Summary
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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References
Dijkstra, E.W.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)
Ebeida, M.S., Patney, A., Owens, J.D., Mestreau, E.: Isotropic conforming refinement of quadrilateral and hexahedral meshes using two-refinement templates. Int. J. Numer. Meth. Engng 88(10), 974–985 (2011)
Edgel, J.: An adaptive grid-based all hexahedral meshing algorithm based on 2-refinement. MS Thesis, Brigham Young University (2010)
Folwell, N., Mitchell, S.: Reliable whisker weaving via curve contraction. Eng. Comput. 15(3), 292–302 (1999)
Freitag, L.A.: On combining Laplacian and optimization-based mesh smoothing techniques. Trends in Unstructured Mesh Generation, ASME 220, 37–43 (1997)
Ito, Y., Shih, A., Soni, B.: Octree-based reasonable-quality hexahedral mesh generation using a new set of refinement templates. Int. J. Numer. Methods Eng. 77(13), 1809–1833 (2009)
Knupp, P.M.: Next-generation sweep tool: a method for generating all-hex meshes on two-and-one-half dimensional geometries. In: 7th Int. Meshing Roundtable, pp. 505–513 (1998)
Liang, X., Ebeida, M., Zhang, Y.: Guaranteed-quality all-quadrilateral mesh generation with feature preservation. Comp. Meth. Appl. Mech. Engr. 199(29-32), 2072–2083 (2010)
Liang, X., Zhang, Y.: Hexagon-based all-quadrilateral mesh generation with guaranteed angle bounds. Comp. Meth. Appl. Mech. Engr. (2011) (accepted)
Qian, J., Zhang, Y.: Automatic unstructured all-hexahedral mesh generation from B-Reps for non-manifold CAD assemblies. Engineering with Computers (2012), doi: 10.1007/s00366-011-0232-z
Schneiders, R.: Refining quadrilateral and hexahedral element Meshes. In: 5th Int. Meshing Roundtable, pp. 383–398 (1996)
Schneiders, R., Schindler, R., Weiler, F.: Octree-based generation of hexahedral element meshes. In: 5th Int. Meshing Roundtable, pp. 205–216 (1996)
Staten, M.L., Kerr, R.A., Owen, S.J., Blacker, T.D.: Unconstrained paving and plastering: progress update. In: 15th Int. Meshing Roundtable, pp. 469–486 (2006)
Zhang, Y., Bajaj, C.: Adaptive and quality quadrilateral/hexahedral meshing from volumetric Data. Comput. Meth. Appl. Mech. Eng. 195(9-12), 942–960 (2006)
Zhang, Y., Bajaj, C., Sohn, B.-S.: 3D finite element meshing from imaging data. Comput. Meth. Appl. Mech. Eng. 194(48-49), 5083–5106 (2005)
Zhang, Y., Bajaj, C., Xu, G.: Surface smoothing and quality improvement of quadrilateral/hexahedral meshes with geometric flow. Commun. Numer. Meth. Eng. 25(1), 1–18 (2009)
Zhang, Y., Xu, G., Bajaj, C.: Quality meshing of implicit solvation models of biomolecular structures. Computer Aided Geometric Design 23(6), 510–530 (2006)
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Zhang, Y., Liang, X., Xu, G. (2013). A Robust 2-Refinement Algorithm in Octree and Rhombic Dodecahedral Tree Based All-Hexahedral Mesh Generation. In: Jiao, X., Weill, JC. (eds) Proceedings of the 21st International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33573-0_10
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DOI: https://doi.org/10.1007/978-3-642-33573-0_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33572-3
Online ISBN: 978-3-642-33573-0
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