A global-in-time domain decomposition method for the coupled nonlinear Stokes and Darcy flows

TL;DR

This paper introduces a domain decomposition method for efficiently solving coupled nonlinear Stokes-Darcy flows with different time steps, using a space-time interface formulation and nested iterative solvers.

Contribution

It presents a novel decoupling iterative algorithm that allows different temporal discretizations in flow and porous media regions for coupled nonlinear flows.

Findings

Efficient handling of multiphysics systems with different time scales.

Numerical results demonstrate the method's effectiveness with nonconforming time grids.

Parallel solution approach improves computational performance.

Abstract

We study a decoupling iterative algorithm based on domain decomposition for the time-dependent nonlinear Stokes-Darcy model, in which different time steps can be used in the flow region and in the porous medium. The coupled system is formulated as a space-time interface problem based on the interface condition for mass conservation. The nonlinear interface problem is then solved by a nested iteration approach which involves, at each Newton iteration, the solution of a linearized interface problem and, at each Krylov iteration, parallel solution of time-dependent linearized Stokes and Darcy problems. Consequently, local discretizations in time (and in space) can be used to efficiently handle multiphysics systems of coupled equations evolving at different temporal scales. Numerical results with nonconforming time grids are presented to illustrate the performance of the proposed method.