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 $L^2$ and $H^1$ 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.

翻译：本文探究了多尺度有限元方法（MsFEM）在高度非均质多孔介质中处理具有BJS界面条件的稳态Stokes-Darcy问题的应用。我们假设Darcy区域存在多尺度特征，并提出了针对多尺度Stokes-Darcy模型的算法。在离线阶段，采用MsFEM构建依赖于渗透率的离线基函数，以实现高效的粗网格模拟，且该过程通过并行计算提升效率。在线阶段，利用Robin-Robin算法推导模型解。随后，基于$L^2$和$H^1$范数进行误差分析，假设Darcy区域具有特定周期性系数。为验证所提方法，我们在高度非均质介质上开展了大量数值测试，展示了误差分析结果。