Diffusion2D is a numerical solver for 2D diffusion equations, implemented using central differencing for spatial discretization and the forward Euler method for time integration. Features

• Steady state solver (uses Eigen's conjugate gradient linear solver)
• Transient solver (forward differencing)
• UDF support (functions of time) using LuaJIT
• Paraview VTR (rectilinear) mesh output
• Python bindings

The solver handles the following equations:

1. Laplace Equation:

   $$\nabla^2 T = 0$$

2. Poisson Equation:

   $$\nabla^2 T + f = 0$$

   Here, f represents the source term.

3. Unsteady Diffusion Equation:

   $$\nabla^2 T + f = \frac{\partial T}{\partial t}$$

The numerical methods used are:

• Spatial Discretization: Central differencing
• Time Integration: Forward differencing

Using the Python bindings, arbitrary initial conditions can be specified to the solver.

UDFs can be specified using valid lua code, either by direct text (string) input, or by specifying a lua script. The lua code is jit compiled (LuaJIT) for near C performance without need to recompile.

This was developed on Windows 10 using MSVC 2022, C++ Standard 17, and Python 3.11. The included .sln (msvc solution file) requires that you have the path to your python installation in an environment variable called PYTHON_HOME. It also requires that you build LuaJIT (included as a submodule) for whatever architecture that you're using. In totality, this project depends on Eigen, TinyXML2, pybind11, and LuaJIT. You can start by:

• git clone --recursive https://github.com/ddm-j/Diffusion2D.git
• Fire up a MSVC Developer console for whatever architecture (x64, 32)
• cd external/LuaJIT/src
• msvcbuild.bat (this will build LuaJIT. If you need the debug config build as well, use msvcbuild.bat debug)
• Copy the newly built lua51.dll file from external/LuaJIT/src to bin (of the root directory)
• Open the main solution file in MSVC
• Switch to the PythonBindings configuration and build

It would make it easier on you for me to just publish this on PyPy or something, but I can't be bothered. If you've found your way to this strange corner of the internet, you can build this project yourself.

You really want to use this? There are instructions that are somewhat decently documented in the Diffusion2D Jupyter notebook which is in the py folder.