Abstract

This talk considers a coupling of two second-order implicit-explicit (IMEX) methods for solving the mixed Stokes-Darcy model that governs flows in karst aquifers. The first is a second-order explicit two step MacCormack scheme and the second is a second-order implicit Crank-Nicolson method. Both algorithms only require the solution of two decoupled problems at each time step, one Stokes and the other Darcy. This combination the so-called MacCormack rapid solver method is very efficient and effective (faster, at least second order accuracy in time and space) and can be easily implemented using legacy codes. Under a suitable time step limitation both long time stability and convergence rate of the method are analyzed. A large set of numerical evidences that confirm the theoretical results are presented and critically discussed.

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