Abstract

The Stokes-Darcy coupled fluid flow model is one of the most popularmulti-domain and multi-physics problems. We propose herein a newparallel domain decomposition method to study the fully-mixed Stokes-Darcy coupled problem with the Beavers-Joseph-Saffman (BJS) interface condition.  The method is based on Robin-type boundary conditions, instead of using any Lagrange multiplier, which allows to decouple the problem into two subproblems.  The equivalence between the original coupled problem and the decoupled subproblems is derived with the compatibility conditions. Moreover, we show the convergence of the iterative parallel method in a general setting. With the suitable  choice of parameters, mesh-independent  convergence rates are proved rigorously for both the parallel domain decomposition method and the corresponding mixed FEM discrete system. Two numerical examples are presented to show the exclusive features of the proposed parallel domain decomposition method. Furthermore, the proposed method is easy to  implement since there are many “legacy" algorithms and codes available for each of the two uncoupled subproblems.