Finite Volume model in 2D Poisson Equation

Table of contents

1. Overview
   1. Downloads

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Overview

This page has links to MATLAB code and documentation for the finite volume solution to the two-dimensional Poisson equation

$$\frac{\partial}{\partial x}\left(\Gamma \frac{\partial \phi}{\partial x}\right) + \frac{\partial}{\partial x}\left(\Gamma \frac{\partial \phi}{\partial x}\right) + S = 0$$

where $\phi$ is the scalar field variable, $S$ is a volumetric source term, and $x$ and $y$ are the Cartesian coordinates. This equation is a model of fully-developed flow in a rectangular duct, heat conduction in rectangle, and the pressure Poisson equation for finite volume models of fluid flow.

The code allows for non-uniform meshes and variable diffusion coefficient. The code base also provides a test bed for stationary iterative methods (Gauss-Seidel, Jacobi, SOR) and preconditioned Conjugate gradient and Krylov subspace methods.

Downloads

• Code archive
• Documentation as article or slides

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