Multiscale Modeling &Simulation, Volume 19, Issue 2, Page 731-757, January 2021.
Boundary conditions at the interface between the free-flow region and the adjacent porous medium is a key issue for physically consistent modeling and accurate numerical simulation of flow and transport processes in coupled systems due to the interface driven nature of such processes. Interface conditions available in the literature have several weak points: most of them are suitable only for flows parallel to the fluid-porous interface, some are restricted to specific boundary value problems, and others contain unknown model parameters which still need to be determined. These facts severely restrict the variety of applications that can be successfully modeled. We propose new interface conditions which are valid for arbitrary flow directions. These coupling conditions are rigorously derived using the theory of homogenization and boundary layers. All effective parameters appearing in these conditions are computed numerically based on the geometrical configuration of the coupled system. The developed conditions are validated by the comparison of numerical simulation results for the coupled Stokes--Darcy model and the pore-scale resolved model. In addition, the new interface conditions are compared with the classical conditions to demonstrate the advantage of the proposed conditions.

中文翻译：

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斯托克斯中任意流的有效耦合条件--达西系统

多尺度建模与仿真，第 19 卷，第 2 期，第 731-757 页，2021 年 1 月。
由于这些过程的界面驱动性质，在自由流动区域和相邻多孔介质之间的界面处的边界条件是耦合系统中流动和传输过程的物理一致性建模和精确数值模拟的关键问题。文献中可用的界面条件有几个弱点：大多数仅适用于平行于流体-多孔界面的流动，一些仅限于特定的边界值问题，而另一些包含未知的模型参数，这些参数仍需要确定。这些事实严重限制了可以成功建模的应用程序的多样性。我们提出了对任意流向有效的新界面条件。这些耦合条件是使用均匀化和边界层理论严格推导出来的。在这些条件下出现的所有有效参数都是基于耦合系统的几何配置进行数值计算的。通过对耦合 Stokes-Darcy 模型和孔隙尺度解析模型的数值模拟结果进行比较，验证了所开发的条件。此外，新的界面条件与经典条件进行了比较，以证明所提出条件的优势。