01-22
Coupling Fluid Flow with Porous Media Flow
by Layton, W.J.; Schieweck, F.; Yotov, I.
Preprint series: 01-22, Preprints
- MSC:
- 35Q35 Other equations arising in fluid mechanics
- 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
- 65N15 Error bounds
- 76D07 Stokes flows
- 76S05 Flows in porous media; filtration; Seepage
Abstract: The transport of substances back and forth between surface and ground water 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 Darcy\'s equations in the porous medium, coupled across the interface by the Beavers-Joseph 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.
Keywords: coupled porous media and fluid flow, Stokes and Darcy\'s equations, Beavers-Joseph condition, weak solutions, finite element scheme, error estimates
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