Abstract Free surface flow analysis in porous media is challenging in many practical applications with strong non-linearity. An equivalent pipe network model is proposed for the simulation and evaluation of free surface flow in porous media. On the basis of representative elementary volume with homogeneous pore-scale patterns, the pore space of the homogeneous isotropic porous media is conceptualized as a collection of capillary tubes. According to Hagen-Poiseulle's law and flux equivalence principle, equivalent hydraulic parameters and unified governing formulations for the pipe network model are deduced. The two-dimensional free surface flow problem is reduced to a one-dimensional problem of pipe networks and a one-dimensional procedure based on the finite element method is then developed by introducing a continuous penalized Heaviside function. The proposed equivalent pipe network model is verified with results from numerical solutions and laboratory-measured data available in the literature, and good agreements are obtained. The proposed equivalent pipe network model is shown to be effective in analyzing the free surface flow in porous media. The numerical results also indicate that the proposed equivalent pipe network model has weak sensitivity of the mesh size and penalty parameters.

中文翻译：

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多孔介质中自由表面流动的等效管网模型

摘要 多孔介质中的自由表面流动分析在许多具有强非线性的实际应用中具有挑战性。提出了一种等效管网模型，用于多孔介质中自由表面流动的模拟和评估。在具有均匀孔隙尺度模式的代表性单元体积的基础上，均匀各向同性多孔介质的孔隙空间被概念化为毛细管的集合。根据Hagen-Poiseulle定律和通量等价原理，推导出管网模型的等效水力参数和统一控制公式。二维自由表面流动问题被简化为管网的一维问题，然后通过引入连续惩罚 Heaviside 函数开发基于有限元方法的一维程序。所提出的等效管网模型通过文献中可用的数值解和实验室测量数据的结果进行了验证，并获得了良好的一致性。表明所提出的等效管网模型在分析多孔介质中的自由表面流动方面是有效的。数值结果还表明，所提出的等效管网模型对网格尺寸和惩罚参数的敏感性较弱。并获得了良好的协议。表明所提出的等效管网模型在分析多孔介质中的自由表面流动方面是有效的。数值结果还表明，所提出的等效管网模型对网格尺寸和惩罚参数的敏感性较弱。并获得了良好的协议。表明所提出的等效管网模型在分析多孔介质中的自由表面流动方面是有效的。数值结果还表明，所提出的等效管网模型对网格尺寸和惩罚参数的敏感性较弱。