heatSolverFenicsX

A Python-based finite element solver for the heat equation problems using the FEniCSx ecosystem, including dolfinx, ufl, and PETSc-backed linear solvers. This solver is coupled with Openfoam as a part of the ParaSiF partitioned solver for Thermal-Fluid-Structure Interaction (TFSI) using the Multiscale Universal Interface (MUI).

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Table of Contents

• Project Structure
• Requirements
• Installation
• Usage
• Visualisation

Project Structure

heatSolverFenicsX
│
├──src
  ├── solver.py              # Main solver containing outer and inner loops
  ├── heatEquationFenics     # Definition of variational form of heat eqation, creation of function spaces and PETSc solvers
  ├── meshGeneration.py      # Creation of mesh topology
  ├── boundarys.py           # Various BC definitions, includuding CoupledBoundaries responsible for MUI coupling
  ├── input.py               # Responsible for parsing case files; case.json and solver.json.
  ├── output.py              # Responsible for exporting mesh and field data to xdmf format for ParaView
├── README.md
├── originalCode.py          # Orginal code written by Wendi Liu from which this work is derived.
└── spack.yaml               # Spack environment dependencies

Requirements

The project depends on the FEniCSx finite element ecosystem and mui4py (MUI Python Wrappers). The code has been tested using Python 3.12.

Required packages:

• scipy v1.16.3
• dolfinx v0.9.0
• ufl v2024.2.0
• basix v0.9.0
• mpi4py v4.1.1
• petsc4py v3.24.3
• numpy v2.3.5
• mui4py @ master

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Installation

If you are using the ParaSiF framework follow the installation details there, this will install any required dependencies for heatSolverFEniCSx. Otherwise, the best way to get started is using spack. Using the spack.yaml file run the following with an environment name of your choice.

spack env create <environment name> spack.yaml
spack env activate -p <environment name>
spack install   # this will take a while

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Usage

To use the solver, create a case directory called "solid", similar to Openfoam with the following structure:

├──solid
  ├── output/
  ├── input/
    ├── case.json          # Specifies case parameters (e.g mesh lengths, thermal conductivity....)
    └── solver.json        # Specifies solver parameters (e.g mesh resolution, timestep...)

The json files should have the following formats:

case.json

{
    "lx": 0.2,        # mesh length in x-direction
    "ly": 1.0,        # mesh length in y-direction
    "lz": 0.01,       # mesh length in z-direction
    "kappa": 54,      # thermal conductivity
    "alpha": 0.003,   # thermal diffuisivity
    "initial_temp": 273.15,    # initial field temperature
    "left_bc_temp": 273.15,    # left boundary temp
    "right_bc_temp": 274.15   # right boundary temp
    # Note: top and bottom boundarys are currently assumed to be insualted walls (ZeroGradient)
}

solver.json

{
    "end_time": 5,      # end time in seconds for simulation
    "deltaT": 0.05,     # timestep
    "poly_order": 2,    # polynomial order of FEM solution
    "nx": 20,           # mesh resolution in x-direction
    "ny": 20,           # mesh resolution in y-direction
    "nz": 1,            # mesh resolution in z-direction
    "coupled_boundary_type": "neumann",      # coupled boundary type, possible options are: neumann, dirichlet, linearInterpolation, none
    "inner_loop_iterations": 8,              # iteration of inner loop for strong coupling
    "write_interval": 1.0               # how often (in seconds) to write field data to xdmf file.
}

Then run the heat solver from the directory above "solid" as below. Note that if coupled_boundary_type is not set to 'none' then a corresponding openfoam script is required.

export PYTHONPATH=<path_to_heatSolverFenicsX>/heatSolverFenicsX/src:$PYTHONPATH
mpirun -np y python -m solver
# OR
mpirun -np y <openfoam script > : -np x python -m solver

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Visualisation

Solutions can be visualised using Paraview by opening "output/fenicsx_solid_data.xdmf".