Parallel kinetic scheme for transport equations in complex toroidal geometry
Boileau, Matthieu1 ; Bramas, Bérenger2 ; Franck, Emmanuel1 ; Hélie, Romane1 ; Helluy, Philippe1 ; Navoret, Laurent1
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, Tome 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.

Publié le :
DOI : 10.5802/smai-jcm.86
Classification : 35L65, 65M12, 35Q83, 82D10
Mots clés : plasma physics, kinetic scheme, discontinuous Galerkin
Boileau, Matthieu 1 ; Bramas, Bérenger 2 ; Franck, Emmanuel 1 ; Hélie, Romane 1 ; Helluy, Philippe 1 ; Navoret, Laurent 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 
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     author = {Boileau, Matthieu and Bramas, B\'erenger and Franck, Emmanuel and H\'elie, Romane and Helluy, Philippe and Navoret, Laurent},
     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},
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     url = {http://archive.numdam.org/articles/10.5802/smai-jcm.86/}
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Boileau, Matthieu; Bramas, Bérenger; Franck, Emmanuel; Hélie, Romane; Helluy, Philippe; Navoret, Laurent. Parallel kinetic scheme for transport equations in complex toroidal geometry. The SMAI Journal of computational mathematics, Tome 8 (2022), pp. 249-271. doi : 10.5802/smai-jcm.86. http://archive.numdam.org/articles/10.5802/smai-jcm.86/

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