Commenced in January 2007
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Paper Count: 30172
Development of Improved Three Dimensional Unstructured Tetrahedral Mesh Generator

Authors: Ng Yee Luon, Mohd Zamri Yusoff, Norshah Hafeez Shuaib

Abstract:

Meshing is the process of discretizing problem domain into many sub domains before the numerical calculation can be performed. One of the most popular meshes among many types of meshes is tetrahedral mesh, due to their flexibility to fit into almost any domain shape. In both 2D and 3D domains, triangular and tetrahedral meshes can be generated by using Delaunay triangulation. The quality of mesh is an important factor in performing any Computational Fluid Dynamics (CFD) simulations as the results is highly affected by the mesh quality. Many efforts had been done in order to improve the quality of the mesh. The paper describes a mesh generation routine which has been developed capable of generating high quality tetrahedral cells in arbitrary complex geometry. A few test cases in CFD problems are used for testing the mesh generator. The result of the mesh is compared with the one generated by a commercial software. The results show that no sliver exists for the meshes generated, and the overall quality is acceptable since the percentage of the bad tetrahedral is relatively small. The boundary recovery was also successfully done where all the missing faces are rebuilt.

Keywords: Mesh generation, tetrahedral, CFD, Delaunay.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1070169

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References:


[1] A. Bowyer, Computing Dirichlet tessellations, The Computer Journal, 24(2):162-166, 1981.
[2] D. F. Watson, Computing the n-dimensional tessellation with application to Voronoi polytopes, The Computer Journal, 24(2):167-172, 1981.
[3] J.R. Shewchuk, Tetrahedral Mesh Generation by Delaunay Refinement, Proceedings of the Fourteenth Annual Symposium on Computational Geometry, 86-95, 1998.
[4] G. Timothy, Block-Structured Applications. Handbook of Grid Generation . Thompson, Joe F.; Bharat K.Soni, Weatherill , Nigel P..Editors. CRC Press, 13-1, 1999.
[5] H. Borouchaki and S.H. Lo, Fast Delaunay Triangulation in Three Dimensions, Comput. Methods Appl. Mech. Engrg. 128: 153-167, 1995.
[6] R. Maehara, The Jordan curve theorem via the Brouwer fixed point theorem, American Mathematical Monthly 91, no. 10, pp. 641-643,1984.
[7] C.J. Ogayar, R.J. Segura, F.R. Feito, F.R. Point in solid strategies, Computer & Graphics 29, 616-624, 2005.
[8] J.R. Shewchuk, Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator. In First Workshop on Applied Computational Geometry. ACM, 124-133, 1996.
[9] B.M. Klingner, J.R. Shewchuk, Aggressive Tetrahedral Mesh Improvement, Proceedings of the Sixteenth International Meshing Roundtable. 3-23, 2007.
[10] S.W. Cheng, T.K. Dey, H. Edelsbrunner, M.A. Facello, S.H. Teng, liver Exudation, J.ACM, 47, 883-904, 2000.
[11] A. Pierre, S.D. Cohen, Y. Mariette, D. Mathieu, Variational Tetrahedral Meshing, Special issue on Proceedings of SIGGRAPH, ACM Transactions on Graphics 24: 617-625, 2005.
[12] J.R. Shewchuk, Theoretically Guaranteed Delaunay Mesh Generation - In practice, Short course, Fourteenth International Meshing Roundtable, San Diego, 2005.