Numerical Simulations Using Eulerian Schemes for the Vlasov–Poisson Model

Abstract

The Vlasov equation describes the temporal evolution of the distribution function of particles in a collisionless plasma and, if magnetic fields are negligible, the mean electric field is prescribed by Poisson equation. Eulerian numerical methods discretize and directly solve the Vlasov equation on a mesh in phase space and can provide high accuracy with low numerical noise. In this paper, we present a comprehensive analysis and comparison between the most used Eulerian methods for the two-dimensional Vlasov–Poisson system, including finite-differences, finite-volumes and semi-Lagrangian ones. The schemes are evaluated and compared through classical problems and conclusions are drawn regarding their accuracy and performance.