Time‐dependent Stokes flow through a randomly perforated porous medium

Article type: Research Article

Authors: Wright, Steve

Affiliations: Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309‐4438, USA E‐mail: wright@oakland.edu

Abstract: An incompressible fluid is assumed to satisfy the time‐dependent Stokes equations in a porous medium. The porous medium is modeled by a bounded domain in R^n that is perforated for each ε > 0 by ε‐dilations of a subset of R^n arising from a family of stochastic processes which generalize the homogeneous random fields. The solution of the Stokes equations on these perforated domains is homogenized as ε → 0 by means of stochastic two‐scale convergence in the mean, and the homogenized limit is shown to satisfy a two‐pressure Stokes system containing both deterministic and stochastic derivatives and a Darcy‐type law with memory which generalizes the Darcy law obtained for fluid flow in periodically perforated porous media.

Journal: Asymptotic Analysis, vol. 23, no. 3-4, pp. 257-272, 2000