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

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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.

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Authors and Affiliations

  1. Centre de Mathématiques Appliquées (UMR 7641), Ecole Polytechnique, 91128, Palaiseau, France

    R. Belaouar

  2. INRIA Nancy-Grand-EST (CALVI Project), and IRMA-Université de Strasbourg and CNRS, 67084, Strasbourg Cedex, France

    N. Crouseilles & E. Sonnendrücker

  3. 1-Université de Toulouse, UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, 31062, Toulouse, France

    P. Degond

  4. 2-CNRS, Institut de Mathématiques de Toulouse UMR 5219, 31062, Toulouse, France

    P. Degond

Authors
  1. R. Belaouar
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  2. N. Crouseilles
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  3. P. Degond
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  4. E. Sonnendrücker
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Correspondence to N. Crouseilles.

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Belaouar, R., Crouseilles, N., Degond, P. et al. An Asymptotically Stable Semi-Lagrangian scheme in the Quasi-neutral Limit. J Sci Comput 41, 341–365 (2009). https://doi.org/10.1007/s10915-009-9302-4

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  • DOI: https://doi.org/10.1007/s10915-009-9302-4

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