Analysis of a new class of Forward Semi-Lagrangian schemes for the 1D Vlasov-Poisson Equations
For researchers in kinetic plasma simulations, this provides a novel numerical method with proven conservation and convergence properties, though it is incremental in nature.
The paper introduces a new class of forward Semi-Lagrangian schemes for the 1D Vlasov-Poisson equations using a Cauchy-Kovalevsky procedure, proving exact conservation of first moments and convergence in L1 norm with error estimates.
The Vlasov equation is a kinetic model describing the evolution of charged particles, and is coupled with Poisson's equation, which rules the evolution of the self-consistent electric field. In this paper, we introduce a new class of forward Semi-Lagrangian schemes for the Vlasov-Poisson system based on a Cauchy Kovalevsky (CK) procedure for the numerical solution of the characteristic curves. Exact conservation properties of the first moments of the distribution function for the schemes are derived and a convergence study is performed that applies as well for the CK scheme as for a more classical Verlet scheme. The convergence in L1 norm of the schemes is proved and error estimates are obtained.