A robust 2-refinement algorithm in octree or rhombic dodecahedral tree based all-hexahedral mesh generation

In this paper, we present a novel 2-refinement algorithm for adaptive all-hexahedral mesh generation based on two tree structures: octree or rhombic dodecahedral tree. Given a smooth boundary surface, we first use a pre-defined error function to detect the main surface features, and build a strongly-balanced octree. Then a novel 2-refinement algorithm is developed to eliminate all hanging nodes in the octree, which is robust for any unstructured meshes and induces a smooth transition with very little propagation. Later, all elements outside and around the boundary are removed to create the octree core mesh and a buffer zone. The boundary points on the core mesh are projected onto the surface and form the final mesh. Motivated from nature, a new tree structure based on rhombic dodecahedron is introduced. Sharp features are also detected and preserved during mesh generation. Finally, pillowing, geometric flow and optimization-based smoothing are applied to improve quality of the constructed meshes.