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On the Chebyshev collocation spectral approach to stability of fluid flow in a porous medium
Author(s) -
Makinde O. D.
Publication year - 2008
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1847
Subject(s) - porous medium , mathematics , reynolds number , chebyshev polynomials , chebyshev filter , spectral method , inviscid flow , wavenumber , flow (mathematics) , mechanics , hele shaw flow , collocation method , open channel flow , mathematical analysis , physics , porosity , geometry , materials science , turbulence , differential equation , optics , ordinary differential equation , composite material
In this paper, the temporal development of small disturbances in a pressure‐driven fluid flow through a channel filled with a saturated porous medium is investigated. The Brinkman flow model is employed in order to obtain the basic flow velocity distribution. Under normal mode assumption, the linearized governing equations for disturbances yield a fourth‐order eigenvalue problem, which reduces to the well‐known Orr–Sommerfeld equation in some limiting cases solved numerically by a spectral collocation technique with expansions in Chebyshev polynomials. The critical Reynolds number Re c , the critical wave number α c , and the critical wave speed c c are obtained for a wide range of the porous medium shape factor parameter S . It is found that a decrease in porous medium permeability has a stabilizing effect on the fluid flow. Copyright © 2008 John Wiley & Sons, Ltd.