
+    hplusz = npf.wplus[2][i0][i1]
+
+    hcenter = npf.wcenter[i2]
+    diag_inv = diag_inv[i1]
+
+    corrf = dt * ud.coriolis_strength[0]
+
+    return lambda p: lap3D(
+        p,
+        hplusx,
+        hplusy,
+        hplusz,
+        hcenter,
+        oodx2,
+        oody2,
+        oodz2,
+        periodicity,
+        diag_inv,
+        corrf,
+        odx,
+        odz,
+    )
+
+
+@nb.jit(nopython=True, cache=False, nogil=False)
+def lap3D(
+    p0,
+    hplusx,
+    hplusy,
+    hplusz,
+    hcenter,
+    oodx2,
+    oody2,
+    oodz2,
+    periodicity,
+    diag_inv,
+    corrf,
+    odx,
+    odz,
+):
+    shx, shy, shz = hcenter.shape
+    p = p0.reshape(shz + 2, shy + 2, shx + 2)
+
+    coeff = 1.0 / 16
+    lap = np.zeros_like(p)
+
+    # cut out four cubes from the 3d array corresponding to the nodes... in each axial direction.
+    toplefts = [
+        (slice(0, None), slice(0, -1), slice(0, -1)),
+        (slice(0, -1), slice(0, None), slice(0, -1)),
+        (slice(0, -1), slice(0, -1), slice(0, None)),
+    ]
+    toprights = [
+        (slice(0, None), slice(0, -1), slice(1, None)),
+        (slice(1, None), slice(0, None), slice(0, -1)),
+        (slice(0, -1), slice(1, None), slice(0, None)),
+    ]
+
+    botlefts = [
+        (slice(0, None), slice(1, None), slice(0, -1)),
+        (slice(0, -1), slice(0, None), slice(1, None)),
+        (slice(1, None), slice(0, -1), slice(0, None)),
+    ]
+    botrights = [
+        (slice(0, None), slice(1, None), slice(1, None)),
+        (slice(1, None), slice(0, None), slice(1, None)),
+        (slice(1, None), slice(1, None), slice(0, None)),
+    ]
+
+    cnt = 0
+    for bc in periodicity:
+        if bc == True and cnt == 0:
+            tmp = p[1, :, :]
+            p[0, :, :] = p[-3, :, :]
+            p[-1, :, :] = p[2, :, :]
+            p[1, :, :] = p[-2, :, :]
+            p[-2, :, :] = tmp
+        elif bc == False and cnt == 0:
+            hplusx[0, :, :] = 0.0
+            hplusx[-1, :, :] = 0.0
+            hplusy[0, :, :] = 0.0
+            hplusy[-1, :, :] = 0.0
+            hplusz[0, :, :] = 0.0
+            hplusz[-1, :, :] = 0.0
+        if bc == True and cnt == 1:
+            tmp = p[:, 1, :]
+            p[:, 0, :] = p[:, -3, :]
+            p[:, -1, :] = p[:, 2, :]
+            p[:, 1, :] = p[:, -2, :]
+            p[:, -2, :] = tmp
+        elif bc == False and cnt == 1:
+            hplusx[:, 0, :] = 0.0
+            hplusx[:, -1, :] = 0.0
+            hplusy[:, 0, :] = 0.0
+            hplusy[:, -1, :] = 0.0
+            hplusz[:, 0, :] = 0.0
+            hplusz[:, -1, :] = 0.0
+        if bc == True and cnt == 2:
+            tmp = p[:, :, 1]
+            p[:, :, 0] = p[:, :, -3]
+            p[:, :, -1] = p[:, :, 2]
+            p[:, :, 1] = p[:, :, -2]
+            p[:, :, -2] = tmp
+        elif bc == False and cnt == 2:
+            hplusx[:, :, 0] = 0.0
+            hplusx[:, :, -1] = 0.0
+            hplusy[:, :, 0] = 0.0
+            hplusy[:, :, -1] = 0.0
+            hplusz[:, :, 0] = 0.0
+            hplusz[:, :, -1] = 0.0
+        cnt += 1
+
+    leftz = p[:, :, :-1]
+    rightz = p[:, :, 1:]
+
+    z_fluxes = rightz - leftz
+
+    lefty = p[:, :-1, :]
+    righty = p[:, 1:, :]
+
+    y_fluxes = righty - lefty
+
+    leftx = p[:-1, :, :]
+    rightx = p[1:, :, :]
+
+    x_fluxes = rightx - leftx
+
+    x_flx = (
+        x_fluxes[toplefts[0]]
+        + x_fluxes[toprights[0]]
+        + x_fluxes[botlefts[0]]
+        + x_fluxes[botrights[0]]
+    )
+    y_flx = (
+        y_fluxes[toplefts[1]]
+        + y_fluxes[toprights[1]]
+        + y_fluxes[botlefts[1]]
+        + y_fluxes[botrights[1]]
+    )
+    z_flx = (
+        z_fluxes[toplefts[2]]
+        + z_fluxes[toprights[2]]
+        + z_fluxes[botlefts[2]]
+        + z_fluxes[botrights[2]]
+    )
+
+    hxzp = hplusx * z_flx
+    hxzpm = hxzp[:-1, :, :]
+    hxzpm = (
+        hxzpm[toplefts[0]]
+        + hxzpm[toprights[0]]
+        + hxzpm[botlefts[0]]
+        + hxzpm[botrights[0]]
+    )
+    hxzpp = hxzp[1:, :, :]
+    hxzpp = (
+        hxzpp[toplefts[0]]
+        + hxzpp[toprights[0]]
+        + hxzpp[botlefts[0]]
+        + hxzpp[botrights[0]]
+    )
+
+    hzxp = hplusz * x_flx
+    hzxpm = hzxp[:, :, :-1]
+    hzxpm = (
+        hzxpm[toplefts[2]]
+        + hzxpm[toprights[2]]
+        + hzxpm[botlefts[2]]
+        + hzxpm[botrights[2]]
+    )
+    hzxpp = hzxp[:, :, 1:]
+    hzxpp = (
+        hzxpp[toplefts[2]]
+        + hzxpp[toprights[2]]
+        + hzxpp[botlefts[2]]
+        + hzxpp[botrights[2]]
+    )
+
+    x_flx = hplusx * x_flx
+    x_flxm = x_flx[:-1, :, :]
+    x_flxm = (
+        x_flxm[toplefts[0]]
+        + x_flxm[toprights[0]]
+        + x_flxm[botlefts[0]]
+        + x_flxm[botrights[0]]
+    )
+    x_flxp = x_flx[1:, :, :]
+    x_flxp = (
+        x_flxp[toplefts[0]]
+        + x_flxp[toprights[0]]
+        + x_flxp[botlefts[0]]
+        + x_flxp[botrights[0]]
+    )
+
+    y_flx = hplusy * y_flx
+    y_flxm = y_flx[:, :-1, :]
+    y_flxm = (
+        y_flxm[toplefts[1]]
+        + y_flxm[toprights[1]]
+        + y_flxm[botlefts[1]]
+        + y_flxm[botrights[1]]
+    )
+    y_flxp = y_flx[:, 1:, :]
+    y_flxp = (
+        y_flxp[toplefts[1]]
+        + y_flxp[toprights[1]]
+        + y_flxp[botlefts[1]]
+        + y_flxp[botrights[1]]
+    )
+
+    z_flx = hplusz * z_flx
+    z_flxm = z_flx[:, :, :-1]
+    z_flxm = (
+        z_flxm[toplefts[2]]
+        + z_flxm[toprights[2]]
+        + z_flxm[botlefts[2]]
+        + z_flxm[botrights[2]]
+    )
+    z_flxp = z_flx[:, :, 1:]
+    z_flxp = (
+        z_flxp[toplefts[2]]
+        + z_flxp[toprights[2]]
+        + z_flxp[botlefts[2]]
+        + z_flxp[botrights[2]]
+    )
+
+    lap[1:-1, 1:-1, 1:-1] = (
+        oodx2 * coeff * (-x_flxm + x_flxp)
+        + oody2 * coeff * (-y_flxm + y_flxp)
+        + oodz2 * coeff * (-z_flxm + z_flxp)
+        + +1.0 * odx * odz * coeff * corrf * (hxzpp - hxzpm)
+        + -1.0 * odx * odz * coeff * corrf * (hzxpp - hzxpm)
+        + hcenter * p[1:-1, 1:-1, 1:-1]
+    )
+
+    lap = lap * diag_inv
+
+    return lap
diff --git a/src/pybella/utils/operators/laplacian/preconditioner.py b/src/pybella/utils/operators/laplacian/preconditioner.py
new file mode 100644
index 00000000..3a6045b6
--- /dev/null
+++ b/src/pybella/utils/operators/laplacian/preconditioner.py
@@ -0,0 +1,52 @@
+from .. import convolution
+
+
+def prepare_diag(npf, node):
+    """Highly optimized version with minimal function calls."""
+    ndim = node.ndim
+
+    coeff = 0.75 if ndim == 2 else 0.0625 if ndim == 3 else None
+    if coeff is None:
+        raise ValueError(f"Unsupported ndim: {ndim}")
+
+    dx, dy, dz = node.dx, node.dy, node.dz
+    inv_dx2, inv_dy2 = 1.0 / (dx**2), 1.0 / (dy**2)
+
+    diag_kernel = convolution.get_averaging_kernel(ndim, width=2)
+
+    diag = npf.wcenter.copy()
+
+    # Main diagonal terms
+    diag -= (
+        coeff
+        * inv_dx2
+        * convolution.apply_convolution_kernel(npf.wplus[0], diag_kernel)
+    )
+    diag -= (
+        coeff
+        * inv_dy2
+        * convolution.apply_convolution_kernel(npf.wplus[1], diag_kernel)
+    )
+
+    if ndim == 2:
+        # Cross terms
+        inv_dxdy = 1.0 / (dx * dy)
+        diag -= (
+            coeff
+            * inv_dxdy
+            * convolution.apply_convolution_kernel(npf.wplus[0], diag_kernel)
+        )
+        diag -= (
+            coeff
+            * inv_dxdy
+            * convolution.apply_convolution_kernel(npf.wplus[1], diag_kernel)
+        )
+    elif ndim == 3:
+        inv_dz2 = 1.0 / (dz**2)
+        diag -= (
+            coeff
+            * inv_dz2
+            * convolution.apply_convolution_kernel(npf.wplus[2], diag_kernel)
+        )
+
+    return 1.0 / diag
diff --git a/src/pybella/utils/slices.py b/src/pybella/utils/slices.py
index b53a51bc..0c0f5152 100644
--- a/src/pybella/utils/slices.py
+++ b/src/pybella/utils/slices.py
@@ -1,12 +1,15 @@
+import numpy as np
+from . import options as opts
+
 
 def get_neighbor_indices(ndim):
     """Create left and right neighbor indices for n-dimensional arrays."""
     lefts_idx = [slice(None)] * ndim
     rights_idx = [slice(None)] * ndim
-    
+
     lefts_idx[-1] = slice(0, -1)
     rights_idx[-1] = slice(1, None)
-    
+
     return tuple(lefts_idx), tuple(rights_idx)
 
 
@@ -14,6 +17,7 @@ def get_inner_slice(ndim):
     """Get slice tuple for inner cells (excluding outermost ghost cells)."""
     return tuple([slice(1, -1)] * ndim)
 
+
 def get_last_dim_inner_slice(ndim):
     """Get slice for inner faces in the last dimension only."""
     idx = [slice(None)] * ndim
@@ -24,35 +28,35 @@ def get_last_dim_inner_slice(ndim):
 def get_interface_indices(ndim):
     """
     Get complete set of indices for interface calculations.
-    
+
     Parameters
     ----------
     ndim : int
         Number of dimensions
-        
+
     Returns
     -------
     tuple
         (lefts_idx, rights_idx, inner_idx) where:
         - lefts_idx: indices for left neighbors
-        - rights_idx: indices for right neighbors  
+        - rights_idx: indices for right neighbors
         - inner_idx: indices for inner cells (face_inner_idx)
     """
     lefts_idx, rights_idx = get_neighbor_indices(ndim)
     inner_idx = get_inner_slice(ndim)
-    
+
     return lefts_idx, rights_idx, inner_idx
 
 
 def get_all_slice_indices(ndim):
     """
     Get all commonly used slice indices for finite volume calculations.
-    
+
     Parameters
     ----------
     ndim : int
         Number of dimensions
-        
+
     Returns
     -------
     dict
@@ -63,27 +67,26 @@ def get_all_slice_indices(ndim):
         - 'face_inner': face inner indices (alias for inner)
     """
     lefts_idx, rights_idx, inner_idx = get_interface_indices(ndim)
-    
+
     return {
-        'lefts': lefts_idx,
-        'rights': rights_idx, 
-        'inner': inner_idx,
-        'face_inner': inner_idx  # alias for clarity in interface flux calculations
+        "lefts": lefts_idx,
+        "rights": rights_idx,
+        "inner": inner_idx,
+        "face_inner": inner_idx,  # alias for clarity in interface flux calculations
     }
 
 
-
 def get_averaging_indices(ndim, axis):
     """
     Get indices for averaging along a specific axis.
-    
+
     Parameters
     ----------
     ndim : int
         Number of dimensions
     axis : int
         Axis along which to average
-        
+
     Returns
     -------
     tuple
@@ -91,17 +94,17 @@ def get_averaging_indices(ndim, axis):
     """
     left_idx = [slice(None)] * ndim
     right_idx = [slice(None)] * ndim
-    
+
     left_idx[axis] = slice(0, -1)
     right_idx[axis] = slice(1, None)
-    
+
     return tuple(left_idx), tuple(right_idx)
 
 
 def get_periodic_inner_slice(igs, is_periodic, ndim):
     """
     Get inner slice accounting for periodic boundary conditions.
-    
+
     Parameters
     ----------
     igs : array-like
@@ -110,7 +113,7 @@ def get_periodic_inner_slice(igs, is_periodic, ndim):
         Boolean array indicating periodic boundaries
     ndim : int
         Number of dimensions
-        
+
     Returns
     -------
     tuple
@@ -119,21 +122,25 @@ def get_periodic_inner_slice(igs, is_periodic, ndim):
     inner_idx = []
     for dim in range(ndim):
         start = igs[dim] - int(is_periodic[dim])
-        end = -igs[dim] + int(is_periodic[dim]) if igs[dim] > int(is_periodic[dim]) else None
+        end = (
+            -igs[dim] + int(is_periodic[dim])
+            if igs[dim] > int(is_periodic[dim])
+            else None
+        )
         inner_idx.append(slice(start, end))
-    
+
     return tuple(inner_idx)
 
 
 def get_face_center_averaging_indices(ndim):
     """
     Get indices for averaging finite difference results to face centers.
-    
+
     Parameters
     ----------
     ndim : int
         Number of dimensions
-        
+
     Returns
     -------
     dict
@@ -141,23 +148,75 @@ def get_face_center_averaging_indices(ndim):
         or 'y_avg', 'x_avg', 'z_avg' for 3D averaging operations
     """
     indices = {}
-    
+
     if ndim >= 2:
         # For averaging in y-direction (axis=1)
-        indices['y_avg'] = (slice(None, -1), slice(None))
-        indices['y_avg_right'] = (slice(1, None), slice(None))
-        
-        # For averaging in x-direction (axis=0)  
-        indices['x_avg'] = (slice(None), slice(None, -1))
-        indices['x_avg_right'] = (slice(None), slice(1, None))
-        
+        indices["y_avg"] = (slice(None, -1), slice(None))
+        indices["y_avg_right"] = (slice(1, None), slice(None))
+
+        # For averaging in x-direction (axis=0)
+        indices["x_avg"] = (slice(None), slice(None, -1))
+        indices["x_avg_right"] = (slice(None), slice(1, None))
+
     if ndim == 3:
         # For averaging in z-direction (axis=2)
-        indices['z_avg'] = (slice(None), slice(None), slice(None, -1))
-        indices['z_avg_right'] = (slice(None), slice(None), slice(1, None))
-        
+        indices["z_avg"] = (slice(None), slice(None), slice(None, -1))
+        indices["z_avg_right"] = (slice(None), slice(None), slice(1, None))
+
         # 3D specific averaging combinations
-        indices['xy_avg'] = (slice(None, -1), slice(None, -1), slice(None))
-        indices['xy_avg_right'] = (slice(1, None), slice(1, None), slice(None))
-        
-    return indices
\ No newline at end of file
+        indices["xy_avg"] = (slice(None, -1), slice(None, -1), slice(None))
+        indices["xy_avg_right"] = (slice(1, None), slice(1, None), slice(None))
+
+    return indices
+
+
+# ...existing code...
+
+
+def get_boundary_condition_slices(elem, node, ud):
+    """
+    Create slice indices for boundary conditions including periodic, element, and node slices.
+
+    Parameters
+    ----------
+    elem : object
+        Element object with ndim attribute
+    node : object
+        Node object with igs attribute (number of ghost cells)
+    ud : object
+        User data object with bdry_type attribute
+    opts : module
+        Options module with BdryType enum
+
+    Returns
+    -------
+    tuple
+        (idx_periodic, idx_e, idx_n, periodicity) where:
+        - idx_periodic: slice tuple for periodic regions
+        - idx_e: slice tuple for element regions
+        - idx_n: slice tuple for node regions
+        - periodicity: boolean tuple for each dimension
+    """
+    x_periodic = ud.bdry_type[0] == opts.BdryType.PERIODIC
+    y_periodic = ud.bdry_type[1] == opts.BdryType.PERIODIC
+    z_periodic = ud.bdry_type[2] == opts.BdryType.PERIODIC
+    periodicity = (x_periodic, y_periodic, z_periodic)
+
+    igs = node.igs
+    ndim = elem.ndim
+
+    idx_periodic = [slice(None)] * elem.ndim
+    idx_n, idx_e = np.copy(idx_periodic), np.copy(idx_periodic)
+
+    for dim in range(ndim):
+        if ud.bdry_type[dim] == opts.BdryType.PERIODIC:
+            idx_periodic[dim] = slice(1, -1)
+
+        idx_e[dim] = slice(
+            igs[dim] - periodicity[dim], -igs[dim] + periodicity[dim] - 1
+        )
+        idx_n[dim] = slice(igs[dim], -igs[dim])
+
+    idx_periodic, idx_e, idx_n = tuple(idx_periodic), tuple(idx_e), tuple(idx_n)
+
+    return idx_periodic, idx_e, idx_n, periodicity