| Issue |
ESAIM: Proc.
Volume 32, October 2011
CEMRACS'10 research achievements: Numerical modeling of fusion
|
|
|---|---|---|
| Page(s) | 134 - 148 | |
| DOI | https://doi.org/10.1051/proc/2011017 | |
| Published online | 03 November 2011 | |
Particle-in-wavelets scheme for the 1D Vlasov-Poisson equations ⋆, ⋆⋆
1
LMD-CNRS-IPSL, École Normale Supérieure, 24 rue Lhomond, 75231
Paris Cedex 5,
France
2
IRMA-CNRS, Université de Strasbourg, 7 rue Ren-Descartes, 67084
Strasbourg Cedex,
France
3
M2P2-CNRS and CMI, Université d’Aix-Marseille,
38 rue Frdric
Joliot-Curie, 13451
Marseille Cedex 13,
France
A new numerical scheme called particle-in-wavelets is proposed for the Vlasov-Poisson equations, and tested in the simplest case of one spatial dimension. The plasma distribution function is discretized using tracer particles, and the charge distribution is reconstructed using wavelet-based density estimation. The latter consists in projecting the Delta distributions corresponding to the particles onto a finite dimensional linear space spanned by a family of wavelets, which is chosen adaptively. The stability and accuracy of the scheme is supported by numerical computations of Landau damping and of the two-stream instability. By direct comparison with a reference solution obtained by a very precise semi-Lagrangian method, we show that the precision is improved roughly by a factor 3 compared to a classical PIC scheme, for a given number of particles.
Résumé
L’objectif de ce travail est de proposer un nouveau schma numrique, appel particle-in-wavelets, pour rsoudre les quations de Vlasov-Poisson, et de le tester dans le cas le plus simple o il n’y a qu’une seule dimension d’espace. La fonction de distribution du plasma est discrtisel’aide d’un ensemble de particules, et la charge peut alors tre reconstruite par la technique d’estimation de la densite en ondelettes. Cette dernire consisteprojeter la distribution de Dirac de chaque particule sur un espace de dimension finie engendr par une famille d’ondelettes choisie de faon adaptative. La stabilit et la prcision du schma sont confirmes par des calculs numriques portant sur l’amortissement Landau et sur l’instabilit double faisceau. En comparant directement les rsultats avec une solution de rfrence obtenue par une mthode semi-lagrangienne trs prcise, nous mettons en vidence une diminution de l’erreur d’un facteur de l’ordre de 3 par rapportla mthode PIC classique, pour un nombre de particules donn.
The authors would like to thank Diego del-Castillo-Negrete for his inspiration in the pursuit of PIC denoising, and Matthieu Haefele for developing and supporting the VLASY platform.
The authors acknowledge financial support from the Euratom-CEA association and the French Federation for Fusion Studies. This work, supported by the European Communities under the contract of Association between EURATOM, CEA and the French Research Federation for fusion studies, was carried out within the framework of the European Fusion Development Agreement. The views and opinions expressed herein do not necessarily reflect those of the European Commission.
© EDP Sciences, SAIM 2011
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.