Outflow boundary conditions for the Fourier transformed three-dimensional Vlasov–Maxwell system

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

A problem with the solution of the Vlasov equation is its tendency to become filamented/oscillatory in velocity space, which in numerical simulations can give rise to unphysical oscillations and recurrence effects. We present a three-dimensional Vlasov–Maxwell solver (three spatial and velocity dimensions, plus time), in which the Vlasov equation is Fourier transformed in velocity space and the resulting equations solved numerically. By designing absorbing outflow boundary conditions in the Fourier transformed velocity space, the highest Fourier modes in velocity space are removed from the numerical solution. This introduces a dissipative effect in velocity space and the numerical recurrence effect is strongly reduced. The well-posedness of the boundary conditions is proved analytically, while the stability of the numerical implementation is assessed by long-time numerical simulations. Well-known wave-modes in magnetized plasmas are shown to be reproduced by the numerical scheme.
LanguageEnglish
Pages1508-1532
Number of pages25
JournalJournal of Computational Physics
Volume225
Issue number2
Early online date17 Feb 2007
DOIs
Publication statusPublished - 10 Aug 2007

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Boundary conditions
boundary conditions
Vlasov equation
vlasov equations
Computer simulation
tendencies
simulation
Plasmas
oscillations

Keywords

  • Vlasov-Maxwell system
  • numerical method
  • Fourier method

Cite this

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title = "Outflow boundary conditions for the Fourier transformed three-dimensional Vlasov–Maxwell system",
abstract = "A problem with the solution of the Vlasov equation is its tendency to become filamented/oscillatory in velocity space, which in numerical simulations can give rise to unphysical oscillations and recurrence effects. We present a three-dimensional Vlasov–Maxwell solver (three spatial and velocity dimensions, plus time), in which the Vlasov equation is Fourier transformed in velocity space and the resulting equations solved numerically. By designing absorbing outflow boundary conditions in the Fourier transformed velocity space, the highest Fourier modes in velocity space are removed from the numerical solution. This introduces a dissipative effect in velocity space and the numerical recurrence effect is strongly reduced. The well-posedness of the boundary conditions is proved analytically, while the stability of the numerical implementation is assessed by long-time numerical simulations. Well-known wave-modes in magnetized plasmas are shown to be reproduced by the numerical scheme.",
keywords = "Vlasov-Maxwell system, numerical method, Fourier method",
author = "Bengt Eliasson",
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Outflow boundary conditions for the Fourier transformed three-dimensional Vlasov–Maxwell system. / Eliasson, Bengt.

In: Journal of Computational Physics, Vol. 225, No. 2, 10.08.2007, p. 1508-1532.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Outflow boundary conditions for the Fourier transformed three-dimensional Vlasov–Maxwell system

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AB - A problem with the solution of the Vlasov equation is its tendency to become filamented/oscillatory in velocity space, which in numerical simulations can give rise to unphysical oscillations and recurrence effects. We present a three-dimensional Vlasov–Maxwell solver (three spatial and velocity dimensions, plus time), in which the Vlasov equation is Fourier transformed in velocity space and the resulting equations solved numerically. By designing absorbing outflow boundary conditions in the Fourier transformed velocity space, the highest Fourier modes in velocity space are removed from the numerical solution. This introduces a dissipative effect in velocity space and the numerical recurrence effect is strongly reduced. The well-posedness of the boundary conditions is proved analytically, while the stability of the numerical implementation is assessed by long-time numerical simulations. Well-known wave-modes in magnetized plasmas are shown to be reproduced by the numerical scheme.

KW - Vlasov-Maxwell system

KW - numerical method

KW - Fourier method

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