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Formulations and analysis of the spectral volume method for the diffusion equation

✍ Scribed by Sun, Yuzhi ;Wang, Z.J.

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
177 KB
Volume
20
Category
Article
ISSN
1069-8299

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✦ Synopsis

Abstract

The spectral volume (SV) method is a newly developed high‐order finite volume method for hyperbolic conservation laws on unstructured grids. It has been successfully demonstrated for multi‐dimensional Euler equations. We wish to extend the SV method to the Navier–Stokes equations. As a first‐step towards achieving that goal, the SV method is extended to and tested for the diffusion equation. In this paper, we present three different formulations of the spectral volume method for the diffusion equation. The first formulation yields an inconsistent and unstable scheme, while the other two formulations are consistent, convergent and stable. A Fourier type analysis is performed for all the formulations, and the analysis agrees well with numerical results. Copyright © 2004 John Wiley & Sons, Ltd.

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