一种基于单元几何变形的网格修匀方法  

Mesh smoothing approach based on element geometrical deformation operation

作　　者：孙树立[1] 苑远[1] 勾志宏 张明磊[1] 

机构地区：[1]北京大学工学院力学与工程科学系,湍流与复杂系统国家重点实验室,北京100871

出　　处：《计算力学学报》2016年第4期478-484,共7页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(11172004);北京市自然科学基金(1102020);973项目子课题(2010CB731503)资助项目

摘　　要：基于单元几何变形操作提出一种高效的非结构网格质量修匀方法。其基本过程是先对每个单元独立地进行拉伸-收缩操作以优化单元的形状,然后在整个网格中通过对各单元的节点位置进行加权平均来获得改善后的网格。为进一步提高修匀方法对网格质量的优化效果,并使得该方法具备一定的网格调整能力,结合动网格技术提出了对单元进行大范围和较大幅度移动的策略;在修匀过程中还通过适当算法调整单元形心位置和单元尺寸,进一步增强了修匀方法对网格局部进行疏密调节的能力。本文方法可适用于平面和三维非结构网格的质量改善及网格调整。若干算例表明了方法的有效性。An efficient mesh smoothing approach for unstructured mesh based on element geometrical deformation operation is proposed. Firstly,shapes of all the individual elements are optimized by a two- step stretching-shrinking operation, and then the grid quality is improved through weighted average of the node position of each element in the mesh. In order to further improve the smoothing effect on the quality of grid,and enable the method to have a certain ability of mesh adjustment, a strategy of wide range and large scale movement of elements is proposed combining dynamic mesh technique. In smoot- hing process appropriate algorithm for changing the position of element centroid and element size is pres- ented to further enhance the adjustment ability of local grid density. The proposed approach can be applied to the quality improvement and adjustment for planar and three-dimensional unstructured mesh. A number of examples are presented to show the effectiveness of the method.

关 键 词：网格修匀 网格调整 单元几何变形 拉伸-收缩操作 动网格 

分 类 号：O242.21[理学—计算数学]