| Issue |
ESAIM: M2AN
Volume 53, Number 2, March-April 2019
|
|
|---|---|---|
| Page(s) | 701 - 728 | |
| DOI | https://doi.org/10.1051/m2an/2018070 | |
| Published online | 29 May 2019 | |
Study of an asymptotic preserving scheme for the quasi neutral Euler–Boltzmann model in the drift regime
Université Paul Sabatier, Institut de Mathématiques de Toulouse (CNRS UMR 5219), France
* Corresponding author: mehdi.badsi@gmail.com
Received:
4
December
2017
Accepted:
8
November
2018
We deal with the numerical approximation of a simplified quasi neutral plasma model in the drift regime. Specifically, we analyze a finite volume scheme for the quasi neutral Euler–Boltzmann equations. We prove the unconditional stability of the scheme and give some bounds on the numerical approximation that are uniform in the asymptotic parameter. The proof relies on the control of the positivity and the decay of a discrete energy. The severe non linearity of the scheme being the price to pay to get the unconditional stability, to solve it, we propose an iterative linear implicit scheme that reduces to an elliptic system. The elliptic system enjoys a maximum principle that enables to prove the conservation of the positivity under a CFL condition that does not involve the asymptotic parameter. The linear L2 stability analysis of the iterative scheme shows that it does not request the mesh size and time step to be smaller than the asymptotic parameter. Numerical illustrations are given to illustrate the stability and consistency of the scheme in the drift regime as well as its ability to compute correct shock speeds.
Mathematics Subject Classification: 65M08 / 65M06 / 65M12 / 65Z05
Key words: Euler–Boltzmann / drift regime / quasi-neutral plasma / asymptotic preserving scheme / stability
© The authors. Published by EDP Sciences, SMAI 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.