| Issue |
ESAIM: Proc.
Volume 53, March 2016
CEMRACS 2014 – Numerical Modeling of Plasmas
|
|
|---|---|---|
| Page(s) | 149 - 176 | |
| DOI | https://doi.org/10.1051/proc/201653010 | |
| Published online | 01 April 2016 | |
Solving the guiding-center model on a regular hexagonal mesh*
1 IRMA, Université de Strasbourg, 7,
rue René Descartes, 67084 Strasbourg & INRIA-Nancy Grand-Est, projet
TONUS
e-mail: mehrenbe@math.unistra.fr
2 Max Planck Institute for Plasma
Physics, Boltzmannstr. 2, 85748
Garching, Germany
e-mail: mela@ipp.mpg.de & sonnen@ipp.mpg.de
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
e-mail: prouveur@math.univ-lyon1.fr
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.
Résumé
Dans cet article nous présentons un solveur semi-Lagrangien pour les équations de Vlasov-Poisson sur un maillage hexagonal uniforme. Ce dernier est composé de triangles équilatéraux, ainsi il ne présente aucune singularité, contrairement au maillage polaire. Nous nous concentrons ici sur le modèle centre-guide. À cette fin nous avons développé en plus du solveur pour Vlasov, un solveur de l’équation de Poisson pour maillage hexagonal. Nous comparons les résultats obtenus avec une interpolation par éléments finis d’Hermite et par des Box-splines. Dans l’avenir, ce code sera adapté à des géométries et modèles plus complexes.
This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.
© EDP Sciences, SMAI 2016
This is an open access article distributed under the terms of the Creative
Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted
use, distribution, and reproduction in any medium, provided the original work is
properly cited.
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