A decoupled preconditioning technique for a mixed Stokes-Darcy model

TL;DR

This paper introduces an efficient decoupled preconditioning method for solving the coupled Stokes-Darcy model, improving computational performance for fluid-porous media simulations on fine meshes.

Contribution

The paper presents a novel decoupled preconditioning technique that ensures asymptotic optimality and robustness for the coupled Stokes-Darcy system.

Findings

Preconditioners maintain performance on arbitrarily fine meshes.

Method is asymptotically optimal.

Requires only good solvers for local subproblems.

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.