Multiscale finite element method for Stokes-Darcy model
Abstract
This paper explores the application of the multiscale finite element method (MsFEM) to address steady-state Stokes-Darcy problems with BJS interface conditions in highly heterogeneous porous media. We assume the existence of multiscale features in the Darcy region and propose an algorithm for the multiscale Stokes-Darcy model. During the offline phase, we employ MsFEM to construct permeability-dependent offline bases for efficient coarse-grid simulation, with this process conducted in parallel to enhance its efficiency. In the online phase, we use the Robin-Robin algorithm to derive the model's solution. Subsequently, we conduct error analysis based on and norms, assuming certain periodic coefficients in the Darcy region. To validate our approach, we present extensive numerical tests on highly heterogeneous media, illustrating the results of the error analysis.
Cite
@article{arxiv.2401.03672,
title = {Multiscale finite element method for Stokes-Darcy model},
author = {Yachen Hong and Wenhan Zhang and Lina Zhao and Haibiao Zheng},
journal= {arXiv preprint arXiv:2401.03672},
year = {2024}
}