A non-oscillatory and conservative semi-Lagrangian scheme with fourth-degree polynomial interpolation for solving the Vlasov equation

Takayuki Umeda*, Yasuhiro Nariyuki, Daichi Kariya

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

Abstract

A conservative semi-Lagrangian scheme for the numerical solution of the Vlasov equation is developed based on the fourth-degree polynomial interpolation. Then, a numerical filter is implemented that preserves positivity and non-oscillatory. The numerical results of both one-dimensional linear advection and two-dimensional Vlasov-Poisson simulations show that the numerical diffusion with the fourth-degree polynomial interpolation is suppressed more than with the cubic polynomial interpolation. It is also found that inherent conservation properties of the Vlasov equation can be improved by combining numerical fluxes of the upwind-biased and central fourth-degree polynomial interpolations.

Original languageEnglish
Pages (from-to)1094-1100
Number of pages7
JournalComputer Physics Communications
Volume183
Issue number5
DOIs
StatePublished - 2012/05

Keywords

  • Conservative scheme
  • Hyperbolic equation
  • Numerical interpolation
  • Vlasov equation

ASJC Scopus subject areas

  • Hardware and Architecture
  • General Physics and Astronomy

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