An asymptotic preserving well-balanced scheme for the isothermal fluid equations in low-temperature plasma applications - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Computational Physics Année : 2020

An asymptotic preserving well-balanced scheme for the isothermal fluid equations in low-temperature plasma applications

Un schéma préservant l'asymptotique et équilibre pour la simulation des équations fluides isothermes en vue d'applications en physique des plasmas à basse température

Résumé

We present a novel numerical scheme for the efficient and accurate solution of the isothermal two-fluid (electron + ion) equations coupled to Poisson's equation for low-temperature plasmas. The model considers electrons and ions as separate fluids, comprising the electron inertia and charge separation. The discretization of this system with standard explicit schemes is constrained by very restrictive time steps and cell sizes related to the resolution of the Debye length, electron plasma frequency, and electron sound waves. Both sheath and electron inertia are fundamental to fully explain the physics in low-pressure and low-temperature plasmas. However, most of the phenomena of interest for fluid models occur at speeds much slower than the electron thermal speed and are quasi-neutral, except in small charged regions. A numerical method that is able to simulate efficiently and accurately all these regimes is a challenge due to the multiscale character of the problem. In this work, we present a scheme based on the Lagrange-projection operator splitting that preserves the asymptotic regime where the plasma is quasi-neutral with massless electrons. As a result, the quasi-neutral regime is treated without the need of an implicit solver nor the resolution of the Debye length and electron plasma frequency. Additionally, the scheme proves to accurately represent the dynamics of the electrons both at low speeds and when the electron speed is comparable to the thermal speed. In addition, a well-balanced treatment of the ion source terms is proposed in order to tackle problems where the ion temperature is very low compared to the electron temperature. The scheme significantly improves the accuracy both in the quasi-neutral limit and in the presence of plasma sheaths when the Debye length is resolved. In order to assess the performance of the scheme in low-temperature plasmas conditions, we propose two specifically designed test-cases: a quasi-neutral two-stream periodic perturbation with analytical solution and a low-temperature discharge that includes sheaths. The numerical strategy, its accuracy, and computational efficiency are assessed on these two discriminating configurations.
Fichier principal
Vignette du fichier
AP_scheme_Alvarez_Laguna_etal_2019.pdf (2.04 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02116610 , version 1 (01-05-2019)

Identifiants

Citer

Alejandro Alvarez-Laguna, Teddy Pichard, Thierry Magin, Pascal Chabert, Anne Bourdon, et al.. An asymptotic preserving well-balanced scheme for the isothermal fluid equations in low-temperature plasma applications. Journal of Computational Physics, 2020, 419, pp.109634. ⟨10.1016/j.jcp.2020.109634⟩. ⟨hal-02116610⟩
472 Consultations
177 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More