A decoupled scheme with leap-frog multi-time step for non-stationary Stokes–Darcy system

In this paper, a multiple-time-step decoupled algorithm for a non-stationary Stokes–Darcy problem is proposed and investigated. Under a modest time step restriction of physical parameters and the time step proportion, we give the stability analysis and convergence analysis of the decoupled scheme with different time step in fluid and porous subregions. Finally, a series of numerical experiments are provided to illustrate the accuracy, efficiency, and stability of the presented method for the coupled problem with the Beavers–Joseph–Saffman–Jones interface conditions.