Finite element method coupled with multiscale finite element method for the non-stationary Stokes-Darcy model

TL;DR

This paper introduces a multiscale finite element algorithm for the non-stationary Stokes-Darcy model that reduces computational costs and improves accuracy on coarse grids, validated through theoretical analysis and numerical experiments.

Contribution

It develops a novel multiscale finite element method for coupled Stokes-Darcy equations, enabling efficient and accurate simulations on coarse meshes.

Findings

The algorithm achieves higher accuracy than standard finite element methods.

It significantly reduces computational costs by solving on coarse grids.

Numerical experiments confirm stability and convergence of the method.

Abstract

In this paper, we combine the multiscale flnite element method to propose an algorithm for solving the non-stationary Stokes-Darcy model, where the permeability coefflcient in the Darcy region exhibits multiscale characteristics. Our algorithm involves two steps: first, conducting the parallel computation of multiscale basis functions in the Darcy region. Second, based on these multiscale basis functions, we employ an implicitexplicit scheme to solve the Stokes-Darcy equations. One signiflcant feature of the algorithm is that it solves problems on relatively coarse grids, thus signiflcantly reducing computational costs. Moreover, under the same coarse grid size, it exhibits higher accuracy compared to standard flnite element method. Under the assumption that the permeability coefflcient is periodic and independent of time, this paper demonstrates the stability and convergence of the algorithm. Finally, the rationality and effectiveness of the algorithm are verifled through three numerical experiments, with experimental results consistent with theoretical analysis.