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A naturally efficient numerical technique for porous convection stability with non‐trivial boundary conditions
Author(s) -
Payne L. E.,
Straughan B.
Publication year - 2000
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/1096-9853(20000825)24:10<815::aid-nag101>3.0.co;2-y
Subject(s) - eigenfunction , eigenvalues and eigenvectors , porous medium , boundary (topology) , convection , boundary value problem , instability , numerical analysis , field (mathematics) , geology , mathematics , mechanics , geotechnical engineering , porosity , mathematical analysis , physics , quantum mechanics , pure mathematics
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 and Bear. Since the salinization study of Gilman and Bear 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. Copyright © 2000 John Wiley & Sons, Ltd.