On the Chebyshev collocation spectral approach to stability of fluid flow in a porous medium

Abstract

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.