Issue |
ESAIM: Proc.
Volume 38, December 2012
CEMRACS’11: Multiscale Coupling of Complex Models in Scientific Computing
|
|
---|---|---|
Page(s) | 348 - 360 | |
DOI | https://doi.org/10.1051/proc/201238019 | |
Published online | 03 January 2013 |
First order Two-Scale Particle-in-Cell numerical method for the Vlasov equation
1
Université Européenne de Bretagne, LMBA (UMR CNRS 6205),
Université de Bretagne-Sud, Centre Yves Coppens, Campus de Tohannic,
F-56017,
Vannes
2
Inria Nancy-Grand Est, CALVI Project & IRMA (UMR 7501),
Université de Strasbourg, 7 rue
René Descartes, F-67084
Strasbourg Cedex,
France
The aim of this work is to build an accurate numerical method for the simulation of the long time evolution of the Vlasov solution fε with an electric field Eε = E0 + εE1 for small ε. To this purpose, we use the Two-Scale Convergence to determine a first order approximation F + εF1 of fε. Then, by means of particle approximations we build an algorithm which is intended for providing a numerical approximation of F + εF1.
Résumé
On cherche à construire une méthode numérique pour l’évolution en temps long de la solution fε de l’équation de Vlasov avec un champ électrique Eε = E0 + εE1 pour ε petit. À cet effet, on utilise la théorie de la convergence à deux échelles pour obtenir une approximation d’ordre un F + εF1 de fε, puis une méthode particulaire pour construire l’algorithme d’approximation numérique de F + εF1.
© EDP Sciences, SMAI 2012
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