Meshing of domains with complex internal geometries.

*(English)*Zbl 1174.76363Summary: This paper presents a meshing algorithm for domains with internal boundaries. It is an extension of the gridding algorithm presented by P.-O. Persson and G. Strang. The resulting triangulation matches all boundaries, and the triangles are all nearly equilateral. Equilateral triangles are beneficial for a finite volume discretization, as fluid flow between elements of very different size is only possible at small timesteps. The mesh generator is compared with the well regarded Triangle programme, where both element quality and simulation performance are checked. It is shown that our mesh generator consistently delivers better meshes.

##### MSC:

76S05 | Flows in porous media; filtration; seepage |

65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |

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\textit{R. Holm} et al., Numer. Linear Algebra Appl. 13, No. 9, 717--731 (2006; Zbl 1174.76363)

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##### References:

[1] | Persson, SIAM Review 46 pp 329– (2004) |

[2] | Aurenhammer, ACM Computing Surveys 23 pp 345– (1991) |

[3] | Geometry and Topology for Mesh Generation. Cambridge University Press: Cambridge, MA, 2001. |

[4] | Shewchuk, Computational Geometry 22 pp 21– (2002) |

[5] | Triangle: engineering a 2D quality mesh generator and Delaunay triangulator. In Applied Computational Geometry: Towards Geometric Engineering, (eds), Lecture Notes in Computer Science, vol. 1148. From the First ACM Workshop on Applied Computational Geometry. Springer: New York, 1996; 203–222. |

[6] | Tveranger, Norwegian Journal of Geology 85 pp 63– (2005) |

[7] | Odling, Journal of Structural Geology 26 pp 1727– (2004) |

[8] | Flodin, Petroleum Geoscience 10 pp 173– (2004) |

[9] | Atomic meshes: from seismic imaging to reservoir simulation. Proceedings of the 8th European Conference on the Mathematics of Oil Recovery, European Association of Geoscientists & Engineers, 2002. ISBN 90-73781-24-8. |

[10] | , , , . Complex gas–water processes in discrete fracture-matrix systems. Upscaling, mass-conservative discretization and efficient multilevel solution. Technischer Bericht Heft 130, IWS, 2004. ISBN: 3-9337 61-22-6. |

[11] | Aavatsmark, SIAM Journal on Scientific Computing 19 pp 1700– (1998) |

[12] | Aavatsmark, SIAM Journal on Scientific Computing 19 pp 1717– (1998) |

[13] | , , . A multi-point flux discretization scheme for general polyhedral grids. International Oil and Gas Conference and Exhibition in China, SPE, November 1998. SPE 48855. |

[14] | Cline, SIAM Journal on Numerical Analysis 27 pp 1305– (1990) |

[15] | Software for C1 surface interpolation. In Mathematical Software III, (ed.). Academic Press: New York, 1977; 161–194. |

[16] | Lee, Discrete and Computational Geometry 1 pp 201– (1986) |

[17] | Constrained Delaunay tetrahedralizations and provably good boundary recovery. Proceedings of the Eleventh International Meshing Roundtable, Ithaca, New York, Sandia National Laboratories, September 2002; 193–204. |

[18] | Numerical Solution of Partial Differential Equations by the Finite Element Method. Studentlitteratur, 1987. |

[19] | Modeling of fracture aquifier systems; geostatistical analysis and deterministic-stochastic fracture generation. Ph.D. Thesis, Universität Stuttgart, January 2003. |

[20] | Karimi-Fard, SPE Journal 9 pp 227– (2004) |

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