Volume 10, Issue 4
A Charge Preserving Scheme for the Numerical Resolution of the Vlasov-Ampère Equations

Nicolas Crouseilles and Thomas Respaud


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

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  • Abstract

In this report, a charge preserving numerical resolution of the 1D VlasovAmp`ere 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 Amp`ere’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.

  • History

Published online: 2011-10

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