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An Efficient And Long-Time Accurate Third-Order Algorithm For The Stokes–Darcy System, Wenbin Chen, Max Gunzburger, Dong Sun, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

A third order in time numerical IMEX-type algorithm for the Stokes–Darcy system for flows in fluid saturated karst aquifers is proposed and analyzed. a novel third-order Adams–Moulton scheme is used for the discretization of the dissipative term whereas a third-order explicit Adams–Bashforth scheme is used for the time discretization of the interface term that couples the Stokes and Darcy components. the scheme is efficient in the sense that one needs to solve, at each time step, decoupled Stokes and Darcy problems. Therefore, legacy Stokes and Darcy solvers can be applied in parallel. the scheme is also unconditionally stable and, with …