Linear Flow in Porous Media with Double Periodicity

Renata Bunoiu and Jeannine Saint Jean Paulin

Abstract: We study the classical steady Stokes equations with homogeneous Dirichlet boundary conditions. We work in a 3-D domain which contains solid obstacles, two-periodically distributed with period $\E$ (respectively $\E^{2}$), where $\E$ is a small parameter. Our aim is to study the asymptotic behaviour, as $\E\arr 0$. We use the 3-scale convergence for getting the 3-scale limit problem. The problem obtained is a three-pressures system.

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