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.

翻译：本文结合多尺度有限元方法，提出了一种求解非稳态Stokes-Darcy模型的算法，其中Darcy区域的渗透系数呈现多尺度特征。该算法分为两步：首先，在Darcy区域并行计算多尺度基函数；其次，基于这些多尺度基函数，采用隐式-显式格式求解Stokes-Darcy方程组。该算法的一个重要特点是可在相对粗网格上求解问题，从而显著降低计算成本。此外，在相同粗网格尺寸下，其精度优于标准有限元方法。在渗透系数具有周期性且不依赖于时间的假设下，本文论证了算法的稳定性和收敛性。最后，通过三个数值实验验证了算法的合理性和有效性，实验结果与理论分析一致。