Coupling incompressible flow with porous media flow

Beatrice Riviere
University of Pittsburgh

Abstract: In this work, we couple the incompressible steady Navier-Stokes
equations with the Darcy equations, by means of the
Beaver-Joseph-Saffman's condition on the interface. Under mild regularity
conditions on the data, we prove existence of a weak solution as well as
some a priori estimates. We establish uniqueness under smallness
restrictions on the data, similar to those that guatantee uniqueness of
the solution of the Navier-Stokes equations. Then we propose a
discontinuous Galerkin scheme for discretizing the equations and do its
numerical analysis.