刘远财, 崔朋飞, 张海容, 赵兰浩. 基于改进Level-Set方法的非稳定渗流自由面数值模拟[J]. 水力发电学报, 2023, 42(11): 68-77.
引用本文: 刘远财, 崔朋飞, 张海容, 赵兰浩. 基于改进Level-Set方法的非稳定渗流自由面数值模拟[J]. 水力发电学报, 2023, 42(11): 68-77.
LIU Yuancai, CUI Pengfei, ZHANG Hairong, ZHAO Lanhao. Numerical simulations of unsteady seepage free surface based on improved conservation Level-Set method[J]. JOURNAL OF HYDROELECTRIC ENGINEERING, 2023, 42(11): 68-77.
Citation: LIU Yuancai, CUI Pengfei, ZHANG Hairong, ZHAO Lanhao. Numerical simulations of unsteady seepage free surface based on improved conservation Level-Set method[J]. JOURNAL OF HYDROELECTRIC ENGINEERING, 2023, 42(11): 68-77.

基于改进Level-Set方法的非稳定渗流自由面数值模拟

Numerical simulations of unsteady seepage free surface based on improved conservation Level-Set method

  • 摘要: 含自由面非稳定渗流问题广泛存在于水利工程及岩土工程中,渗流自由面通常随时间动态变化,属于动边界问题,是非稳定渗流研究的重点和难点。本文在有限元框架内提出基于改进守恒Level-Set方法的非稳定渗流自由面数值模拟方法。采用改进守恒Level Set方法在固定网格上隐式地捕捉非稳定渗流自由面,巧妙避开了其他固定网格方法在处理自由面时的困难,计算方便,且具有良好的质量守恒性和准确性。首先给出了多孔介质非稳定渗流问题的控制方程及其数值离散,之后给出了渗流自由面追踪的方法及物理特性参数的插值方法,最后通过均质土坝、非均质矩形坝、河床下渗问题等经典算例,验证了本文方法的准确性和有效性。

     

    Abstract: The problem of unsteady seepage with a free surface is widely recognized in hydraulic engineering and geotechnical engineering. The free surface, usually changing dynamically with time, poses a dynamic boundary problem, and is a key and difficult issue in unsteady seepage research. A free surface numerical simulation method of unsteady seepage based on the finite element method and the improved conservation Level Set method is presented in this paper. We use the Level Set method to capture unsteady seepage free surfaces implicitly on a fixed grid, subtly avoiding the difficulty of other fixed grid methods in handling free surfaces, and have achieved convenient calculations with a good conservation of mass and good accuracy. This paper first discusses the governing equations and numerical discretization of unsteady seepage in porous media, then describes a method for free surface tracking and an algorithm for interpolating physical characteristic parameters. Finally, the accuracy and effectiveness of this new method are verified via several classical examples, such as homogeneous earth dams, heterogeneous rectangular dams, and riverbed seepage problems.

     

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