基于黎曼度量张量的各向异性网格划分算法研究

由于实际中某些复杂性工程问题的解具有各向异性的特点, 为采用更少的网格单元数及更好的单元质量来进行有限元分析, 以实现高效求解, 各向异性剖分单元则是一种有效的前处理技术. 因此为生成高质量各向异性网格, 首先在给定黎曼度量的基础上形成各向异性背景网格, 然后通过各向异性Delaunay原则进行边交换, 再基于力平衡实现节点的光滑平顺, 由标准化面积和标准化边长规定节点的添加与删除, 以及节点近似投影的边界约束, 得到一个与具有方向性问题相匹配的网格. 最后通过3个实例验证给出的各向异性网格划分算法的可行性.

The anisotropic mesh generation algorithm based on Riemann metric tensor

In real world, some physical problems’ solution has a direction-oriented feature, which exhibits solution changed significantly in a direction. An anisotropic meshing with fewer grids but better element quality is an effective way in pre-processing of the finite element method (FEM). Firstly, a background mesh under Riemann metric tensor is generated to achieve a high-quality anisotropic mesh. Secondly, the anisotropic Delaunay criterion for edge exchanges is employed. Thirdly, the nodes smoothing function is set based on force balance principle. In addition, operations related to node insertion and deletions are conducted in terms of the standardized area and length under the boundary constraints of approximate nodal projection. Finally, three examples are presented to demonstrate the feasibility of the proposed anisotropic meshing algorithm.