The Control-Volume Finite-Difference Approximation to the Diffusion Equation

A two-dimensional computer code for solution of the diffusion equation (Poisson equation) is described. The code is implemented in Matlab, and is intended for educational use. The partial differential equation is converted to a system of linear equations with the finite-volume method. The system is solved by a direct method, though extending the code to use iterative methods would not be difficult. Use of the code requires the user to edit and run Matlab functions. Utility routines for prescribing a variety of boundary conditions and computing wall fluxes are provided to ease the programming tasks. The code is demonstrated with a handful of sample problems.