# American Institute of Mathematical Sciences

December  2011, 4(4): 991-1023. doi: 10.3934/krm.2011.4.991

## Asymptotic-preserving scheme for a bi-fluid Euler-Lorentz model

 1 Université de Bordeaux 1, 351, cours de la Libération, 33405 TALENCE Cedex, France 2 Institut de Mathématiques de Toulouse, 118, route de Narbonne, 31062 TOULOUSE Cedex, France, France 3 Laboratoire Paul Painlevé, UFR de Mathématiques, Cité Scientiﬁque, 59655 VILLENEUVE D’ASCQ Cedex, France

Received  April 2011 Revised  July 2011 Published  November 2011

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 of the form $n_{i}=n_{e}$. 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.
Citation: Stéphane Brull, Pierre Degond, Fabrice Deluzet, Alexandre Mouton. Asymptotic-preserving scheme for a bi-fluid Euler-Lorentz model. Kinetic & Related Models, 2011, 4 (4) : 991-1023. doi: 10.3934/krm.2011.4.991
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