Volume 10, Issue 4
A Charge Preserving Scheme for the Numerical Resolution of the Vlasov-Ampère Equations
10.4208/cicp.210410.211210a

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

• Abstract

In this report, a charge preserving numerical resolution of the 1D VlasovAmpere 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.

• History

Published online: 2011-10

• Keywords