Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-22T18:23:49.493Z Has data issue: false hasContentIssue false
  • English
  • Français

Robust and Quality Boundary Constrained Tetrahedral Mesh Generation

Published online by Cambridge University Press:  03 June 2015

Songhe Song ,
Min Wan ,
Shengxi Wang ,
Desheng Wang  and
Zhengping Zou
Songhe Song*
Affiliation:
Department of Mathematics and Systems Science, State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, P.R. China State Key Laboratory of Aerodynamics, China Aerodynamics and Development Center, Mianyang 621000, P.R. China
Min Wan*
Affiliation:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371
Shengxi Wang*
Affiliation:
Taiyuan Satellite Launch Center, 030027, P.R. China
Desheng Wang*
Affiliation:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371
Zhengping Zou*
Affiliation:
National Key Laboratory of Science and Technology on Aero-Engine Aero-Thermodynamics, School of Jet Propulsion, Beijing University of Aeronautics and Astronautics, Beijing 100191, P.R. China
*
Corresponding author.Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
Get access

Abstract

A novel method for boundary constrained tetrahedral mesh generation is proposed based on Advancing Front Technique (AFT) and conforming Delaunay triangulation. Given a triangulated surface mesh, AFT is firstly applied to mesh several layers of elements adjacent to the boundary. The rest of the domain is then meshed by the conforming Delaunay triangulation. The non-conformal interface between two parts of meshes are adjusted. Mesh refinement and mesh optimization are then preformed to obtain a more reasonable-sized mesh with better quality. Robustness and quality of the proposed method is shown. Convergence proof of each stage as well as the whole algorithm is provided. Various numerical examples are included as well as the quality of the meshes.

Keywords

65L5065M5065N5065D18Unstructured tetrahedral meshAdvancing Front Techniqueconforming Delaunay triangulationboundary constrainedmesh refinementmesh optimization
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 5 , November 2013 , pp. 1304 - 1321
Copyright
Copyright © Global Science Press Limited 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Shephard, M, Georges, M. Automatic three-dimensional mesh generation by the finite octree technique. International Journal for Numerical Methods in Engineering, 2005; 32(4):709–749.CrossRefGoogle Scholar
[2]Rassineux, A.Generation and optimization of tetrahedral meshes by advancing front technique. International Journal for Numerical Methods in Engineering, 1998; 41(4):651–674.Google Scholar
[3]Löhner, R, Parikh, P. Generation of three-dimensional unstructured grids by the advancing-front method. International Journal for Numerical Methods in Fluids, 2005; 8(10):1135–1149.Google Scholar
[4]George, P, Hecht, F, Saltel, E. Automatic mesh generator with specified boundary. Computer Methods in Applied Mechanics and Engineering, 1991; 92(3):269–288.Google Scholar
[5]Weatherill, N. The integrity of geometrical boundaries in the two-dimensional Delaunay triangulation. Communications in Applied Numerical Methods, 2005; 6(2):101–109.Google Scholar
[6]Frey, P, Borouchaki, H, George, P. 3D Delaunay mesh generation coupled with an advancing-front approach. Computer Methods in Applied Mechanics and Engineering, 1998; 157(1-2):115–131.Google Scholar
[7]Shewchuk, J, Miller, G, David, R. Delaunay Refinement Mesh Generation, 1997.Google Scholar
[8]Karamete, B, Beall, M, Shephard, M. Triangulation of arbitrary polyhedra to support automatic mesh generators. International Journal for Numerical Methods in Engineering, 2000; 49(1-2):167–191.Google Scholar
[9]George, P, Borouchaki, H. Delaunay Triangulation and Meshing: Application to Finite Elements. Kogan Page, 1998.Google Scholar
[10]Weatherill, N, Hassan, O. Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints. International Journal for Numerical Methods in Engineering, 1994; 37(12):2005–2039.Google Scholar
[11]Du, Q, Wang, D. Constrained boundary recovery for three dimensional Delaunay triangulations. International Journal for Numerical Methods in Engineering, 2004; 61(9):1471–1500.Google Scholar
[12]Du, Q, Wang, D. Boundary recovery for three dimensional conforming Delaunay triangulation. Computer Methods in Applied Mechanics and Engineering, 2004; 193(23-26):2547–2563.Google Scholar
[13]George, J. Computer Implementation of the Finite Element Method, 1971.Google Scholar
[14]Lo, S. A new mesh generation scheme for arbitrary planar domains. International Journal for Numerical Methods in Engineering, 2005; 21(8):1403–1426.Google Scholar
[15]Löhner, R. Three-dimensional grid generation by the advancing-front method. Numerical Methods in Laminar and Turbulent Flow, 1987.Google Scholar
[16]Mavriplis, D. An advancing front Delaunay triangulation algorithm designed for robustness. Journal of Computational Physics, 1995; 117(1):90–101.Google Scholar
[17]Peraire, J, Vahdati, M, Morgan, K, Zienkiewicz, O. Adaptive remeshing for compressible flow computations. Journal of Computational Physics, 1987; 72(2):449–466.CrossRefGoogle Scholar
[18]Shostko, A, Löhner, R. Three-dimensional parallel unstructured grid generation. International Journal for Numerical Methods in Engineering, 2005; 38(6):905–925.Google Scholar
[19]Ito, Y, Shih, A, Soni, B. Reliable isotropic tetrahedral mesh generation based on an advancing front method. 13th International Meshing Roundtable, Citeseer, 2004; 95–105.Google Scholar
[20]Ruppert, J. A Delaunay refinement algorithm for quality 2-dimensional mesh generation. Journal of Algorithms, 1995; 18(3):548–585.Google Scholar
[21]Frey, P. About surface remeshing. Proceedings of the 9th International Meshing Roundtable, Citeseer, 2000; 123–136.Google Scholar
[22]Wang, D, Hassan, O, Morgan, K, Weatherill, N. EQSM: An efficient high quality surface grid generation method based on remeshing. Computer Methods in Applied Mechanics and Engineering, 2006; 195(41-43):5621–5633.Google Scholar
[23]Du, Q, Wang, D. Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations. Int. J.Numer. Meth. Eng., 2002; 56:1355–1373.Google Scholar