Solving the guiding-center model on a regular hexagonal mesh

Michel Mehrenberger; Laura S. Mendoza; Charles Prouveur; Eric Sonnendrücker

doi:10.1051/proc/201653010

Geodesic

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Solving the guiding-center model on a regular hexagonal mesh

Michel Mehrenberger ¹ ; Laura S. Mendoza ^2,³ ; Charles Prouveur ⁴ ; Eric Sonnendrücker ^2,³

¹ IRMA, Université de Strasbourg, 7, rue René Descartes, 67084 Strasbourg & INRIA-Nancy Grand-Est, projet TONUS
² Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching, Germany
³ Technische Universität München, Boltzmannstr. 3, D-85748 Garching, Germany
⁴ Université de Lyon, UMR5208, Institut Camille Jordan, 43 boulevard 11 novembre 1918, F-69622 Villeurbanne cedex, France

ESAIM. Proceedings, Tome 53 (2016), pp. 149-176.

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Résumé

This paper introduces a Semi-Lagrangian solver for the Vlasov-Poisson equations on a uniform hexagonal mesh. The latter is composed of equilateral triangles, thus it doesn’t contain any singularities, unlike polar meshes. We focus on the guiding-center model, for which we need to develop a Poisson solver for the hexagonal mesh in addition to the Vlasov solver. For the interpolation step of the Semi-Lagrangian scheme, a comparison is made between the use of Box-splines and of Hermite finite elements. The code will be adapted to more complex models and geometries in the future.

DOI : 10.1051/proc/201653010

Affiliations des auteurs :

Michel Mehrenberger ¹ ; Laura S. Mendoza ^{2, 3} ; Charles Prouveur ⁴ ; Eric Sonnendrücker ^{2, 3}

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     author = {Michel Mehrenberger and Laura S. Mendoza and Charles Prouveur and Eric Sonnendr\"ucker},
     title = {Solving the guiding-center model on a regular hexagonal mesh},
     journal = {ESAIM. Proceedings},
     pages = {149--176},
     publisher = {mathdoc},
     volume = {53},
     year = {2016},
     doi = {10.1051/proc/201653010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201653010/}
}

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Michel Mehrenberger; Laura S. Mendoza; Charles Prouveur; Eric Sonnendrücker. Solving the guiding-center model on a regular hexagonal mesh. ESAIM. Proceedings, Tome 53 (2016), pp. 149-176. doi : 10.1051/proc/201653010. http://geodesic.mathdoc.fr/articles/10.1051/proc/201653010/

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