去除表面凸小特征的四面体网格质量优化算法  

Tetrahedral mesh quality improvement algorithm for removing convex small features on surface

作　　者：付营建 关振群[1] 曹杰 赵国忠[1] FU Ying-jian;GUAN Zhen-qun;CAO Jie;ZHAO Guo-zhong(State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology,Dalian 116024,China;School of Mathematics and Physics,University of South China,Hengyang 421001,China)

机构地区：[1]大连理工大学工程力学系工业装备结构分析优化与CAE软件全国重点实验室,大连116024 [2]南华大学数理学院,衡阳421001

出　　处：《计算力学学报》2025年第1期89-97,共9页Chinese Journal of Computational Mechanics

基　　金：国家重点研发计划(2023YFB3309100)资助项目。

摘　　要：针对现有四面体网格优化算法难以解决表面凸小特征区域网格质量差的问题,提出了基于改进优化操作算子的去除表面凸小特征的四面体网格质量优化算法。首先利用边分裂对凸小特征区域网格进行插点,构建出凸小特征尺度方向的短边。然后利用节点合并对短边进行合并,并提出决定节点合并方向的减体积合并准则。针对合并过程中可能出现的错误四面体问题,给出了二分法调整节点位置的解决方法。节点合并后,形成新的网格拓扑,使网格不再覆盖凸小特征区域,从而达到去除表面凸小特征和提高网格质量的目的。最后,通过若干带有表面凸小特征的网格优化的典型算例,验证了本文算法的有效性。To solve the problem that it is difficult for existing tetrahedral mesh quality improvement algorithms are difficult to improve the quality of elements in convex small-feature regions on a surface,this paper proposes a tetrahedral mesh quality improvement algorithm based on improved optimization operators for removing convex small-features.Firstly,in order to construct short edges in the direction of the feature scale,new nodes are inserted into meshes in convex small feature regions by using edge split.Then,the short edges are merged by using node merge,and the reduced volume merging criterion is proposed to determine the direction of node merge.To avoid wrong tetrahedrons that may occur in the merging process,a solution to adjust the node position by dichotomy is given.After the node merge,a new mesh topology is formed so that the mesh no longer covers the convex small feature regions,which achieves the purpose of removing convex small features on a surface and improving the quality of meshes.Finally,several typical examples of mesh quality improvement with convex small features on a surface demonstrate that the proposed algorithm is effective.

关 键 词：小特征去除 四面体网格 网格质量优化 网格拓扑 边分裂 

分 类 号：O302[理学—力学] O224