Abstract A simple and physically sound model has been proposed to investigate the transient free surface flow behavior in porous media. Instead of the continuum-based model, the pore space between solid grains is conceptualized as a network of horizontal and vertical flow paths and then the flow paths are characterized by straight line elements. Based on the Darcy's law and flux equivalence between the continuum-based model and line element model, equivalent hydraulic parameters and continuity equation are derived through the control volume. By introducing a local coordinate system, unified governing equations and equivalent boundary conditions of the line element model are obtained in the form of one-dimensional formulations. The two-dimensional transient free surface flow problem is reduced to a one-dimensional problem of line element network and a finite-element algorithm is developed. The proposed one-dimensional line element model is verified by three illustrative examples, which indicate that the numerical results can satisfactorily match the analytical solutions and experimental observations from different sources. It is found that the solution accuracy has weak sensitivity of time-step size but sensitive to the spacing size, while numerical efficiency can be well guaranteed for different time-step sizes and spacing sizes. Based on the numerical results, the proposed model can give better performance for the evolution of free surfaces than the residual flow procedure, and is efficient to model transient surface flow with a complex drainage system.

中文翻译：

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多孔介质中瞬态自由表面流动的一维线元模型

摘要 为了研究多孔介质中的瞬态自由表面流动行为，提出了一种简单且物理上合理的模型。代替基于连续介质的模型，固体颗粒之间的孔隙空间被概念化为水平和垂直流动路径的网络，然后流动路径以直线元素为特征。基于连续介质模型和线元模型之间的达西定律和通量等价性，通过控制体积推导出等效水力参数和连续性方程。通过引入局部坐标系，以一维公式的形式得到线元模型的统一控制方程和等效边界条件。将二维瞬态自由表面流动问题简化为线元网络的一维问题，并提出了有限元算法。所提出的一维线元模型通过三个说明性例子进行了验证，表明数值结果可以令人满意地匹配不同来源的解析解和实验观察。发现求解精度对时间步长的敏感性较弱，但对间隔大小敏感，而不同时间步长和间隔大小的数值效率可以得到很好的保证。基于数值结果，所提出的模型可以提供比剩余流程序更好的自由表面演化性能，并且可以有效地模拟具有复杂排水系统的瞬态表面流。