High order Asymptotic Preserving penalized numerical schemes for the Euler-Poisson system in the quasi-neutral limit

TL;DR

This paper develops high-order IMEX finite volume schemes for the Euler-Poisson system that remain stable and accurate across different plasma regimes, especially near the quasineutral limit where standard methods fail.

Contribution

Introduction of penalized IMEX Runge-Kutta methods that are uniformly stable and high-order accurate in the quasineutral limit for plasma simulations.

Findings

Schemes are stable across all regimes including the quasineutral limit.

Methods degenerate into high-order schemes as the Debye length approaches zero.

Numerical tests confirm the schemes' stability and accuracy.

Abstract

In this work, we focus on the development of high-order Implicit-Explicit (IMEX) finite volume numerical methods for plasmas in quasineutral regimes. At large temporal and spatial scales, plasmas tend to be quasineutral, meaning that the local net charge density is nearly zero. However, at small time and spatial scales, measured by the the Debye length, quasineutrality breaks down. In such regimes, standard numerical methods face severe stability constraints, rendering them practically unusable. To address this issue, we introduce and analyze a class of penalized IMEX Runge-Kutta methods for the Euler-Poisson (EP) system, specifically designed to handle the quasineutral limit. These schemes are uniformly stable with respect to the Debye length and degenerate into high-order methods as the quasineutral limit is approached. Several numerical tests confirm that the proposed methods exhibit the desired properties.