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Domain decomposition for coupled Stokes and Darcy flows. (English) Zbl 1295.76036

Summary: A non-overlapping domain decomposition method is presented to solve a coupled Stokes-Darcy flow problem in parallel by partitioning the computational domain into multiple subdomains, upon which families of coupled local problems of lower complexity are formulated. The coupling is based on appropriate interface matching conditions. The global problem is reduced to an interface problem by eliminating the interior subdomain variables. The interface problem is solved by an iterative procedure, which requires solving subdomain problems at each iteration. Finite element techniques appropriate for the type of each subdomain problem are used to discretize it. The condition number of the resulting algebraic system is analyzed and numerical tests verifying the theoretical estimates are provided.

MSC:

76S05 Flows in porous media; filtration; seepage
76D07 Stokes and related (Oseen, etc.) flows
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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