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

作者：Crouseilles Nicolas^*; Respaud Thomas

来源：Communications in Computational Physics, 2011, 10(4): 1001-1026.

DOI：10.4208/cicp.210410.211210a

• Semi-Lagrangian method
• charge conservation
• Runge-Kutta
• Cauchy-Kovalevsky
• B-spline deposition

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

• 出版日期2011-10
• 单位INRIA