{"title":"Development of Improved Three Dimensional Unstructured Tetrahedral Mesh Generator","authors":"Ng Yee Luon, Mohd Zamri Yusoff, Norshah Hafeez Shuaib","volume":34,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":788,"pagesEnd":796,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/8054","abstract":"Meshing is the process of discretizing problem\r\ndomain into many sub domains before the numerical calculation can\r\nbe performed. One of the most popular meshes among many types of meshes is tetrahedral mesh, due to their flexibility to fit into almost\r\nany domain shape. In both 2D and 3D domains, triangular and tetrahedral meshes can be generated by using Delaunay triangulation.\r\nThe quality of mesh is an important factor in performing any Computational Fluid Dynamics (CFD) simulations as the results is\r\nhighly affected by the mesh quality. Many efforts had been done in\r\norder to improve the quality of the mesh. The paper describes a mesh\r\ngeneration routine which has been developed capable of generating\r\nhigh quality tetrahedral cells in arbitrary complex geometry. A few\r\ntest cases in CFD problems are used for testing the mesh generator.\r\nThe result of the mesh is compared with the one generated by a\r\ncommercial software. The results show that no sliver exists for the\r\nmeshes generated, and the overall quality is acceptable since the percentage of the bad tetrahedral is relatively small. The boundary\r\nrecovery was also successfully done where all the missing faces are\r\nrebuilt.","references":"[1] A. Bowyer, Computing Dirichlet tessellations, The Computer Journal,\r\n24(2):162-166, 1981.\r\n[2] D. F. Watson, Computing the n-dimensional tessellation with application to Voronoi polytopes, The Computer Journal, 24(2):167-172, 1981.\r\n[3] J.R. Shewchuk, Tetrahedral Mesh Generation by Delaunay Refinement,\r\nProceedings of the Fourteenth Annual Symposium on Computational\r\nGeometry, 86-95, 1998.\r\n[4] G. Timothy, Block-Structured Applications. Handbook of Grid\r\nGeneration . Thompson, Joe F.; Bharat K.Soni, Weatherill , Nigel P..Editors. CRC Press, 13-1, 1999.\r\n[5] H. Borouchaki and S.H. Lo, Fast Delaunay Triangulation in Three\r\nDimensions, Comput. Methods Appl. Mech. Engrg. 128: 153-167, 1995.\r\n[6] R. Maehara, The Jordan curve theorem via the Brouwer fixed point\r\ntheorem, American Mathematical Monthly 91, no. 10, pp. 641-643,1984.\r\n[7] C.J. Ogayar, R.J. Segura, F.R. Feito, F.R. Point in solid strategies, Computer & Graphics 29, 616-624, 2005.\r\n[8] J.R. Shewchuk, Triangle: Engineering a 2D Quality Mesh Generator\r\nand Delaunay Triangulator. In First Workshop on Applied\r\nComputational Geometry. ACM, 124-133, 1996.\r\n[9] B.M. Klingner, J.R. Shewchuk, Aggressive Tetrahedral Mesh\r\nImprovement, Proceedings of the Sixteenth International Meshing Roundtable. 3-23, 2007.\r\n[10] S.W. Cheng, T.K. Dey, H. Edelsbrunner, M.A. Facello, S.H. Teng, liver Exudation, J.ACM, 47, 883-904, 2000.\r\n[11] A. Pierre, S.D. Cohen, Y. Mariette, D. Mathieu, Variational Tetrahedral\r\nMeshing, Special issue on Proceedings of SIGGRAPH, ACM Transactions on Graphics 24: 617-625, 2005.\r\n[12] J.R. Shewchuk, Theoretically Guaranteed Delaunay Mesh Generation -\r\nIn practice, Short course, Fourteenth International Meshing Roundtable,\r\nSan Diego, 2005.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 34, 2009"}