用逐点插入法生成Delaunay四面体自适应网格

介绍一种基于Delaunay算法的四面体自适应网格的自动划分方法。该方法用单元尺度场控制生成网格的疏密分布,在不满足尺度场要求的单元面形心处插入新节点,同时计算新节点单元尺寸参数,实现三维实体的Delaunay四面体自动划分。此方法具有几个特点:一是表面网格与体内网格同步划分,无需区分两者;二是结点与单元同时生成;三是生成网格自适应性好,疏密分布任意。另外,还介绍了三维网格划分中两个相关算法:一个是约束面恢复算法,该算法基于约束面不允许有单元边与之相交的性质而提出的;另一个是将二维射线法推广至三维空间,判断一个点是否在一多面体内,实现了凹多面体的划分。最后通过算例对单元质量进行了评价。本文所述方法是一种有效的四面体自适应单元生成算法。

An adaptive delaunay tetrahedron mesh generation method through point by point insertion

This paper presents an adaptive Delaunay tetrahedron mesh generation method.The method controls mesh density through an element size field.The field grows with mesh generation.Elemental vertexes are inserted one by one in centroids of element facets which do not satisfy the size field requirements.The method has the following features: 1) vertexes and elements are generated at the same step;2) Surfaces meshes and interior meshes of a body can be generated at the same step without distinguishing them;3) Element quality and adaptability are favorable.In addition,two relative algorithms are introduced too.One is constraint facets recovery algorithm.The algorithm is based on the property of constraint facets: no element edges can intersect with constraint facets.The other one is concerning how to judge whether a vertex is inside an arbitrary enclosure polyhedron or not.It is generated from the ray method under two dimensional condition.The element quality is assessed through some examples.Sliver elements are few.The method presented is an effective way to generate adaptive Delaunay tetrahedron mesh.