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

Layton, William J.; Schieweck, Friedhelm; Yotov, Ivan

SIAM J. Numer. Anal. 40, No. 6, 2195-2218 (2003).

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.

MSC:

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

Keywords:

coupled porous media and fluid flow; Stokes and Darcy equations; Beavers-Joseph-Saffman condition; weak solutions; finite element scheme; error estimates