A second-order fractional time-stepping method for a coupled Stokes/Darcy system

In this paper, a second-order fractional time-stepping method for a Stokes/Darcy system is developed and analyzed. The main feature of this fractional time-stepping method is that we only solve one vector-valued elliptic equation and one scalar-valued Poisson equation for the velocity and pressure of the Stokes equations per time step. Moreover, its central advantage is a time-dependent version of domain decomposition, which has second-order accuracy without requiring an incompressibility constraint for the Stokes equations. The stability of the presented method is established, and numerical experiments are also presented to show its performance. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

A second-order fractional time-stepping method for a Stokes/Darcy system is developed in this paper, simplifying the equation solving process per time step and achieving high accuracy without the need for an incompressibility constraint. The method's stability is established and its performance is demonstrated through numerical experiments.