基于数值流形法的渗流问题边界处理新方法

发布时间：2018-04-23 18:28

本文选题：移动最小二乘插值 + 数值流形法　；参考：《岩土工程学报》2017年10期

【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?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。
[Abstract]:Because of the meshless method based on unit decomposition, such as the meshless Galerkin method, the shape functions constructed often do not have? Interpolation attribute makes it difficult to apply the essential boundary condition and the continuity condition of material boundary accurately. The traditional penalty function method and Lagrangian multiplier method are used to select the appropriate penalty factors and to satisfy the inf-sup condition respectively. Therefore, by using the solution property of the unit decomposition method, which "the local solution satisfies the requirement, the global solution constructed by the unit decomposition will automatically meet the requirement", by constructing the local solution on different types of physical slices, An improved MLS-NMMM method based on moving least square interpolation is proposed and applied to the solution of steady seepage problem. This method can not only directly and accurately apply essential boundary and material boundary conditions, but also solve singularity corner problem accurately. The results of typical numerical examples show that the proposed method is feasible and effective and can be used as a reference for engineering seepage analysis.
【作者单位】：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;中国科学院大学;北京工业大学建筑工程学院;
【基金】：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)
【分类号】：O357.3

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