A Darcy-Brinkman Model of Fractures in Porous Media

Abstract

For a fully-coupled Darcy-Stokes system describing the exchange of fluid and stress balance across the interface between a saturated porous medium and an open very narrow channel, the limiting problem is characterized as the width of the channel converges to zero. It is proven that the limit problem is a fully-coupled system of Darcy flow in the porous medium with Brinkman flow in tangential coordinates of the lower dimensional interface.