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28 March 2024
 
  » arxiv » 1009.3046

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A discontinuous Galerkin method for the Vlasov-Poisson system
R. E. Heath ; I.M. Gamba ; P.J. Morrison ; C. Michler ;
Date 15 Sep 2010
AbstractA discontinuous Galerkin method for approximating the Vlasov-Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions are used as a basis, the method preserves the positivity of the electron distribution function. The performance of the method is investigated by computing six examples. In particular, computed results are benchmarked against established theoretical results for linear advection and the phenomenon of linear Landau damping for both the Maxwell and Lorentz distributions. Moreover, two non linear problems are considered: non linear Landau damping and a version of the two-stream instability are computed. For the latter, fine scale details of the resulting long-time BGK-like state are presented. Conservation laws are examined and various comparisons to theory are made. The results obtained demonstrate that the discontinuous Galerkin method is a viable option for integrating the Vlasov-Poisson system.
Source arXiv, 1009.3046
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