A new conservative unsplit method for the solution of the Vlasov equation

  • Authors:

  • N. V. Elkina;J. Büchner

  • Affiliations:

  • M.V. Keldysh Institute for Applied Mathematics Miusskaya sq., 4 Moscow 125047, Russia and Max-Planck-Institut für Sonnensystemforschung, Max-Planck-Str. 2, 37191 Katlenburg-Lindau, Germany;Max-Planck-Institut für Sonnensystemforschung, Max-Planck-Str. 2, 37191 Katlenburg-Lindau, Germany

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2006

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Abstract

We have developed a new conservative method for solving the Vlasov equation without using any splitting technique. Our goal is to maintain the positivity of the distribution function and to avoid un-physical oscillations which might lead to numerical instabilities. Based on a finite volume conservative discretization of the conservative form of the Vlasov equation we implemented a highly accurate second-order upwind scheme. In order to avoid un-physical oscillations and their possible numerical instability we apply a flux-limiter in the second order. We validate our new Vlasov solver by considering standard cases of one-dimensional current-driven ion-acoustic instabilities solving a Vlasov-Ampere set of equations.