# An asymptotic preserving scheme for the two-fluid Euler-Poisson model in the quasineutral limit

## Abstract

This paper deals with the modeling of a plasma in the quasineutral limit using the two-fluid Euler-Poisson system. In this limit, explicit numerical schemes suffer from severe numerical constraints related to the small Debye length and large plasma frequency. Here, we propose an implicit scheme which reduces to a scheme for the quasineutral Euler model in the quasineutral limit. Such a property is referred to as 'asymptotic preservation'. One of the distinctive features of this scheme is that it has a comparable numerical cost to that of an explicit scheme: simply the Poisson equation is replaced by a different (but formally equivalent) elliptic problem. We present numerical simulations for two different one-dimensional test-cases. They confirm the expected stability of the scheme in the quasineutral limit. They also show that this scheme has some accuracy problems in the limit of small electron to ion mass ratio in reproducing the correct electron velocity. But this problem is already present in the results of the classical algorithm. Numerical simulations are also performed for a two-dimensional problem of a plasma expansion in vacuum between two electrodes.

- Authors:

- CNES Centre de Toulouse, 18 av. Ed. Belin, 31401 Toulouse cedex 4 (France) and ONERA Centre de Toulouse, 2 av. Ed. Belin, 31055 Toulouse cedex 4 (France) and MIP, Univ. P. Sabatier, 118 rte de Narbonne, 31062 Toulouse cedex 4 (France). E-mail: crispel@mip.ups-tlse.fr
- MIP, Univ. P. Sabatier, 118 rte de Narbonne, 31062 Toulouse cedex 4 (France). E-mail: degond@mip.ups-tlse.fr
- MIP, Univ. P. Sabatier, 118 rte de Narbonne, 31062 Toulouse cedex 4 (France). E-mail: mhvignal@mip.ups-tlse.fr

- Publication Date:

- OSTI Identifier:
- 20991572

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 223; Journal Issue: 1; Other Information: DOI: 10.1016/j.jcp.2006.09.004; PII: S0021-9991(06)00433-5; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; ALGORITHMS; COMPUTERIZED SIMULATION; DEBYE LENGTH; ELECTRONS; FLUIDS; LANGMUIR FREQUENCY; MATHEMATICAL MODELS; ONE-DIMENSIONAL CALCULATIONS; PLASMA; PLASMA EXPANSION; POISSON EQUATION; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Crispel, Pierre, Degond, Pierre, and Vignal, Marie-Helene.
```*An asymptotic preserving scheme for the two-fluid Euler-Poisson model in the quasineutral limit*. United States: N. p., 2007.
Web. doi:10.1016/j.jcp.2006.09.004.

```
Crispel, Pierre, Degond, Pierre, & Vignal, Marie-Helene.
```*An asymptotic preserving scheme for the two-fluid Euler-Poisson model in the quasineutral limit*. United States. doi:10.1016/j.jcp.2006.09.004.

```
Crispel, Pierre, Degond, Pierre, and Vignal, Marie-Helene. Tue .
"An asymptotic preserving scheme for the two-fluid Euler-Poisson model in the quasineutral limit". United States.
doi:10.1016/j.jcp.2006.09.004.
```

```
@article{osti_20991572,
```

title = {An asymptotic preserving scheme for the two-fluid Euler-Poisson model in the quasineutral limit},

author = {Crispel, Pierre and Degond, Pierre and Vignal, Marie-Helene},

abstractNote = {This paper deals with the modeling of a plasma in the quasineutral limit using the two-fluid Euler-Poisson system. In this limit, explicit numerical schemes suffer from severe numerical constraints related to the small Debye length and large plasma frequency. Here, we propose an implicit scheme which reduces to a scheme for the quasineutral Euler model in the quasineutral limit. Such a property is referred to as 'asymptotic preservation'. One of the distinctive features of this scheme is that it has a comparable numerical cost to that of an explicit scheme: simply the Poisson equation is replaced by a different (but formally equivalent) elliptic problem. We present numerical simulations for two different one-dimensional test-cases. They confirm the expected stability of the scheme in the quasineutral limit. They also show that this scheme has some accuracy problems in the limit of small electron to ion mass ratio in reproducing the correct electron velocity. But this problem is already present in the results of the classical algorithm. Numerical simulations are also performed for a two-dimensional problem of a plasma expansion in vacuum between two electrodes.},

doi = {10.1016/j.jcp.2006.09.004},

journal = {Journal of Computational Physics},

number = 1,

volume = 223,

place = {United States},

year = {Tue Apr 10 00:00:00 EDT 2007},

month = {Tue Apr 10 00:00:00 EDT 2007}

}