Finite element free surface seepage analysis without mesh iteration
Finite element free surface seepage analysis without mesh iteration
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DOI：
10.1002/nag.1610030103
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发表时间：
1979
影响因子：
4
通讯作者：
K. Bathe;M. Khoshgoftaar
中科院分区：
文献类型：
--
作者：
K. Bathe;M. Khoshgoftaar
摘要提出了自由表面渗流问题有限元分析的一种有效的求解方法。求解算法采用材料的非线性磁导率描述，避免了有限元网格的迭代。通过对一些问题的分析所得的结果和经验，说明了该技术的实用性。流体在多孔介质中的流动或渗透现象在工程的各个学科中都可以观察到。2因此，一旦认识到有限元分析方法的普遍性，就很自然地把重点放在发展有限元方法上，也用于分析渗流问题，以便获得更通用的分析工具3除了能够以有效的方式考虑复杂的几何形状和材料特性之外，强调有限元分析程序的发展也很重要，因为该技术在分析耦合应力和流体流动问题方面具有潜力。[45]目前用有限元法分析多孔介质中自由表面流体流动的做法是假定一个自由表面，用有限元将自由表面下的区域离散化，求解有限元模型中的流动条件，并检查自由表面边界条件是否满足足够的精度。如果自由表面的流动条件不满足规定的公差，则调整自由表面，直到满足自由表面的流动条件，问题才得到解决。根据所考虑的问题，在稳态分析中可能需要大约10到30次迭代，而在瞬态分析中，在时间响应计算的时间步长中进行迭代。在自由曲面的迭代中，每一步迭代都代表一个新的问题，每一步都可以建立一个新的有限元网格。然而，为了使分析工作量最小化，通常采用相同的基本有限元网格，但调整了节点的几何位置（可能仅靠近自由表面）。这种方案的缺点是元素可能变得非常扭曲，从而在分析中引入严重的错误，并且需要相对较大的计算量。这些缺点在三维分析中尤为明显。如果是非线性应力和流动条件*副教授。研究助理。
SUMMARY An effective solution procedure for the finite element analysis of free surface seepage problems is presented. The solution algorithm employs a non-linear permeability description of the material and avoids iteration with the finite element mesh. The results and experiences obtained in the analyses of some problems are presented to demonstrate the usefulness of the technique. The phenomena of fluid flow or seepage through porous media is observed in various disciplines of engineering.''2 It appears therefore natural that, as soon as the generality of the finite element method of analysis was recognized, emphasis was directed to develop the finite element method also for analysis of seepage problems in order to obtain a more genera1 analysis tooL3 Apart from being able to consider in an effective manner complex geometries and material properties, emphasis on the development of the finite element analysis pro- cedures is also important because of the potential of the technique for analysis of coupled stress and fluid flow problems.4s5 The current practice using the finite element method in the analysis of free surface fluid flow through porous media is to assume a free surface, discretize the domain below the free surface using finite elements, solve for the flow conditions in the finite element model, and check whether the free surface boundary conditions are satisfied with sufficient accuracy. If the flow conditions at the free surface are not satisfied to a specified tolerance, the free surface is adjusted and the problem is resolved until the free surface flow conditions are met. Depending on the problems considered, some 10 to 30 iterations may be necessary in steady-state analysis, and in transient analysis an iteration is carried out in the time steps of the time response calculation. In the iteration for the free surface, each iteration step represents a new problem, and a new finite element mesh could be established in each step. However, to keep the analysis effort to a minimum, usually the same basic finite element mesh is employed, but the geometric locations of the nodal points (possibly only near the free surface) are adjusted. The disadvantages of this scheme are that the elements can become very distorted, thus introducing severe errors in the analysis, and that a relatively large computational effort is required. These disadvantages are particularly pronounced in three-dimensional analysis. If non-linear stress and flow conditions * Associate Professor. t Research Assistant.