A meshless generalized finite difference method for solving the Stokes–Darcy coupled problem in static and moving systems

In this paper, a meshless Generalized Finite Difference Method (GFDM) is proposed to deal with the Stokes–Darcy coupled problem with the Beavers–Joseph–Saffman (BJS) interface conditions. Some high order GFDMs are proposed to show the advantages of the high order GFDM for the Stokes–Darcy coupled problem. These advantages include high-order accuracy and convergence. Some Stokes–Darcy coupled problems with closed interfaces, which has more complex geometric shape, are given to show the advantage of the GFDM for the complex interface. The interface location has been changed to show the influence of the interface location for the Stokes–Darcy coupled problem. The BJS interface conditions has related to the partial derivatives of unknown variables and the GFDM has advantage in dealing with the interface conditions with the jump of derivatives. Four numerical examples have been provided to verify the existence of the good performance of the GFDM for the Stokes–Darcy coupled problems, including that the simplicity, accuracy, and stability in static and moving systems. Especially, the GFDM has the tolerance of the large jump. This means that we can change the ratio of coefficients and the results will not be affected. The Neumann boundary condition is used in numerical simulations.