Numerical investigation based on radial basis function-finite-difference (RBF-FD) method for solving the Stokes-Darcy equations

A meshless method is presented to numerically study an interface problem between a flow in a porous medium governed by Darcy equations and a fluid flow, governed by Stokes equations. In fact, the domain of the problem has two parts, one governed by Stokes equations and the another governed by Darcy law. Governing equations on these two parts are mutually coupled by interface conditions. The approximation solution is based on local radial basis function-finite-difference (RBF-FD) which is carried out within a small influence domain instead of a global one. By this strategy, the final linear system is more sparse and well posed than the global one. Several numerical results are provided to illustrate the good performance of the proposed scheme.