Stability analysis of MacCormack rapid solver method for evolutionary Stokes-Darcy problem

A numerical method based on the explicit-implicit scheme of MacCormack finite difference scheme was applied to the solution of Parabolized Navier-Stokes equations. Partitioned methods, which solve the coupled problem by successively solving the sub-physics problems, have recently been studied for the full evolutionary groundwater-surface water flow with convergence established over both bounded and long time intervals. A MacCormack rapid solver method based on interface approximation via temporal extrapolation is proposed for devising decoupled marching algorithms for the mixed model. Under a time step limitation of the form C1h≤Δt≤C2h (where h,Δt are mesh size and time step, respectively, and Cj,j∈{1,2}, are two physical parameters) we prove both uniform and asymptotic stabilities over long time intervals. Some numerical experiments are presented and discussed.