基于数值流形法的渗流问题边界处理新方法

李伟; 郑宏

doi:10.11779/CJGE201710015

基于数值流形法的渗流问题边界处理新方法 English Version

李伟^1,2,
郑宏^1,2,3

1. 中国科学院武汉岩土力学研究所岩土力学与工程国家重点实验室,湖北武汉 430071;
2. 中国科学院大学,北京 100049;
3. 北京工业大学建筑工程学院,北京 100124

基金项目: 国家自然科学基金项目（11172313,11572009,51538001）; 国家基础研究计划（“973”计划）项目（2014CB047100）

详细信息

作者简介:
李伟(1988- ),男,博士研究生,主要从事计算岩土力学方面的研究。E-mail: liw9012@163.com。

中图分类号: TV139.14
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出版历程
- 收稿日期: 2016-07-25
- 发布日期: 2017-10-24

New boundary treatment for seepage flow problem based on numerical manifold method

LI Wei^1,2,
ZHENG Hong^1,2,3

1. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China;
2. University of Chinese Academy of Sciences, Beijing 100049, China;
3. College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China

摘要

摘要: 由于基于单位分解的无网格法,如无网格伽辽金法等,所构造的形函数往往不具有δ插值属性,因此难以准确施加本质边界条件和材料边界的连续性条件。而采用传统的罚函数法和拉氏乘子法,分别有合适罚因子的选取和需满足inf-sup条件等问题。所以,利用“局部解满足了要求,则由单位分解所构造的整体解会自动满足要求”的单位分解法的求解性质,通过构造不同类型物理片上的局部解,提出了改进的基于移动最小二乘插值的数值流形法（MLS-NMM）,并将其应用于稳定渗流问题的求解中。该方法不仅能直接准确施加本质边界和材料边界条件,而且能精确地求解奇异角点问题。典型算例的计算结果表明,我们所建议的方法是可行的、有效的,可为工程渗流分析提供参考。
- 移动最小二乘插值 /
- 数值流形法 /
- 单位分解法 /
- 非均质 /
- 渗流分析
Abstract: Since the shape functions derived from the partition of unity-based meshless method, such as the element-free Galerkin method, are free of the Kronecker delta property, there are great troubles in the exact imposition of the essential boundary condition and boundary continuity of materials. Nevertheless, if adopting the penalty method or the Lagrange multiplier method, problems, like the selection of proper penalty factor and the satisfaction of the inf-sup condition, will occur. This study utilizes the property of partition of unity that once the local solutions satisfy some condition, the global solution will automatically satisfy the same condition. By constructing local approximations in physical patches of different types according to the boundary condition, a new moving least square interpolation-based numerical manifold method（MLS-NMM） is developed. Through the solution of some typical seepage flow problems, it is demonstrated that the proposed procedure is capable to deal with the problems of the singular angular point precisely and may provide an alternative solution for the seepage analysis in engineering.
- moving least square interpolation /
- numerical manifold method /
- partition of unity /
- heterogeneity /
- seepage analysis

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参考文献(16)

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