A strongly conservative finite element method for the coupling of Stokes and Darcy flow

• Published in: Journal of computational physics Vol. 229; no. 17; pp. 5933 - 5943
• Main Authors: Kanschat, G., Rivière, B.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 20.08.2010; Elsevier
• Subjects: Beavers–Joseph–Saffman condition; Computational fluid dynamics; Computational techniques; Convergence; Darcy flow; Discontinuous Galerkin; Exact sciences and technology; Finite element method; Fluid flow; Galerkin methods; Mathematical analysis; Mathematical methods in physics; Mathematical models; Mixed finite elements; Multiphysics; Physics; Stokes flow; Stokes law (fluid mechanics); Finite element method; Multiphysics; Discontinuous Galerkin; Beavers–Joseph–Saffman condition; Stokes flow; Darcy flow; Mixed finite elements; Stokes equation; Porous medium; Calculation methods; Divergences; Beavers-Joseph-Saffman condition; Discretization; Models; Calculation
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2010.04.021

We consider a model of coupled free and porous media flow governed by Stokes and Darcy equations with the Beavers–Joseph–Saffman interface condition. This model is discretized using divergence-conforming finite elements for the velocities in the whole domain. Discontinuous Galerkin techniques and mixed methods are used in the Stokes and Darcy subdomains, respectively. This discretization is strongly conservative in H div( Ω) and we show convergence. Numerical results validate our findings and indicate optimal convergence orders.