MULTISCALE MODELING OF POROUS MEDIA

Paper in proceeding, 2010

Homogenization of flow in porous media is studied. The continuity equation in conjunction with Darcy’s law as a constitutive relation on the macroscale, where the permeability is a function of the pressure gradient, is applied to a macroscopic domain. On the heterogenous mesoscale, a Stokes flow problem is formulated on a Representative Volume Element with a prescribed pressure gradient and suitable boundary condition. The numerical procedure for finite element simulations of the two-scale problem is outlined and illustrated by a few example problems.