A decoupled preconditioning technique for a mixed Stokes-Darcy model
This work addresses the need for efficient solvers for coupled fluid-porous media flow problems, which are important in geoscience and engineering applications.
The paper proposes an efficient iterative method for solving the mixed Stokes-Darcy model, using a decoupled preconditioning technique that requires only local solvers. Numerical experiments confirm the method is asymptotically optimal and its performance does not deteriorate on fine meshes.
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.