Coupling fluid flow with porous media flow. (English) Zbl 1037.76014

Summary: The transport of substances back and forth between surface water and groundwater is a very serious problem. We study herein the mathematical model of this setting consisting of the Stokes equations in the fluid region coupled with the Darcy equations in the porous medium, coupled across the interface by the Beavers-Joseph-Saffman conditions. We prove existence of weak solutions and give a complete analysis of a finite element scheme which allows a simulation of the coupled problem to be uncoupled into steps involving porous media and fluid flow subproblems. This is important because there are many “legacy” codes available which have been optimized for uncoupled porous media and fluid flow.


76D07 Stokes and related (Oseen, etc.) flows
35Q30 Navier-Stokes equations
76M10 Finite element methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
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