A frontal approach to hex-dominant mesh generation

Abstract

Indirect quad mesh generation methods rely on an initial triangular mesh. So called triangle-merge techniques are then used to recombine the triangles of the initial mesh into quadrilaterals. This way, high-quality full-quad meshes suitable for finite element calculations can be generated for arbitrary two-dimensional geometries. In this paper, a similar indirect approach is applied to the three-dimensional case, i.e., a method to recombine tetrahedra into hexahedra. Contrary to the 2D case, a 100% recombination rate is seldom attained in 3D. Instead, part of the remaining tetrahedra are combined into prisms and pyramids, eventually yielding a mixed mesh. We show that the percentage of recombined hexahedra strongly depends on the location of the vertices in the initial 3D mesh. If the vertices are placed at random, less than 50% of the tetrahedra will be combined into hexahedra. In order to reach larger ratios, the vertices of the initial mesh need to be anticipatively organized into a lattice-like structure. This can be achieved with a frontal algorithm, which is applicable to both the two- and three-dimensional cases. The quality of the vertex alignment inside the volumes relies on the quality of the alignment on the surfaces. Once the vertex placement process is completed, the region is tetrahedralized with a Delaunay kernel. A maximum number of tetrahedra are then merged into hexahedra using the algorithm of Yamakawa-Shimada. Non-uniform mixed meshes obtained following our approach show a volumic percentage of hexahedra that usually exceeds 80%. The execution times are reasonable. However, non-conformal quadrilateral faces adjacent to triangular faces are present in the final meshes.