Mathematics

In this talk we consider the modeling and numerical simulation of coupled free/porous–media flows. We present different modeling approaches involving the Navier–Stokes equations to represent the incompressible fluid and Darcy of Fochheimer equations in the porous region. We discuss and compare different coupling strategies based on the so–called penalization method or on the application of the transmission conditions of Beavers–Joseph–Saffman. After giving some results on the well–posedness of the resulting coupled models, we illustrate a domain decomposition framework to set up possible iterative methods to compute their finite element solution. We discuss the effectiveness and robustness of such algorithms showing several numerical results. Finally, we present some possible applications of the models that we have studied.