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Space-Time Finite Element Method for Transient and Unconfined Seepage Flow Analysis
Finite Elements in Analysis and Design ( IF 3.1 ) Pub Date : 2021-07-06 , DOI: 10.1016/j.finel.2021.103632
Vikas Sharma 1 , Kazunori Fujisawa 1 , Akira Murakami 1
Affiliation  

This paper aims to develop a moving-mesh type Finite Element Method for the computation of the transient unconfined seepage flow through the porous medium. The proposed method is based on the time discontinuous Galerkin Space-Time Finite Element Method (ST/FEM). It solves the seepage problem in the saturated region. The primary unknown in ST/FEM is piezometric pressure. Fluid velocities are derived from the pressure using Darcy's law. Further, an iterative algorithm has been proposed in this paper to implement the proposed method. In each iteration step, the computation domain is updated according to the flow velocity on the phreatic boundary. Subsequently, internal nodes are moved using the mesh moving technique to accommodate the newly updated computation domain. The mesh moving technique, which is discussed in this paper, is based on an elasticity problem. ST/FEM is employed to analyze several unconfined seepage flow problems, and results of steady state solutions are compared with those available in the literature to demonstrate the efficacy of the proposed scheme.



中文翻译:

瞬态无侧限渗流分析的时空有限元法

本文旨在开发一种移动网格类型的有限元方法,用于计算通过多孔介质的瞬态无侧限渗流。所提出的方法基于时间不连续伽辽金时空有限元方法(ST/FEM)。解决了饱和区的渗流问题。ST/FEM 中的主要未知数是测压压力。流体速度是使用达西定律从压力推导出来的。此外,本文提出了一种迭代算法来实现所提出的方法。在每个迭代步骤中,计算域根据潜水边界上的流速进行更新。随后,使用网格移动技术移动内部节点以适应新更新的计算域。本文讨论的网格移动技术,基于弹性问题。ST/FEM 被用来分析几个无侧限渗流问题,并将稳态解的结果与文献中可用的结果进行比较,以证明所提出方案的有效性。

更新日期:2021-07-06
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