基于气泡堆积的非结构化网格生成技术

Bubble Packing Method Based Unstructured Grid Generation

为了有效地提高网格的质量,基于物理思想发展了一种基于气泡堆积的非结构化网格生成算法.该算法不同于其他典型的非结构化网格生成算法,具体步骤为:首先按一定的规则向给定区域内添加具有虚拟质量的气泡,使其紧密堆积以充满整个计算区域;然后引入气泡之间的相互作用力得到各气泡的运动控制方程,通过求解该方程来调整各气泡的位置,反复迭代使所有气泡受力最小,最终达到整个系统的受力平衡,从而有效避免相邻气泡过于重叠或分离,实现调整节点位置优化网格的目的;最后通过Delaunay三角形化方法有效地联接这些气泡的中心,生成非结构化三角形网格.基于上述算法开发了相应的程序,将网格生成结果与Delaunay划分并结合拉普拉斯光顺化方法生成的网格进行了对比,发现网格的几何不规则度大大减小,质量得到了明显的提高.

An algorithm of bubble packing method （BPM） based unstructured grid generation was developed, which can improve the quality of unstructured grid effectively. Unlike the conventional methods of unstructured grid generation, the implementation procedure of BPM is： firstly, bubbles with virtual mass are added to the physical domain according to certain rules until it is fully filled by the closely packing bubbles; then the bubbles are moved by solving the motion equations constructed with the inter-bubble force, and this process is repeated to make the interbubble force minimum until the bubble system reaches equilibrium, thus the overlaps and gaps existing between bubbles can be eliminated efficiently to realize the optimization of nodes positions and improvement of grid quality; finally, the center positions of all bubbles are connected by Delaunay triangulation method （DTM） to generate an unstructured grid. Based on the present algorithm, the corresponding program was developed, and different grids generated by BPM and DTM were compared. The results show that the geometric irregularity of BPM grid decreases greatly and the grid quality improves significantly.