Comptes Rendus
Mathematical Physics/Numerical Analysis
An asymptotically stable Particle-in-Cell (PIC) scheme for collisionless plasma simulations near quasineutrality
[Une méthode ‘Particle-in-cell’ asymptotiquement stable pour les plasmas non-collisionnels proches de la quasineutralité]
Comptes Rendus. Mathématique, Volume 343 (2006) no. 9, pp. 613-618.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.09.033

Pierre Degond 1 ; Fabrice Deluzet 1 ; Laurent Navoret 1, 2

1 MIP, UMR 5640 (CNRS-UPS-INSA-UT1), université Paul-Sabatier, 31062 Toulouse cedex 09, France
2 Département de mathématiques, École normale supérieure de Cachan, 61, avenue du Président Wilson, 94235 Cachan cedex, France
@article{CRMATH_2006__343_9_613_0,
     author = {Pierre Degond and Fabrice Deluzet and Laurent Navoret},
     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},
}
TY  - JOUR
AU  - Pierre Degond
AU  - Fabrice Deluzet
AU  - Laurent Navoret
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
DO  - 10.1016/j.crma.2006.09.033
LA  - en
ID  - CRMATH_2006__343_9_613_0
ER  - 
%0 Journal Article
%A Pierre Degond
%A Fabrice Deluzet
%A Laurent Navoret
%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
%R 10.1016/j.crma.2006.09.033
%G en
%F CRMATH_2006__343_9_613_0
Pierre Degond; Fabrice Deluzet; Laurent Navoret. An asymptotically stable Particle-in-Cell (PIC) scheme for collisionless plasma simulations near quasineutrality. Comptes Rendus. Mathématique, Volume 343 (2006) no. 9, pp. 613-618. doi : 10.1016/j.crma.2006.09.033. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.09.033/

[1] C.K. Birdsall; A.B. Langdon Plasma Physics Via Computer Simulation, Institute of Physics, 2004

[2] Y. Brenier Convergence of the Vlasov–Poisson system to the incompressible Euler equations, Comm. Partial Differential Equations, Volume 25 (2000), pp. 737-754

[3] F.F. Chen Introduction to Plasma Physics and Controlled Fusion, vol. 1, Plenum Press, 1974

[4] B.I. Cohen; A.B. Langdon; A. Friedman Implicit time integration for plasma simulation, J. Comput. Phys., Volume 46 (1982), p. 15

[5] G.-H. Cottet; P.-A. Raviart Particle methods for the one-dimensional Vlasov–Poisson equations, SIAM J. Numer. Anal., Volume 21 (1984), pp. 52-76

[6] P. Crispel; P. Degond; M.-H. Vignal An asymptotically stable discretization for the Euler–Poisson system in the quasineutral limit, C. R. Acad. Sci. Paris, Ser. I, Volume 341 (2005), pp. 341-346

[7] P. Crispel, P. Degond, M.-H. Vignal, An asymptotic preserving scheme for the two-fluid Euler–Poisson model in the quasineutral limit, J. Comput. Phys., in press

[8] K. Ganguly; H.D. Victory On the convergence of particle methods for multidimensional Vlasov–Poisson systems, SIAM J. Numer. Anal., Volume 26 (1989), pp. 249-288

[9] R. Glassey; J. Schaeffer Convergence of a particle method for the relativistic Vlasov–Maxwell system, SIAM J. Numer. Anal., Volume 28 (1991), pp. 1-25

[10] R.W. Hockney; J.W. Eastwood Computer Simulation Using Particles, Institute of Physics, 1988

[11] N.A. Krall; A.W. Trivelpiece Principles of Plasma Physics, San Francisco Press, 1986

[12] A.B. Langdon; B.I. Cohen; A. Friedman Direct implicit large time-step particle simulation of plasmas, J. Comput. Phys., Volume 51 (1983), p. 107

[13] R.J. Mason Implicit moment particle simulation of plasmas, J. Comput. Phys., Volume 41 (1981), p. 233

[14] R.J. Mason Implicit moment PIC-hybrid simulation of collisional plasmas, J. Comput. Phys., Volume 51 (1983), p. 484

Cité par Sources :

Commentaires - Politique