Analysis of a new class of Forward Semi-Lagrangian schemes for the 1D Vlasov-Poisson Equations

TL;DR

This paper introduces a new class of forward Semi-Lagrangian schemes for the 1D Vlasov-Poisson equations, utilizing a Cauchy Kovalevsky procedure, with proven convergence and conservation properties.

Contribution

It presents a novel Semi-Lagrangian scheme based on CK procedures for the Vlasov-Poisson system, with rigorous convergence and conservation analysis.

Findings

Exact conservation of first moments achieved

Proven convergence in L1 norm

Error estimates provided for the schemes

Abstract

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.