改进的三维ODT四面体网格质量优化算法

Enhanced 3D Optimal Delaunay Triangulation Optimization Method for Tetrahedral Mesh Quality

针对密度非均匀四面体网格,提出一种改进的三维ODT(optimal Delaunay triangulation)网格光顺算法,提高了ODT的适应性.在四面体网格中,以每一内部节点为核心节点,创建由与该节点相连接的四面体单元构成的星形结构;根据网格尺寸场把其星形结构转换到以核心点为中心的归一化空间内,然后在归一化空间内应用经典ODT光顺算法对核心点位置进行优化;通过中值重心坐标将核心点转换回物理空间;这样,通过逐一优化内部节点的空间位置达到优化四面体网格整体质量的目的.算例表明,该算法有效、健壮;对于密度非均匀的四面体网格,其光顺效果比经典的ODT算法更好.

For tetrahedral meshes with non-uniform density, an enhanced 3D ODT（optimal Delaunay triangulation） optimization method for mesh quality is proposed in this paper, which extends the adaptability of ODT. In a tetrahedral mesh, taking an inner node as a core, its vicinity elements form a star structure. Then the core node is transformed into a uniform size space according to size field. The optimal position of the core is obtained by applying the classical ODT optimization method. Finally, the optimal position is transformed into physical space through mean value coordinates. Through the above steps, all inner nodes are optimized and the quality of the tetrahedral mesh is improved. The numerical applications illustrate that the proposed method is effective and robust, and the smoothing result is better than the classical ODT optimization method.