3D Mesh Generation in Geocomputing

Mesh generation has been widely used in engineering computing, but seems to be relatively “new" for geoscience community. This paper firstly lists such relevant progresses of mesh generation for the engineering computing and then discusses the possibility for applying/extending them to geoscience computing (i.e. geocomputing). for geoscience, the available input data are normally a large quantity of point data in the 3D space rather than the defined shapes and dimensions with reasonable tolerances provided by the industrial designers, thus quite different from the engineering cases. To deal with such geoscience data, this paper briefly introduces the relevant progresses on geometrical modeling, hexahedral and tetrahedral shaped mesh generation, and then focuses on the applying and/or extending the related methods to generate all hexahedral/tetrahedral shaped meshes in 3D for geoscience purposes, which is described through the different practical application examples, such as the all-hexahedral shaped mesh generation for a fracture dominated reservoir system, the South Australia interacting fault system and the entire earth model without or with the simplified/practical plate boundaries; and all-tetrahedral shaped mesh generation for a multi-layer un- derground geological model, and visualizing and meshing with the microseismicity data recorded during a hydraulic stimulation process in a geothermal reservoir.

[1]  Chi King Lee.  Automatic metric 3D surface mesh generation using subdivision surface geometrical model. Part 2 : mesh generation algorithm and examples , 2003 .

[2]  Barry Joe,et al.  Construction of three-dimensional Delaunay triangulations using local transformations , 1991, Comput. Aided Geom. Des..

[3]  C. Lee,et al.  A new scheme for the generation of a graded quadrilateral mesh , 1994 .

[4]  Desheng Wang,et al.  Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations , 2003 .

[5]  Timothy J. Tautges,et al.  The Geode Algorithm: Combining Hex/Tet Plastering, Dicing and Transition Elements for Automatic, All-Hex Mesh Generation , 1998, IMR.

[6]  Patrick M. Knupp,et al.  Applications of mesh smoothing: copy, morph, and sweep on unstructured quadrilateral meshes , 1999 .

[7]  H. Borouchaki,et al.  Fast Delaunay triangulation in three dimensions , 1995 .

[8]  David R. White,et al.  Automated Hexahedral Mesh Generation by Generalized Multiple Source to Multiple Target Sweeping , 2000 .

[9]  Rainald Löhner,et al.  Generation of non‐isotropic unstructured grids via directional enrichment , 2000 .

[10]  R. E. Hobbs,et al.  Automatic adaptive finite element mesh generation over arbitrary two-dimensional domain using advancing front technique , 1999 .

[11]  T. Baker.  Automatic mesh generation for complex three-dimensional regions using a constrained Delaunay triangulation , 1989, Engineering with Computers.

[12]  Paul-Louis George,et al.  ASPECTS OF 2-D DELAUNAY MESH GENERATION , 1997 .

[13]  P. George.  Improvements on Delaunay-based three-dimensional automatic mesh generator , 1997 .

[14]  P. George,et al.  Parametric surface meshing using a combined advancing-front generalized Delaunay approach , 2000 .

[15]  R. Schneiders,et al.  A grid-based algorithm for the generation of hexahedral element meshes , 1996, Engineering with Computers.

[16]  S. H. Lo.  Generation of high-quality gradation finite element mesh , 1992 .

[17]  Loïc Maréchal.  A New Approach to Octree-Based Hexahedral Meshing , 2001, IMR.

[18]  F. Weiler,et al.  Octree-based Generation of Hexahedral Element Meshes , 2007 .

[19]  Ichiro Nishigaki,et al.  Automatic Hexahedral Mesh Generation with Feature Line Extraction , 2006, IMR.

[20]  Ted D. Blacker,et al.  Paving: A new approach to automated quadrilateral mesh generation , 1991 .

[21]  Mark S. Shephard,et al.  Automatic three‐dimensional mesh generation by the finite octree technique , 1984 .

[22]  Sergio Idelsohn,et al.  All-hexahedral element meshing: Generation of the dual mesh by recurrent subdivision , 2000 .

[23]  Y. K. Lee,et al.  Automatic generation of anisotropic quadrilateral meshes on three‐dimensional surfaces using metric specifications , 2002 .

[24]  Li Hua,et al.  New method for graded mesh generation of quadrilateral finite elements , 1996 .

[25]  Paul-Louis George,et al.  The advancing-front mesh generation method revisited , 1994 .

[26]  Reza Taghavi.  Automatic Block Decomposition Using Fuzzy Logic Analysis , 2000, IMR.

[27]  S. Lo.  Volume discretization into tetrahedra-I. Verification and orientation of boundary surfaces , 1991 .

[28]  Rainald Löhner,et al.  An advancing front point generation technique , 1998 .

[29]  S. Owen,et al.  H-Morph: an indirect approach to advancing front hex meshing , 1999 .

[30]  K. Fujishiro,et al.  A flexible automatic hexahedral mesh generation by boundary-fit method , 1998 .

[31]  P. Frey,et al.  Fully automatic mesh generation for 3-D domains based upon voxel sets , 1994 .

[32]  P. George,et al.  Automatic mesh generator with specified boundary , 1991 .

[33]  Kenji Shimada,et al.  Anisotropic tetrahedral meshing via bubble packing and advancing front , 2003 .

[34]  David R. White,et al.  Automatic Scheme Selection for Toolkit Hex Meshing , 2000 .

[35]  A. Kageyama,et al.  ``Yin-Yang grid'': An overset grid in spherical geometry , 2004, physics/0403123.

[36]  Matthew L. Staten,et al.  Unconstrained Paving & Plastering: A New Idea for All Hexahedral Mesh Generation , 2005, IMR.

[37]  Steven J. Owen,et al.  PYRAMID ELEMENTS FOR MAINTAINING TETRAHEDRA TO HEXAHEDRA CONFORMABILITY , 2000 .

[38]  H. Xing,et al.  A finite element analysis of tidal deformation of the entire earth with a discontinuous outer layer , 2007 .

[39]  Jonathan Richard Shewchuk,et al.  Delaunay refinement algorithms for triangular mesh generation , 2002, Comput. Geom..

[40]  David R. O'Hallaron,et al.  Extracting Hexahedral Mesh Structures from Balanced Linear Octrees , 2004, IMR.

[41]  N. Weatherill,et al.  Efficient three‐dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints , 1994 .

[42]  Huilin Xing,et al.  Construction of an Intraplate Fault System Model of South Australia, and Simulation Tool for the iSERVO Institute Seed Project , 2006 .

[43]  Rolf Bünten,et al.  Automatic generation of hexahedral finite element meshes , 1995, Comput. Aided Geom. Des..

[44]  Steven E. Benzley,et al.  Adaptive sweeping techniques , 2009, Engineering with Computers.

[45]  A. Jack,et al.  Aspects of three‐dimensional constrained Delaunay meshing , 1994 .

[46]  Timothy J. Tautges,et al.  The "Hex-Tet" Hex-Dominant Meshing Algorithm as Implemented in CUBIT , 1998, IMR.

[47]  D. T. Lee,et al.  Two algorithms for constructing a Delaunay triangulation , 1980, International Journal of Computer & Information Sciences.

[48]  D. F. Watson.  Computing the n-Dimensional Delaunay Tesselation with Application to Voronoi Polytopes , 1981, Comput. J..

[49]  P. George,et al.  OPTIMAL DELAUNAY POINT INSERTION , 1996 .

[50]  H. Borouchaki,et al.  Adaptive triangular–quadrilateral mesh generation , 1998 .

[51]  David R. White,et al.  Methods for Multisweep Automation , 2000, IMR.

[52]  Huilin Xing,et al.  Finite element modelling of interacting fault systems , 2007 .

[53]  G. Lister,et al.  Reconstruction of the tectonic evolution of the western Mediterranean since the Oligocene , 2002 .

[54]  Rainald Löhner,et al.  Extensions and improvements of the advancing front grid generation technique , 1996 .

[55]  R. Löhner,et al.  Progress in grid generation via the advancing front technique , 2005, Engineering with Computers.

[56]  David R. White,et al.  CCSweep: automatic decomposition of multi-sweep volumes , 2003, Engineering with Computers.

[57]  D. L. Anderson,et al.  Preliminary reference earth model , 1981 .

[58]  B. Joe,et al.  GEOMPACK — a software package for the generation of meshes using geometric algorithms☆ , 1991 .

[59]  Chi King Lee,et al.  A new indirect anisotropic quadrilateral mesh generation scheme with enhanced local mesh smoothing procedures , 2003 .

[60]  Barry Joe,et al.  Construction of Three-Dimensional Improved-Quality Triangulations Using Local Transformations , 1995, SIAM J. Sci. Comput..

[61]  Barry Joe,et al.  Delaunay versus max‐min solid angle triangulations for three‐dimensional mesh generation , 1991 .

[62]  M. Shephard,et al.  Reliability of automatic 3D mesh generation , 1992 .

[63]  S. Lo.  Volume discretization into tetrahedra—II. 3D triangulation by advancing front approach , 1991 .

[64]  R. Löhner.  Regridding Surface Triangulations , 1996 .

[65]  Matthew L. Staten,et al.  BMSweep: Locating Interior Nodes During Sweeping , 1999, Engineering with Computers.