Abstract

A Naturally Efficient Numerical Technique for Porous Convection Stability with Non-trivial Boundary Conditions L.E. Payne (Cornell) & B. Straughan (Glasgow) A highly efficient numerical technique is presented for solving eigenvalue problems which arise in complicated convection - instability studies in porous media. The differential equations are written as a system of ``natural" variables which are suggested by the way the boundary conditions arise. The method easily gives high resolution in boundary layers, yields all the eigenvalues and eigenfunctions, deals with complex coefficients, and can handle spatially dependent coefficients in a very efficient manner. The numerical technique is motivated by the practical problem of salinization in porous sands in arid zones as is beautifully modelled by Gilman \& Bear (1996). Since the salinization study of Gilman \& Bear (1996) is a prototype for the field of convective motion in unsaturated porous soils and this field is one which is increasingly occupying geotechnical attention, we believe the numerical method presented here has much potential.

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