A charge preserving scheme for the numerical resolution of the Vlasov-Ampère equations

Nicolas Crouseilles (1) , Thomas Respaud (2)

1 CALVI - Scientific computation and visualization
2 IRMA - Institut de Recherche Mathématique Avancée

In this report, a charge preserving numerical resolution of the 1D Vlasov-Ampère equation is achieved, with a forward Semi-Lagrangian method introduced in \cite{4respaud}. 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.

Domaines: Analyse numérique [math.NA]

Nicolas Crouseilles, Thomas Respaud. A charge preserving scheme for the numerical resolution of the Vlasov-Ampère equations. Communications in Computational Physics, 2011, 10 (4), pp.1001 - 1026. ⟨10.4208/cicp.210410.211210a⟩. ⟨hal-00533390⟩