Modeling coupled systems of free flow adjacent to a porous medium by means of fully resolved Navier–Stokes equations is limited by the immense computational cost and is thus only feasible for relatively small domains. Coupled, hybrid-dimensional models can be much more efficient by simplifying the porous domain, e.g., in terms of a pore-network model. In this work, we present a coupled pore-network/free-flow model taking into account pore-scale slip at the local interfaces between free flow and the pores. We consider two-dimensional and three-dimensional setups and show that our proposed slip condition can significantly increase the coupled model’s accuracy: compared to fully resolved equidimensional numerical reference solutions, the normalized errors for velocity are reduced by a factor of more than five, depending on the flow configuration. A pore-scale slip parameter βpore\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _{{{{\rm pore}}}}$$\end{document} required by the slip condition was determined numerically in a preprocessing step. We found a linear scaling behavior of βpore\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _{{{{\rm pore}}}}$$\end{document} with the size of the interface pore body for three-dimensional and two-dimensional domains. The slip condition can thus be applied without incurring any run-time cost. In the last section of this work, we used the coupled model to recalculate a microfluidic experiment where we additionally exploited the flat structure of the micromodel which permits the use of a quasi-3D free-flow model. The extended coupled model is accurate and efficient.

中文翻译：

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包含孔隙尺度滑移的混合维耦合孔隙网络/自由流动模型及其在微模型实验中的应用

通过完全解析的 Navier-Stokes 方程模拟多孔介质附近的自由流动耦合系统受到巨大计算成本的限制，因此仅适用于相对较小的域。通过简化多孔域，例如，在孔隙网络模型方面，耦合的混合维模型可以更加有效。在这项工作中，我们提出了一个耦合的孔隙网络/自由流动模型，考虑到自由流动和孔隙之间局部界面处的孔隙尺度滑移。我们考虑了二维和三维设置，并表明我们提出的滑移条件可以显着提高耦合模型的精度：与完全解析的等维数值参考解相比，速度的归一化误差减少了五倍以上，具体取决于关于流量配置。孔隙尺度滑移参数 βpore\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _{{{{\rm pore}}}}$$\end{document} 滑动条件所需的在预处理步骤中以数字方式确定. 我们发现 βpore\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek 的线性缩放行为} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _{{{{\rm pore}}}}$$\end{document} 与接口孔隙体的大小为三个-维域和二维域。因此可以在不产生任何运行时间成本的情况下应用滑动条件。在这项工作的最后一部分，我们使用耦合模型来重新计算微流体实验，我们另外利用了微模型的平面结构，允许使用准 3D 自由流动模型。扩展耦合模型准确有效。