Journal of Scientific Computing

, Volume 41, Issue 3, pp 341–365 | Cite as

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

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


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.


Vlasov equation Quasi-neutral limit Semi-Lagrangian method Asymptotic preserving scheme 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • R. Belaouar
    • 1
  • N. Crouseilles
    • 2
  • P. Degond
    • 3
    • 4
  • E. Sonnendrücker
    • 2
  1. 1.Centre de Mathématiques Appliquées (UMR 7641)Ecole PolytechniquePalaiseauFrance
  2. 2.INRIA Nancy-Grand-EST (CALVI Project), and IRMA-Université de Strasbourg and CNRSStrasbourg CedexFrance
  3. 3.1-Université de Toulouse, UPS, INSA, UT1, UTM, Institut de Mathématiques de ToulouseToulouseFrance
  4. 4.2-CNRS, Institut de Mathématiques de Toulouse UMR 5219ToulouseFrance

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