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

  • Authors:

  • Pierre Crispel;Pierre Degond;Marie-Hélène Vignal

  • Affiliations:

  • 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 Narbo ...;MIP, Univ. P. Sabatier, 118 rte de Narbonne, 31062 Toulouse cedex 4, France;MIP, Univ. P. Sabatier, 118 rte de Narbonne, 31062 Toulouse cedex 4, France

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

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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.