Conduction

Implicit heat conduction solver on a structured grid written in Python. It interfaces with PETSc to provide highly scalable meshes and solve the steady-state heat equation using direct or iterative methods.

Dependencies

• Python 2.7 and above
• Numpy 1.9 and above
• Scipy 0.14 and above
• mpi4py
• petsc4py
• h5py (optional - for saving parallel data)
• Matplotlib (optional - for visualisation)

PETSc installation

PETSc is used extensively via the Python frontend, petsc4py. It is required that PETSc be configured and installed on your local machine prior to using this module. You can use pip to install petsc4py and its dependencies.

pip install [--user] numpy mpi4py
pip install [--user] petsc petsc4py

If that fails, you must compile these dependencies manually.

Usage

All of the scripts in the tests directory can be run in parallel, e.g.

mpirun -np 4 python conduction3d_benchmark.py

where the number after the np flag specifies the number of processors.

API

A ConductionND object can be defined based on the extent of the domain and the number of cells. The simplified use-case below outlines the following tasks:

1. Define a mesh on which to solve the heat equation
2. Populate the thermal conductivity and heat production fields
3. Set boundary conditions on the top and bottom walls
4. Solve for temperature

from conduction import ConductionND

# define the mesh
minX, minY, minZ = 0.0, 0.0, 0.0
maxX, maxY, maxZ = 1.0, 1.0, 1.0
resX, resY, resZ = 10, 10, 10

mesh = ConductionND((minX, minY, minZ), (maxX, maxY, maxZ), (resX, resY, resZ))

# populate thermal conductivity and heat production fields
n = resX*resY*resZ
k = np.ones(n)
H = np.ones(n)

mesh.update_properties(k, H)

# set boundary conditions
mesh.boundary_condition("maxZ", 0.0, flux=False) # Dirichlet BC
mesh.boundary_condition("minZ", 1.0, flux=True) # Neumann BC

# solve temperature
T = mesh.solve()

More complex examples can be found in the Examples directory.