[Une méthode ‘Particle-in-cell’ asymptotiquement stable pour les plasmas non-collisionnels proches de la quasineutralité]
Nous proposons un nouveau schéma ‘Particle-in-cell’ pour l'équation de Vlasov–Poisson. Ce schéma reste stable même quand la longueur de Debye et la période plasma tendent vers zéro sans restriction sur la taille des mailles spatiale et temporelle. Il repose sur une méthode d'intégration semi-implicite de la trajectoire des particules. Le coût d'intégration numérique est celui d'une méthode explicite habituelle grâce à une reformulation de l'équation de Poisson.
We propose a new Particle-in-Cell scheme for the Vlasov–Poisson equation. This scheme remains stable when the Debye length and plasma period tend to zero without any restriction on the size of the time and length step. It relies on a semi-implicit integration of the particle trajectories. The numerical integration cost is that of the standard explicit method thanks to the use of a reformulation of the Poisson equation.
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@article{CRMATH_2006__343_9_613_0,
author = {Degond, Pierre and Deluzet, Fabrice and Navoret, Laurent},
title = {An asymptotically stable {Particle-in-Cell} {(PIC)} scheme for collisionless plasma simulations near quasineutrality},
journal = {Comptes Rendus. Math\'ematique},
pages = {613--618},
publisher = {Elsevier},
volume = {343},
number = {9},
year = {2006},
doi = {10.1016/j.crma.2006.09.033},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2006.09.033/}
}
TY - JOUR AU - Degond, Pierre AU - Deluzet, Fabrice AU - Navoret, Laurent TI - An asymptotically stable Particle-in-Cell (PIC) scheme for collisionless plasma simulations near quasineutrality JO - Comptes Rendus. Mathématique PY - 2006 SP - 613 EP - 618 VL - 343 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.09.033/ DO - 10.1016/j.crma.2006.09.033 LA - en ID - CRMATH_2006__343_9_613_0 ER -
%0 Journal Article %A Degond, Pierre %A Deluzet, Fabrice %A Navoret, Laurent %T An asymptotically stable Particle-in-Cell (PIC) scheme for collisionless plasma simulations near quasineutrality %J Comptes Rendus. Mathématique %D 2006 %P 613-618 %V 343 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.09.033/ %R 10.1016/j.crma.2006.09.033 %G en %F CRMATH_2006__343_9_613_0
Degond, Pierre; Deluzet, Fabrice; Navoret, Laurent. An asymptotically stable Particle-in-Cell (PIC) scheme for collisionless plasma simulations near quasineutrality. Comptes Rendus. Mathématique, Tome 343 (2006) no. 9, pp. 613-618. doi : 10.1016/j.crma.2006.09.033. http://www.numdam.org/articles/10.1016/j.crma.2006.09.033/
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