Numerical approximation of the Euler-Maxwell model in the quasineutral limit

TL;DR

This paper develops an Asymptotic-Preserving numerical scheme for the Euler-Maxwell system in the quasi-neutral limit, ensuring stability and convergence independent of the Debye length, and demonstrating significant computational efficiency gains.

Contribution

The authors introduce a novel AP-scheme for the Euler-Maxwell system that remains stable and accurate as the Debye length approaches zero, with proven convergence and consistency properties.

Findings

The scheme's stability condition is independent of the Debye length as it tends to zero.

Numerical results confirm convergence to the Euler-Maxwell solution under specific discretization limits.

The AP-scheme allows larger time and space steps, greatly reducing computational resources.

Abstract

We derive and analyze an Asymptotic-Preserving scheme for the Euler-Maxwell system in the quasi-neutral limit. We prove that the linear stability condition on the time-step is independent of the scaled Debye length $\lambda$ when $\lambda \to 0$. Numerical validation performed on Riemann initial data and for a model Plasma Opening Switch device show that the AP-scheme is convergent to the Euler-Maxwell solution when $\Delta x/ \lambda \to 0$ where $\Delta x$ is the spatial discretization. But, when $\lambda /\Delta x \to 0$, the AP-scheme is consistent with the quasi-neutral Euler-Maxwell system. The scheme is also perfectly consistent with the Gauss equation. The possibility of using large time and space steps leads to several orders of magnitude reductions in computer time and storage.