Efficient and Long-Time Accurate Third-Order Algorithm for the Stokes-Darcy System

We propose and analyze a third-order in time numerical algorithm for the Stokes-Darcy system for flows in fluid saturated karst aquifers. A novel third-order Adams-Moulton scheme is used for the discretization of the dissipative term while a third-order explicit Adams-Bashforth scheme is utilized for the time discretization of the interface term. The scheme is efficient in the sense that one needs to solve two decoupled problems at each time step: one Stokes and one Darcy. Therefore, legacy Stokes solver and Darcy solver can be utilized in parallel efficiently. The scheme is also unconditionally stable and long-time accurate in the sense that the error is bounded uniformly in time. Our numerical experiments confirm our theoretical results. This is the first third-order numerical algorithm for the Stokes-Darcy system with such kind of efficiency, stability and accuracy so far as we know.