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

TL;DR

This paper introduces a meshless generalized finite difference method for solving complex Stokes-Darcy coupled problems, demonstrating high accuracy, stability, and effectiveness in static and moving systems with complex interfaces.

Contribution

The paper develops high order meshless GFDMs for Stokes-Darcy problems, effectively handling complex interfaces and derivative jumps, with demonstrated high accuracy and stability.

Findings

High order GFDM achieves high accuracy and convergence.

Method effectively handles complex geometries and interface jumps.

Demonstrates stability and accuracy in static and moving systems.

Abstract

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 advantage of the high order GFDM for the Stokes-Darcy coupled problem, which is that the high order method has high order accuracy and the convergence order. 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. The Neaumann boundary condition is used in numerical simulations.