Tetrahedral remeshing in the context of large-scale numerical simulation and high performance computing
MathematicS In Action, Volume 11 (2022) no. 1, pp. 129-164.

The purpose of this article is to discuss several modern aspects of remeshing, which is the task of modifying an ill-shaped tetrahedral mesh with bad size elements so that it features an appropriate density of high-quality elements. After a brief sketch of classical stakes about meshes and local mesh operations, we notably expose (i) how the local size of the elements of a mesh can be adapted to a user-defined prescription (guided, e.g., by an error estimate attached to a numerical simulation), (ii) how a mesh can be deformed to efficiently track the motion of the underlying domain, (iii) how to construct a mesh of an implicitly-defined domain, and (iv) how remeshing procedures can be conducted in a parallel fashion when large-scale applications are targeted. These ideas are illustrated with several applications involving high-performance computing. In particular, we show how mesh adaptation and parallel remeshing strategies make it possible to achieve a high accuracy in large-scale simulations of complex flows, and how the aforementioned methods for meshing implicitly defined surfaces allow to represent faithfully intricate geophysical interfaces, and to account for the dramatic evolutions of shapes featured by shape optimization processes.

Published online:
DOI: 10.5802/msia.22
Classification: 65X50, 65Y05, 90C06
Keywords: remeshing, implicit domain meshing, level-set discretization, topology optimization, mesh adaptation, h-adaptation, error estimator, metric, “lagrangian” mesh deformation, distributed memory parallel remeshing, hybrid RANS/LES, LES, geophysical inverse problem
G. Balarac 1; F. Basile 2; P. Bénard 3; F. Bordeu 4; J.-B. Chapelier 5; L. Cirrottola 6; G. Caumon 7; C. Dapogny 8; P. Frey 9; A. Froehly 10; G. Ghigliotti 11; R. Laraufie 12; G. Lartigue 3; C. Legentil 7; R. Mercier 4; V. Moureau 3; C. Nardoni 13; S. Pertant 11; M. Zakari 7

1 Univ Grenoble Alpes, CNRS, Grenoble INP, LEGI UMR 5519, 38000 Grenoble, France
2 ONERA - Université Paris-Saclay, 92322 Châtillon, France; Airbus Operations SAS, 31060 Toulouse, France
3 CORIA, Normandie Univ, UNIROUEN, INSA Rouen, CNRS, 76000 Rouen, France
4 SAFRAN Tech, Digital Sciences & Technologies, Rue des Jeunes Bois, 78114 Magny-Les-Hameaux, France
5 ONERA - Université Paris-Saclay, 92322 Châtillon, France
6 INRIA, Univ. Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, 33405 Talence cedex, France
7 Université de Lorraine, CNRS, GeoRessources, 54000 Nancy, France
8 Univ Grenoble Alpes, CNRS, Grenoble INP, LJK, 38000 Grenoble, France
9 Sorbonne Université, CNRS, Laboratoire J.L. Lions, UMR 7598, 75005 Paris, France
10 INRIA Service d’Expérimentation et de Développement, 33405 Talence cedex, France
11 Univ Grenoble Alpes, CNRS, Grenoble INP, LEGI UMR 5519, F-38000 Grenoble, France
12 Airbus Operations SAS, 31060 Toulouse, France
13 Institut de Recherche Technologique SystemX, 2 Boulevard Thomas Gobert 91120 Palaiseau, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {Tetrahedral remeshing in the context of large-scale numerical simulation and high performance computing},
     journal = {MathematicS In Action},
     pages = {129--164},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
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     year = {2022},
     doi = {10.5802/msia.22},
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G. Balarac; F. Basile; P. Bénard; F. Bordeu; J.-B. Chapelier; L. Cirrottola; G. Caumon; C. Dapogny; P. Frey; A. Froehly; G. Ghigliotti; R. Laraufie; G. Lartigue; C. Legentil; R. Mercier; V. Moureau; C. Nardoni; S. Pertant; M. Zakari. Tetrahedral remeshing in the context of large-scale numerical simulation and high performance computing. MathematicS In Action, Volume 11 (2022) no. 1, pp. 129-164. doi : 10.5802/msia.22. https://msia.centre-mersenne.org/articles/10.5802/msia.22/

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