| Issue |
ESAIM: Proc.
Volume 53, March 2016
CEMRACS 2014 – Numerical Modeling of Plasmas
|
|
|---|---|---|
| Page(s) | 99 - 119 | |
| DOI | https://doi.org/10.1051/proc/201653007 | |
| Published online | 01 April 2016 | |
Guiding center simulations on curvilinear grids*
1 IRMA, Université de Strasbourg, 7, rue René Descartes,
F-67084 Strasbourg & INRIA-Nancy Grand-Est, projet TONUS
e-mail: hzadnane@gmail.com
2 IRMA, Université de Strasbourg, 7, rue René Descartes,
F-67084 Strasbourg & INRIA-Nancy Grand-Est, projet TONUS
e-mail: mehrenbe@math.unistra.fr
3 Institut Élie Cartan (Mathématiques)
Université Henri Poincaré Nancy 1 B.P. 70239, F-54506
Vandoeuvre-lès-Nancy Cedex,
France
e-mail: aurore.back@univ-lorraine.fr.
4 IRMA, Université de Strasbourg, 7, rue René Descartes,
F-67084 Strasbourg & INRIA-Nancy Grand-Est, projet TONUS
e-mail: navaro@math.unistra.fr
Semi-Lagrangian guiding center simulations are performed on sinusoidal perturbations of cartesian grids, and on deformed polar grid with different boundary conditions. Key ingredients are: the use of a B-spline finite element solver for the Poisson equation and the classical backward semi-Lagrangian method (BSL) for the advection. We are able to reproduce standard Kelvin-Helmholtz and diocotron instability tests on such grids. When the perturbation leads to a strong distorted mesh, we observe that the solution differs if one takes standard numerical parameters that are used in the cartesian reference case. We can recover good results together with correct mass conservation, by diminishing the time step.
Résumé
Des simulations semi-lagrangiennes du modèle centre-guide sont effectuées sur des perturbations sinusoïdales de maillages cartésiens et sur des maillages polaires déformés. Les ingrédients clés sont : l’utilisation d’un solveur éléments finis splines pour l’équation de Poisson et la méthode semi-Lagrangienne en arrière classique (BSL) pour l’advection. Nous pouvons reproduire des tests standards d’instabilité de Kelvin-Helmholtz et diocotron sur ces grilles. Lorsque la déformation du maillage est forte, on observe que la solution diffère, si on prend les paramètres numériques standards qui sont utilisés dans le cas cartésien de référence. On peut retrouver néanmoins les bons résultats et une conservation de masse correcte, en diminuant le pas de temps.
This work was carried out within the framework the European Fusion Development Agreement and the French Research Federation for Fusion Studies. It is supported by the European Communities under the contract of Association between Euratom and CEA. 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
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