基于逐点修匀的Ball-IDW网格变形方法
Ball-IDWMeshDeformationMethodBasedonPointby Point Smoothing
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摘要: 为了提高网格变形的效率, 提出一种基于逐点修匀的反距离加权函数(IDW)插值网格变形方法(简称Ball-IDW方法). 根据网格拓扑关系, 以每个内部节点为中心构造子网格系统, 将整体网格分解为多个局部子网格. 通过在中心节点到子网格的边界上添加辅助插值节点来增强IDW方法的保形能力. 遍历所有内部节点, 利用逐点修匀的方式进行迭代, 直到满足收敛条件. 当网格变形幅度过大时, 通过递归二分法修正中心节点的位移来防止单元交叉, 提高方法鲁棒性. Ball-IDW方法的计算过程是显式的, 不需要求解任何线性方程, 因此具有较高的计算效率. 几个通用实例表明, 与径向基函数(RBF)方法和IDW方法相比, 该方法在质量更高的前提下, 计算效率分别提高了20%-85%、10%-80%, 解决三维问题时的变形能力提高了2倍.Abstract: Mesh deformation is a key technique for studying numerical simulation problems with moving boundaries. This paper presents the use of Ball-IDW, a point by point smoothing based inverse distance weighted function(IDW)interpolation mesh deformation method, to improve the efficiency of mesh deformation. A sub-mesh system centered around each internal node is constructed based on mesh topology relationships. Auxiliary interpolation nodes on the boundary from the center node are added to the sub-mesh to enhance the shape preserving ability of the IDW method. And all internal nodes and iterating are traversed using point by point smoothing until convergence conditions are met. Numerical examples demonstrate that due to its explicit calculation process, this method has improved computational efficiency by 20%~85% and 10%~80%, respectively, compared to the radial basis function(RBF)method and IDW method, with better quality, and the deformation ability has been improved by 2 times.