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Journal of Computational Mathematics

Parallel kinetic scheme for transport equations in complex toroidal geometry
Matthieu Boileau1; Bérenger Bramas2; Emmanuel Franck1; Romane Hélie1; Philippe Helluy1; Laurent Navoret1
1 Institut de Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, 7 rue René Descartes, 67000 Strasbourg, France & INRIA Nancy-Grand Est, TONUS Project, Strasbourg, France
2 INRIA Nancy-Grand Est, CAMUS Project, Strasbourg, France
The SMAI Journal of computational mathematics, Volume 8 (2022), pp. 249-271.

We present an efficient solver for the conservative transport equation with variable coefficients in complex toroidal geometries. The solver is based on a kinetic formulation resembling the Lattice-Boltzmann approach. The chosen formalism allows obtaining an explicit and conservative scheme that requires no matrix inversion and whose CFL stability condition is independent from the poloidal dynamics. We present the method and its optimized parallel implementation on toroidal geometries. Two and three dimensional plasma physics test cases are carried out.

Published online:
DOI: 10.5802/smai-jcm.86
Classification: 35L65, 65M12, 35Q83, 82D10
Keywords: plasma physics, kinetic scheme, discontinuous Galerkin
Matthieu Boileau 1; Bérenger Bramas 2; Emmanuel Franck 1; Romane Hélie 1; Philippe Helluy 1; Laurent Navoret 1

1 Institut de Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, 7 rue René Descartes, 67000 Strasbourg, France & INRIA Nancy-Grand Est, TONUS Project, Strasbourg, France
2 INRIA Nancy-Grand Est, CAMUS Project, Strasbourg, France
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     author = {Matthieu Boileau and B\'erenger Bramas and Emmanuel Franck and Romane H\'elie and Philippe Helluy and Laurent Navoret},
     title = {Parallel kinetic scheme for transport equations in complex toroidal geometry},
     journal = {The SMAI Journal of computational mathematics},
     pages = {249--271},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
     volume = {8},
     year = {2022},
     doi = {10.5802/smai-jcm.86},
     language = {en},
     url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.86/}
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Matthieu Boileau; Bérenger Bramas; Emmanuel Franck; Romane Hélie; Philippe Helluy; Laurent Navoret. Parallel kinetic scheme for transport equations in complex toroidal geometry. The SMAI Journal of computational mathematics, Volume 8 (2022), pp. 249-271. doi : 10.5802/smai-jcm.86. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.86/

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