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

Abstract

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.