Commun. Comput. Phys., 10 (2011), pp. 1001-1026.


A Charge Preserving Scheme for the Numerical Resolution of the Vlasov-Ampere Equations

Nicolas Crouseilles 1*, Thomas Respaud 2

1 INRIA-Nancy-Grand Est, CALVI Project, Strasbourg, France.
2 IRMA, Universite de Strasbourg and INRIA-Nancy-Grand Est, CALVI Project, Strasbourg, France.

Received 21 April 2010; Accepted (in revised version) 21 December 2010
Available online 24 June 2011
doi:10.4208/cicp.210410.211210a

Abstract

In this report, a charge preserving numerical resolution of the 1D Vlasov-Ampere equation is achieved, with a forward Semi-Lagrangian method introduced in [10]. The Vlasov equation belongs to the kinetic way of simulating plasmas evolution, and is coupled with the Poisson's equation, or equivalently under charge conservation, the Ampere's one, which self-consistently rules the electric field evolution. In order to ensure having proper physical solutions, it is necessary that the scheme preserves charge numerically. B-spline deposition will be used for the interpolation step. The solving of the characteristics will be made with a Runge-Kutta 2 method and with a Cauchy-Kovalevsky procedure.

AMS subject classifications: 65C20, 85-08, 68U20, 65Z05

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Key words: Semi-Lagrangian method, charge conservation, Runge-Kutta, Cauchy-Kovalevsky, B-spline deposition.

*Corresponding author.
Email: crouseil@math.u-strasbg.fr (N. Crouseilles)
 

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