© V. L. Savatorova, 2010
HOMOGENIZATION OF EQUATIONS FOR THE FILTRATION OF A FLUID THROUGH A RIGID SOLID WITH PERIODIC STRUCTURE OF PORES
In this paper we consider Brinkman’s equation governing the flow of an incompressible fluid through a porous medium to take into account the variation of viscosity with pressure. We use a homogenization procedure, that exploits a multiple scale structure possessed by a solid porous medium, a ‘micro-scale’ comparable to the pore size and a ‘macro-scale’ associated with the global size of the body, to carry out a multiple-scale asymptotic analysis. We deduce the governing equations for both scales and solve periodic problems in cells in order to find effective permeability, pressure distribution and velocity of the fluid.
Keywords: homogenization, filtration, Brinkman’s equation, pressure dependent viscosity
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