Tensor-Guided Hex-Dominant Mesh Generation with Targeted All-Hex Regions

Abstract

In this paper, we present a method for generating hex-dominant meshes with targeted all-hex regions over closed volumes. The method begins by generating a piecewise-continuous metric tensor field over the volume. This field specifies desired anisotropy and directionality during the subsequent meshing stages. Meshing begins with field-guided tiling of individual structured hexahedral fronts wherever suitable and in regions of interest (ROI). Then, the hexahedral fronts are incorporated into an existing hex-dominant meshing procedure, resulting in a good quality hex-dominant mesh. Presently, many successful hex meshing methods require significant preprocessing and have limited control over mesh directionality and anisotropy. In light of this, hex-dominant meshes have gained traction for industry analyses. In turn, this presents the challenge of increasing the hex-to-tet ratio in hex-dominant meshes, especially in ROI specified by analysts. Here, a novel three-part strategy addresses this goal: generation of a guiding tensor field, application of topological insertion operators to tile elements and grow fronts towards the boundary, and incorporation of the fronts into a hex-dominant meshing procedure. The field directionality is generated from boundary information, which is then adjusted to specified uniform anisotropy. Carefully placed streamsurfaces of the metric field are intersected to shape new elements, and the insertion operators maintain mesh integrity while tiling new elements. Finally, the effectiveness of the proposed method is demonstrated with a non-linear, large deformation, finite element analysis.