On the solution of the coupled Navier-Stokes and Darcy equations. (English) Zbl 1230.76023

Chidyagwai, Prince; Rivière, Béatrice

Comput. Methods Appl. Mech. Eng. 198, No. 47-48, 3806-3820 (2009).

Summary: 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.

MSC:

76M10	Finite element methods applied to problems in fluid mechanics
76D05	Navier-Stokes equations for incompressible viscous fluids
76S05	Flows in porous media; filtration; seepage
76M30	Variational methods applied to problems in fluid mechanics

Keywords:

coupled problems; surface flow; subsurface flow; weak solution; finite elements; discontinuous Galerkin

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