ON THE STEADY-STATE FLOW OF AN INCOMPRESSIBLE FLUID THROUGH A RANDOMLY PERFORATED POROUS-MEDIUM

An incompressible fluid is assumed to satisfy the time-independent Sto kes equations in a porous medium. The porous medium is modeled by a bo unded domain in R-n that is perforated for each epsilon > 0 by epsilon -dilations of a subset of R-n arising from a family of stochastic proc esses which generalize the homogeneous random fields. The solution of the Stokes equations on these perforated domains is homogenized as eps ilon --> 0 by means of stochastic two-scale convergence in the mean an d the homogenized limit is shown to satisfy a two-pressure Stokes syst em containing both deterministic and stochastic derivatives and a Darc y-type law which generalizes the Darcy law obtained for fluid now in p eriodically perforated porous media. (C) 1998 Academic Press.