A decoupled preconditioning technique for a mixed Stokes-Darcy model

2012/08/08 by Márquez, Antonio, Meddahi, Salim, Sayas, Francisco-Javier
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1208.1685

Abstract

We propose an efficient iterative method to solve the mixed Stokes-Dracy model for coupling fluid and porous media flow. The weak formulation of this problem leads to a coupled, indefinite, ill-conditioned and symmetric linear system of equations. We apply a decoupled preconditioning technique requiring only good solvers for the local mixed-Darcy and Stokes subproblems. We prove that the method is asymptotically optimal and confirm, with numerical experiments, that the performance of the preconditioners does not deteriorate on arbitrarily fine meshes.

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