MeshVoro: A three-dimensional Voronoi mesh building tool for the TOUGH family of codes

Few tools exist for creating and visualizing complex three-dimensional simulation meshes, and these have limitations that restrict their application to particular geometries and circumstances. Mesh generation needs to trend toward ever more general applications. To that end, we have developed MeshVoro, a tool that is based on the Voro++ (Chris H. Rycroft, 2009. Chaos 19, 041111) library and is capable of generating complex three-dimensional Voronoi tessellation-based (unstructured) meshes for the solution of problems of flow and transport in subsurface geologic media that are addressed by the TOUGH (Pruess, K., Oldenburg C., Moridis G., 1999. Report LBNL-43134, 582. Lawrence Berkeley National Laboratory, Berkeley, CA) family of codes. MeshVoro, which includes built-in data visualization routines, is a particularly useful tool because it extends the applicability of the TOUGH family of codes by enabling the scientifically robust and relatively easy discretization of systems with challenging 3D geometries. We describe several applications of MeshVoro. We illustrate the ability of the tool to straightforwardly transform a complex geological grid into a simulation mesh that conforms to the specifications of the TOUGH family of codes. We demonstrate how MeshVoro can describe complex system geometries with a relatively small number of grid blocks, and we construct meshes for geometries that would have been practically intractable with a standard Cartesian grid approach. We also discuss the limitations and appropriate applications of this new technology.

[1]  T. Narasimhan,et al.  Numerical model for saturated‐unsaturated flow in deformable porous media: 2. The algorithm , 1977 .

[2]  Luc Florack,et al.  Mathematical Methods for Signal and Image Analysis and Representation , 2012, Computational Imaging and Vision.

[3]  M. W. Conway,et al.  Multiphase Non-Darcy Flow in Proppant Packs , 2009 .

[4]  K. Pruess,et al.  TOUGH2 User's Guide Version 2 , 1999 .

[5]  Knut Arne Birkedal,et al.  ELECTRICAL RESISTIVITY MEASURMENTS OF CH 4 HYDRATE-BEARING SANDSTONE DURING FORMATION , 2011 .

[6]  Janet E. Jones On the determination of molecular fields. III.—From crystal measurements and kinetic theory data , 1924 .

[7]  T. Narasimhan,et al.  AN INTEGRATED FINITE DIFFERENCE METHOD FOR ANALYZING FLUID FLOW IN POROUS MEDIA , 1976 .

[8]  Guillaume Caumon,et al.  Building PEBI Grids Conforming To 3D Geological Features Using Centroidal Voronoi Tessellations , 2011 .

[9]  Mohamed S. Ebeida,et al.  Mesh Generation for Modeling and Simulation of Carbon Sequestration Process. , 2011 .

[10]  A. Edelman,et al.  Mesh generation for implicit geometries , 2005 .

[11]  Qiang Du,et al.  Grid generation and optimization based on centroidal Voronoi tessellations , 2002, Appl. Math. Comput..

[12]  M. W. Conway,et al.  Beyond Beta Factors: A Complete Model for Darcy, Forchheimer, and Trans-Forchheimer Flow in Porous Media , 2004 .

[13]  Georges Voronoi Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Deuxième mémoire. Recherches sur les parallélloèdres primitifs. , 1908 .

[14]  William E. Lorensen,et al.  The visualization toolkit (2nd ed.): an object-oriented approach to 3D graphics , 1998 .

[15]  B. Chazelle Computational geometry and convexity , 1980 .

[16]  M. Kowalsky,et al.  TOUGH+Hydrate v1.0 User's Manual: A Code for the Simulation of System Behavior in Hydrate-Bearing Geologic Media , 2008 .

[17]  Chris H. Rycroft Voro++: a three-dimensional Voronoi cell library in C++ , 2009 .

[18]  Qiang Du,et al.  Centroidal Voronoi Tessellations: Applications and Algorithms , 1999, SIAM Rev..

[19]  Per-Olof Persson,et al.  A Simple Mesh Generator in MATLAB , 2004, SIAM Rev..

[20]  William Schroeder,et al.  The Visualization Toolkit: An Object-Oriented Approach to 3-D Graphics , 1997 .

[21]  Chris H Rycroft,et al.  VORO++: a three-dimensional voronoi cell library in C++. , 2009, Chaos.

[22]  N. T.,et al.  NUMERICAL MODEL FOR SATURATED-UNSATURATED FLOW IN * DEFORMABLE POROUS MEDIA, PART I: THEORY , 2007 .

[23]  S. P. Lloyd,et al.  Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.