Outflow boundary conditions for the Fourier transformed two-dimensional Vlasov equation

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

In order to facilitate numerical simulations of plasma phenomena where kinetic processes are important, we have studied the technique of Fourier transforming the Vlasov equation analytically in velocity space, and solving the resulting equation numerically. Particular attention has been paid to the boundary conditions of the Fourier transformed system. By using outgoing wave boundary conditions in the Fourier transformed space, small-scale information in velocity space is carried outside the computational domain and is removed, representing a dissipative loss mechanism. Thereby the so-called recurrence phenomenon is reduced. In the present article, a previously developed method in one spatial and one velocity dimension plus time is generalised to two spatial and two velocity dimensions plus time. Different high-order methods are used for computing derivatives as well as for the time stepping.
LanguageEnglish
Pages98-125
Number of pages28
JournalJournal of Computational Physics
Volume181
Issue number1
DOIs
Publication statusPublished - 1 Sep 2002

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Vlasov equation
vlasov equations
Boundary conditions
boundary conditions
Derivatives
Plasmas
Kinetics
Computer simulation
kinetics
simulation

Keywords

  • Vlasov equation
  • Fourier method
  • outflow boundary

Cite this

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title = "Outflow boundary conditions for the Fourier transformed two-dimensional Vlasov equation",
abstract = "In order to facilitate numerical simulations of plasma phenomena where kinetic processes are important, we have studied the technique of Fourier transforming the Vlasov equation analytically in velocity space, and solving the resulting equation numerically. Particular attention has been paid to the boundary conditions of the Fourier transformed system. By using outgoing wave boundary conditions in the Fourier transformed space, small-scale information in velocity space is carried outside the computational domain and is removed, representing a dissipative loss mechanism. Thereby the so-called recurrence phenomenon is reduced. In the present article, a previously developed method in one spatial and one velocity dimension plus time is generalised to two spatial and two velocity dimensions plus time. Different high-order methods are used for computing derivatives as well as for the time stepping.",
keywords = "Vlasov equation, Fourier method, outflow boundary",
author = "Bengt Eliasson",
year = "2002",
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Outflow boundary conditions for the Fourier transformed two-dimensional Vlasov equation. / Eliasson, Bengt.

In: Journal of Computational Physics, Vol. 181, No. 1, 01.09.2002, p. 98-125.

Research output: Contribution to journalArticle

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AB - In order to facilitate numerical simulations of plasma phenomena where kinetic processes are important, we have studied the technique of Fourier transforming the Vlasov equation analytically in velocity space, and solving the resulting equation numerically. Particular attention has been paid to the boundary conditions of the Fourier transformed system. By using outgoing wave boundary conditions in the Fourier transformed space, small-scale information in velocity space is carried outside the computational domain and is removed, representing a dissipative loss mechanism. Thereby the so-called recurrence phenomenon is reduced. In the present article, a previously developed method in one spatial and one velocity dimension plus time is generalised to two spatial and two velocity dimensions plus time. Different high-order methods are used for computing derivatives as well as for the time stepping.

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