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

Published online by Cambridge University Press:  20 August 2015

Nicolas Crouseilles  and
Thomas Respaud
Nicolas Crouseilles*
Affiliation:
INRIA-Nancy-Grand Est, CALVI Project, Strasbourg, France
Thomas Respaud
Affiliation:
IRMA, Universitè de Strasbourg and INRIA-Nancy-Grand Est, CALVI Project, Strasbourg, France
*
*Corresponding author.Email:crouseil@math.u-strasbg.fr
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Abstract

In this report, a charge preserving numerical resolution of the 1D Vlasov-Ampère 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 Ampère’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.

Keywords

65C2085-0868U2065Z05Semi-Lagrangian methodcharge conservationRunge-KuttaCauchy-KovalevskyB-spline deposition
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 4 , October 2011 , pp. 1001 - 1026
Copyright
Copyright © Global Science Press Limited 2011

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