Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit

TL;DR

This paper compares numerical schemes for the Euler-Poisson-Boltzmann model in plasma physics, focusing on their accuracy in the quasi-neutral limit, and introduces a reformulation that improves this accuracy.

Contribution

It introduces and analyzes a reformulated scheme (REPB) that better captures the quasi-neutral limit compared to traditional EPB schemes.

Findings

REPB scheme more accurately captures the quasi-neutral limit.

Comparison shows REPB outperforms standard EPB in numerical tests.

The reformulation simplifies the analysis of plasma models.

Abstract

This paper analyzes various schemes for the Euler-Poisson-Boltzmann (EPB) model of plasma physics. This model consists of the pressureless gas dynamics equations coupled with the Poisson equation and where the Boltzmann relation relates the potential to the electron density. If the quasi-neutral assumption is made, the Poisson equation is replaced by the constraint of zero local charge and the model reduces to the Isothermal Compressible Euler (ICE) model. We compare a numerical strategy based on the EPB model to a strategy using a reformulation (called REPB formulation). The REPB scheme captures the quasi-neutral limit more accurately.