Preconditioning techniques for a mixed Stokes/Darcy model in porous media applications

Authors:
Mingchao Cai;Mo Mu;Jinchao Xu
Affiliations:
Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong;Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong;Department of Mathematics, Penn State University, United States
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 12
Cited 4

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Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations

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A Two-Grid Method of a Mixed Stokes-Darcy Model for Coupling Fluid Flow with Porous Media Flow

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A multilevel decoupled method for a mixed Stokes/Darcy model

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Long time stability of four methods for splitting the evolutionary Stokes-Darcy problem into Stokes and Darcy subproblems

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A Decoupled Preconditioning Technique for a Mixed Stokes---Darcy Model

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Abstract

We study numerical methods for a mixed Stokes/Darcy model in porous media applications. The global model is composed of two different submodels in a fluid region and a porous media region, coupled through a set of interface conditions. The weak formulation of the coupled model is of a saddle point type. The mixed finite element discretization applied to the saddle point problem leads to a coupled, indefinite, and nonsymmetric linear system of algebraic equations. We apply the preconditioned GMRES method to solve the discrete system and are particularly interested in efficient and effective decoupled preconditioning techniques. Several decoupled preconditioners are proposed. Theoretical analysis and numerical experiments show the effectiveness and efficiency of the preconditioners. Effects of physical parameters on the convergence performance are also investigated.