Darcy equation for random porous media
A. Yu. Beliaev, Serguei M. Kozlov · Communications on Pure and Applied Mathematics · 1996
Many attempts have been made recently to deduce Darcy equations for flows through porous media. Much has been done for models having a periodic microstructure. This paper presents a mathematical analysis based on the more general and more realistic assumption that the microstructure of porous media is random and stochastically homogeneous. For this type of random domain we consider homogenization of the Poisson and Stokes equations supplemented by homogeneous Dirichlet boundary conditions on the random boundary. With this approach we get the Darcy equation in general as well as present details for the particular case of a checkerboard model of porous media. © 1996 John Wiley & Sons, Inc.