Coupling Darcy and Stokes equations for porous media with cracks

Bernardi, Christine; Hecht, Frédéric; Pironneau, Olivier

ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 1, pp. 7-35.

In order to handle the flow of a viscous incompressible fluid in a porous medium with cracks, the thickness of which cannot be neglected, we consider a model which couples the Darcy equations in the medium with the Stokes equations in the cracks by a new boundary condition at the interface, namely the continuity of the pressure. We prove that this model admits a unique solution and propose a mixed formulation of it. Relying on this formulation, we describe a finite element discretization and derive a priori and a posteriori error estimates. We present some numerical experiments that are in good agreement with the analysis.

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