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Effect of anisotropic permeability on Darcy's law
Author(s) -
Payne L. E.,
Rodrigues J. F.,
Straughan B.
Publication year - 2001
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.228
Subject(s) - porous medium , mathematics , permeability (electromagnetism) , darcy's law , a priori and a posteriori , anisotropy , convection , natural convection , mathematical analysis , context (archaeology) , hopf bifurcation , bifurcation , mechanics , porosity , physics , geology , nonlinear system , chemistry , geotechnical engineering , paleontology , biochemistry , philosophy , epistemology , quantum mechanics , membrane
Abstract The concept of structural stability is discussed and briefly reviewed within the context of fluid flow in porous media. Then the equations for non‐Boussinesq (penetrative) convection in a porous medium with anisotropic permeability are analysed. It is shown, by deriving truly a priori estimates, that the solution exists in the natural functional framework and depends continuously on changes in the permeability. Since under appropriate circumstances the onset of thermal convection may be via Hopf bifurcation rather than stationary convection, such a priori continuous dependence estimates are of much value. Copyright © 2001 John Wiley & Sons, Ltd.