LAUSR

In this paper, we present a second-order decoupled scheme based on the artificial compression method for the time-dependent Stokes-Darcy equations. This method not only uncouples the velocity and hydraulic head by implicit-explicit method but also uncouples the velocity and pressure by artificial compression method; therefore, it only requires one velocity, one pressure, and one hydraulic head problem at each time step by treating the coupling terms explicitly and relaxing the incompressibility constraint. We derive the long-time stability for the velocity and the hydraulic head and give the error analysis for the fully discrete scheme with finite element spatial discretization. Numerical tests are presented to show the accuracy and efficiency of this method.