Finite Volume model of 1D convection

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Overview

This page has links to MATLAB code and documentation for the finite volume method solution to the one-dimensional convection equation

$$\frac{d}{dx}(u\phi) - \frac{d}{dx}\left(\Gamma\frac{\partial \phi}{\partial x}\right) - S = 0$$

where $u$ is the $x$-direction velocity, $\phi$ is a convective passive scalar, $\Gamma$ is the diffusion coefficient for $\phi$, and $x$ is the spatial coordinate.

This demonstrates the “wiggle” that occurs at large cell Peclet number, how that wiggle can be suppressed with upwinding, the accuracy cost of upwinding, and how the central-difference scheme can be used (in spite of wiggles) if the mesh is sufficiently refined.

Downloads

• Code archive
• Documentation in article format and lecture slide format

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