VARIATIONALLY CONSISTENT HOMOGENIZATION OF STOKES FLOWIN POROUS MEDIA

Abstract

Seepage through a strongly heterogeneous material, consisting of open saturated pores, is modeled as a Stokes flow contained in a rigid matrix. Through homogenization of the problem, a two-scale formulation is derived. The subscale problem is that of a Stokes flow whereas the macroscale problem pertains to a Darcy flow. The prolongation of the macroscale Darcy flow fulfills the variational consistent macrohomogeniety condition and is valid for both linear and nonlinear subscale flows. The subscale problem is solved using the finite element method. Numerical results concerning both linear and nonlinear flow are presented.