An Asymptotic Preserving Scheme for the Euler-Poisson-Boltzmann System in the Quasineutral Limit

TL;DR

This paper introduces an energy stable, positivity preserving semi-implicit finite volume scheme for the Euler-Poisson-Boltzmann system that remains accurate in the quasineutral limit, effectively capturing plasma dynamics and sheaths.

Contribution

The paper develops an asymptotic preserving scheme with stabilization for the EPB system, ensuring stability, positivity, and consistency across regimes, including the quasineutral limit.

Findings

Scheme is energy stable and positivity preserving.

Accurately captures plasma sheaths and dynamics.

Remains consistent with the Euler system in the quasineutral limit.

Abstract

In this paper, we study an asymptotic preserving (AP), energy stable and positivity preserving semi-implicit finite volume scheme for the Euler-Poisson-Boltzmann (EPB) system in the quasineutral limit. The key to energy stability is the addition of appropriate stabilisation terms into the convective fluxes of mass and momenta, and the source term. The space-time fully-discrete scheme admits the positivity of the mass density, and is consistent with the weak formulation of the EPB system upon mesh refinement. In the quasineutral limit, the numerical scheme yields a consistent, semi-implicit discretisation of the isothermal compressible Euler system, thus leading to the AP property. Several benchmark numerical case studies are performed to confirm the robustness and efficacy of the proposed scheme in the dispersive as well as the quasineutral regimes. The numerical results also corroborates scheme's ability to very well resolve plasma sheaths and the related dynamics, which indicates its potential to applications involving low-temperature plasma problems.