TY - JOUR T1 - A Charge Preserving Scheme for the Numerical Resolution of the Vlasov-Ampère Equations JO - Communications in Computational Physics VL - 4 SP - 1001 EP - 1026 PY - 2011 DA - 2011/10 SN - 10 DO - http://doi.org/10.4208/cicp.210410.211210a UR - https://global-sci.org/intro/article_detail/cicp/7472.html KW - AB -

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.