Simulation of coupled Stokes-Darcy equations using the combination of balanced H(div)-L2 approximation spaces

Abstract

The performance of a strongly conservative finite element formulation for cou-
pled Stokes-Darcy problems is discussed. The same pair of balanced H(div)-L2 approximation spaces is used for flow an pressure variables, in both sides. For Darcy’s flux, H(div)conforming spaces is the natural context. In the Stokes side, the discontinuity of tangential flux components is treated by a penalization term, as in usual Discontinuous Galerkin methods. For incompressible fluids, this method naturally gives exact divergence-free velocity fields, a property that few schemes can achieve. Furthermore, the coupling Stoke-Darcy interface conditions is naturally enforced. The method is implemented using an objectoriented computational environment, and a test problem is simulated to illustrate numerical approximation properties, verifying errors and rates of convergence.