The efficient rotational pressure-correction schemes for the coupling Stokes/Darcy problem

In this paper, the rotational pressure-correction methods for the Stokes/Darcy system are developed and analyzed. The central advantage of these methods is a time-dependent version of domain decomposition. These methods have first-order/second-order accuracy without the incompressibility constraint of the Stokes/Darcy system. Their main feature is the implementation efficiency in that we only solve one vector-valued elliptic equation and one scalar-valued Poisson equation for the Stokes equations per time step. The unconditional stability and long time stability are established and numerical experiments are also presented to show their performance.