User Guide: Lunar Convection Simulation with Dedalus

Overview

This script simulates thermal convection in the Moon's interior using the Dedalus framework. It is based on the spherical shell convection example but includes modifications for:

• Infinite Prandtl number
• Phase change at the LMO-cumulates boundary
• Core cooling
• Customizable initial temperature profiles and boundary conditions

The simulation is controlled via a param.toml configuration file.

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Requirements

• Python 3.7+
• Dedalus (see Dedalus Roject)
• MPI (for parallel execution)
• TOML parser (pip install tomli)

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Configuration File: param.toml

The simulation is configured via a TOML file. Below are the available parameters:

Parameter	Description	Example Value
GAMMA	Aspect ratio (Ri/Ro)	0.24
RAYLEIGH	Rayleigh number	1e4
PHI	Phase change number (set to false for no phase change)	6
FACTOR	Curvature factor for temperature profile	4.45
GRAVITY	Gravity profile: true for uniform, false for radius-dependent	true
DT	Initial and maximum time step	1e-5
STOP	Stop simulation time	0.1
Nr	Radial resolution	128
Nphi	Azimuthal resolution	96
Ntheta	Polar resolution	64
SAFETY	Safety factor for CFL number	3
NOISE	Initial noise amplitude	1e-3
BC	Thermal boundary conditions: Dirichlet or CoreCooling	CoreCooling
TempProf	Initial temperature profile: Conductive, Parabolic, or RefProf	RefProf
DIR_SAVE	Directory to save simulation data	./Datas

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Running the Simulation

Basic Usage

To run the simulation using 4 MPI processes:

mpiexec -n 4 python3 shell_convection.py param.toml

Restarting a Simulation

To restart from the latest checkpoint:

mpiexec -n 4 python3 shell_convection.py param.toml --restart

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Outputs

The script saves the following data in the specified DIR_SAVE/name directory:

• Snapshots: Temperature and flux fields at regular intervals.
• Scalars: Time series of averaged quantities (e.g., mean flux, temperature, velocity).
• Checkpoints: Simulation state for restarting. The name of the directory depends of the value of parameters:
• Datas/Rayleigh_1-0e+04_Phi_6-0e+00_gam_0-24_T_RefProf_BC_CoreCooling_g_r_safety_3-0_dt_1e-05_res_96-64-128 for exemple

Output Files Structure

DIR_SAVE/
├── snapshots/
│   ├── snapshots_s1.h5
│   └── ...
├── scalars/
│   ├── scalars_s1.h5
│   └── ...
└── checkpoints/
    ├── checkpoints_s1.h5
    └── ...

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Key Features

• Phase Change: Enabled by setting PHI to a positive value.
• Core Cooling: Activated with BC = CoreCooling.
• Gravity Profile: Uniform or radius-dependent, controlled by GRAVITY.
• Initial Temperature Profiles: Choose between Conductive, Parabolic, or RefProf.

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Notes

• The script uses the SBDF1 timestepper by default.
• For high-resolution simulations, increase Nr, Nphi, and Ntheta accordingly.
• The CFL condition is automatically adjusted for stability, be carreful.

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Troubleshooting

• Divergence: If the simulation diverges, reduce the initial time step (DT) or increase the safety factor (SAFETY, can bi higer than 1).
• Checkpoint Errors: Ensure the checkpoint directory exists and contains valid .h5 files.

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