Analysis of a Second-Order, Unconditionally Stable, Partitioned Method for the Evolutionary Stokes-Darcy Model

Abstract

We propose and analyze a partitioned numerical method for the fully evolutionary Stokes-Darcy equations that model the coupling between surface and groundwater flows. The proposed method uncouples the surface from the groundwater flow by using the implicit-explicit combination of the Crank-Nicolson and Leapfrog methods for the discretization in time with added stabilization terms. We prove that the method is asymptotically, unconditionally stable — requiring no time step condition — and second-order accurate in time with optimal rates in space. We verify the method's unconditional stability and second-order accuracy numerically.