An Asymptotically Stable Semi-Lagrangian scheme in the Quasi-neutral Limit

  • Authors:

  • R. Belaouar;N. Crouseilles;P. Degond;E. Sonnendrücker

  • Affiliations:

  • Centre de Mathématiques Appliquées (UMR 7641), Ecole Polytechnique, Palaiseau, France 91128;INRIA Nancy-Grand-EST (CALVI Project), and IRMA-Université de Strasbourg and CNRS, Strasbourg Cedex, France 67084;1-Université de Toulouse, UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, Toulouse, France 31062 and 2-CNRS, Institut de Mathématiques de Toulouse UMR 5219, Toulouse, Fr ...;INRIA Nancy-Grand-EST (CALVI Project), and IRMA-Université de Strasbourg and CNRS, Strasbourg Cedex, France 67084

  • Venue:
  • Journal of Scientific Computing
  • Year:
  • 2009

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Abstract

This paper deals with the numerical simulations of the Vlasov-Poisson equation using a phase space grid in the quasi-neutral regime. In this limit, explicit numerical schemes suffer from numerical constraints related to the small Debye length and large plasma frequency. Here, we propose a semi-Lagrangian scheme for the Vlasov-Poisson model in the quasi-neutral limit. The main ingredient relies on a reformulation of the Poisson equation derived in (Crispel et al. in C. R. Acad. Sci. Paris, Ser. I 341:341---346, 2005) which enables asymptotically stable simulations. This scheme has a comparable numerical cost per time step to that of an explicit scheme. Moreover, it is not constrained by a restriction on the size of the time and length step when the Debye length and plasma period go to zero. A stability analysis and numerical simulations confirm this statement.