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A Robust 2-Refinement Algorithm in Octree and Rhombic Dodecahedral Tree Based All-Hexahedral Mesh Generation

Zhang, Yongjie, Xinghua Liang, and Guoliang Xu

21st International Meshing Roundtable, Springer-Verlag, pp.155-172, October 7-10 2012


21st International Meshing Roundtable
San Jose, CA
October 7-10,2012

Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA

In this paper, we present a novel 2-refinement algorithm for adaptive all-hexahedral mesh generation based on two tree structures: octree and 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.

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