Automatic Hexahedral Mesh Generation Algorithm For Many-To-Many Sweep Volumes

Finite element analyses on hexahedral meshes usually behave better than the analyses on tetrahedral meshes in terms of accuracy and efficiency. However, automatic generation of a hexahedral mesh is more difficult than the generation of a tetrahedral mesh for a complex geometry. None of the current hexahedral mesh generation schemes can automatically generate an all-hexahedral mesh for any geometry so far. The sweep method is one particular hexhedral mesh method for sweep volumes. Because sweep volumes are very popular in modeling, the sweep method is one of the prevailing methods for hexahedral mesh generation in practice.Sweep volumes are categorized into one-to-one, many-to-one and many-to-many volumes according to the number of their source faces and target faces. The hexahedral mesh generation algorithm for the simplest one-to-one sweep volume is addressed first. Next, an automatic scheme is employed to decompose the sweep volume with many source and one target faces (many-to-one volume) into a combination of smaller one-to-one volumes, which can then be meshed by the one-to-one algorithm individually. Furthermore, the decomposition scheme is enhanced to subdivide the volume with many source and target faces (many-to-many volume) into a combination of smaller many-to-one volumes, which can then be meshed by the many-to-one algorithms individually.Besides the decomposition schemes, an automatic many-to-many hexahedral mesh generation algorithm is composed of many other issues, such as automatic identification of source and target faces, structured mesh generation of lateral faces, determination of the interval assignment of model curves, mesh projection, boundary loop imprinting and etc. In addition to review the prevailing algorithms for these issues and integrate them together, a novel interior node placement algorithm for the mesh projection issue and a novel imprinting algorithm are detailed in this study.Interior node placement is the key step of the mesh projection scheme that is required by meshing the target faces and the interior layers of a sweep volume. Affine mapping is the prevailing placement technique, which is vital to ensure the element quality of the resulting meshes. In this study, a novel computing technique for the mapping function is proposed in order to overcome two drawbacks of the previous techniques. One drawback is that the mapping function is not unique when the boundary nodes to be projected are coplanar. The other is that the generated interior elements by the projection may twist when the volume is composed of curved source and target faces or curved sweep path.Imprinting is a key step of the decomposition scheme for many-to-many volumes, which imprints a target loop onto the source loop to make the overlap part of both loops matches in topology. This step is essentially a Boolean operation for two polygons. The previous imprint procedures need discuss various cases to ensure robustness, thus suffers heavy coding efforts in practice. The proposed imprinting procedure is based on the well-known Delaunay triangulation and conceptually simpler. Moreover, the imprinting procedure can be enhanced as a general polygon Boolean operation that can manage various degenerate cases, e.g. the concave polygons, the polygons with holes, the self-intersecting polygons, the number of polygons being more than two.