Numerical study of an anisotropic Vlasov equation arising in plasma physics

TL;DR

This paper compares various numerical schemes for anisotropic Vlasov equations derived from plasma physics, focusing on their asymptotic-preserving properties to identify the most suitable method for realistic tokamak plasma simulations.

Contribution

It provides a systematic analysis of numerical schemes for anisotropic Vlasov equations, emphasizing their asymptotic-preserving features in simplified models.

Findings

Certain schemes demonstrate superior asymptotic-preserving properties.

The study identifies the most effective numerical approach for future realistic plasma simulations.

Toy-model analysis clarifies scheme behaviors in anisotropic kinetic equations.

Abstract

Goal of this paper is to investigate several numerical schemes for the resolution of two anisotropic Vlasov equations. These two toy-models arise from a kinetic description of a tokamak plasma confined by strong magnetic fields. The simplicity of our toy-models permits to better understand the features of each scheme, in particular to investigate their asymptotic-preserving properties, in the aim to choose then the most adequate numerical scheme for upcoming, more realistic simulations.