On the solution of the coupled Navier–Stokes and Darcy equations

This paper introduces and analyzes two mathematical models for coupling the incompressible Navier–Stokes equations with the porous media flow equations. A numerical method that uses continuous finite elements in the incompressible flow region and discontinuous finite elements in the porous medium, is proposed. Existence and uniqueness results under small data condition of the numerical solution are proved. Optimal a priori error estimates are derived. Numerical examples comparing the two models under varying physical parameters are provided.