A research Python code for 2D incompressible fluid–structure interaction using the Reference Map Technique (RMT): a fully Eulerian, collocated-grid, diffuse-interface method where a neo-Hookean solid and a Newtonian fluid share one velocity field and one pressure solve. Based on Jain, Kamrin & Mani (2019).
- Collocated grid with Rhie–Chow interpolation (no checkerboard).
- Direct Poisson solvers: DCT for walls (Neumann), FFT for periodic — both O(N log N); AMG fallback for variable density.
- Switchable reference-map advection: semi-Lagrangian RK4 (default), or central2 / WENO5 + SSP-RK3.
- Neo-Hookean solid stress from the reference map; one-fluid blending of solid and fluid stress through a smoothed Heaviside.
- Least-squares extrapolation of the reference map into a narrow band; level set reconstructed from the reference map.
- Numba-JIT kernels.
git clone https://github.com/samanseifi/pyRMT.git
cd pyRMT
pip install -e ".[test]" # omit [test] if you don't need pytestRequires Python 3.10+ (numpy, scipy, matplotlib, h5py, pyamg, numba).
# Fluid solver vs Ghia (1982)
python benchmarks/lid_driven_cavity.py 1000 # Re=1000, N=129
# Primary FSI case vs Sugiyama (2011)
python benchmarks/soft_disc_in_lid_driven.py 128 semilagrangian 8.0
# Soft disc in a Taylor–Green vortex (energy)
python benchmarks/disc_in_taylor_green.py 128
# Spatial convergence study
python benchmarks/convergence_taylor_green.pyOutputs (CSV + figures) land under outputs/. See benchmarks/README.md
for BC/pressure pairings, the stress_band accuracy/order tradeoff, and the
convergence findings.
Lid-driven cavity (pure fluid) vs Ghia et al. (1982) — RMS error in u(y) at
x=0.5: 1.7×10⁻³ (Re=100), 2.8×10⁻² (Re=1000), N=129.
Soft disc in lid-driven cavity — neo-Hookean disc carried by the cavity flow, at the Jain (2019) Fig. 16 time instances; centroid matches Sugiyama (2011), and the deformed interface is grid-converged (N=64 ≈ N=128).
Soft disc in a Taylor–Green vortex — kinetic ↔ strain energy exchange (oscillation); total energy conserved.
Spatial convergence (disc in TG) — energies ~2nd order; velocity/pressure
~1st order, limited by the diffuse interface (not advection). Details in
benchmarks/README.md.
pytest # 19 unit tests (operators, Poisson, projection, stress, energy)CI runs the suite on Python 3.10/3.11 via GitHub Actions.
MIT.
- S. S. Jain, K. Kamrin, A. Mani, A conservative and non-dissipative Eulerian formulation for the simulation of soft solids in fluids, J. Comput. Phys. 399, 108922 (2019). doi:10.1016/j.jcp.2019.108922
- K. Kamrin, C. H. Rycroft, J.-C. Nave, Reference map technique for finite-strain elasticity and fluid–solid interaction, JMPS 60, 1952–1969 (2012). doi:10.1016/j.jmps.2012.06.003
- B. Valkov, C. H. Rycroft, K. Kamrin, Eulerian method for multiphase interactions of soft solid bodies in fluids, J. Appl. Mech. 82, 041011 (2015). doi:10.1115/1.4029765