Mathematical and numerical models for coupling surface and groundwater flows

In this paper we present some results about the coupling of Navier–Stokes and Shallow Water equations for surface flows and Darcy's equation for groundwater flows. We discuss suitable interface conditions and show the well-posedness of the coupled problem in the case of a linear Stokes problem. An iterative method to compute the solution is proposed. At each step this method requires the solution of one problem in the fluid part and one in the porous medium. Finally we introduce the Steklov–Poincaré equation associated to the coupled problem.