Regular Article
Two Very Accurate and Efficient Methods for Computing Eigenvalues and Eigenfunctions in Porous Convection Problems

https://doi.org/10.1006/jcph.1996.0163Get rights and content

Abstract

We develop the compound matrix method and the Chebyshev tau method to be applicable to linear and nonlinear stability problems for convection in porous media, in a natural way. It is shown how to obtain highly accurate answers to problems which may be stiff, and spurious eigenvalues are avoided. A detailed analysis is provided for a porous convection problem of much current interest, namely convection with a horizontally varying temperature gradient.

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This work was supported in part by ARPA under Contract DAAL 03-91-C-0047 administered by the Army Research Office.

Permanent address: Department of Mathematics, The University, Glasgow, G12 8QW, United Kingdom.

Present address: Department of Computer Science, University of Wales, Cardiff, P.O. Box 916, Cardiff CF2 3XF, United Kingdom.

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