Multi-moment advection scheme for Vlasov simulations

  • Authors:

  • Takashi Minoshima;Yosuke Matsumoto;Takanobu Amano

  • Affiliations:

  • Institute for Research on Earth Evolution, Japan Agency for Marine-Earth Science and Technology, 3173-25 Syowa-machi, Kanazawaku, Yokohama 236-0001, Japan;Solar-Terrestrial Environment Laboratory, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan;Department of Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2011

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Abstract

We present a new numerical scheme for solving the advection equation and its application to Vlasov simulations. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent variables, for better conservation of the information entropy. We have developed one-and two-dimensional schemes and show that they provide quite accurate solutions within reasonable usage of computational resources compared to other existing schemes. The two-dimensional scheme can accurately solve the solid body rotation problem of a gaussian profile for more than hundred rotation periods with little numerical diffusion. This is crucially important for Vlasov simulations of magnetized plasmas. Applications of the one- and two-dimensional schemes to electrostatic and electromagnetic Vlasov simulations are presented with some benchmark tests.