Asymptotic-Preserving scheme for a bi-fluid Euler-Lorentz model

TL;DR

This paper develops an Asymptotic-Preserving numerical scheme for simulating strongly magnetized plasmas modeled by a two-fluid Euler-Lorentz system, ensuring accuracy across different regimes.

Contribution

It introduces a semi-discrete Asymptotic-Preserving scheme for a perturbed two-fluid Euler-Lorentz model with quasi-neutrality, enhancing simulation stability and accuracy.

Findings

The scheme accurately captures plasma behavior in various magnetic field strengths.

Numerical results demonstrate stability and consistency of the method.

The approach effectively handles the small perturbation in quasi-neutrality.

Abstract

The present work is devoted to the simulation of a strongly magnetized plasma considered as a mixture of an ion fluid and an electron fluid. For the sake of simplicity, we assume that the model is isothermal and described by Euler equations coupled with a term representing the Lorentz force. Moreover we assume that both Euler systems are coupled through a quasi-neutrality constraint. The numerical method which is described in the present document is based on an Asymptotic-Preserving semi-discretization in time of a variant of this two-fluid Euler-Lorentz model with a small perturbation of the quasi-neutrality constraint. Firstly, we present the two-fluid model and the motivations for introducing a small perturbation into the quasi-neutrality equation, then we describe the time semi-discretization of the perturbed model and a fully-discrete finite volume scheme based on it. Finally, we present some numerical results which have been obtained with this method.