### Abstract

Original language | English |
---|---|

Pages (from-to) | 1508-1532 |

Number of pages | 25 |

Journal | Journal of Computational Physics |

Volume | 225 |

Issue number | 2 |

Early online date | 17 Feb 2007 |

DOIs | |

Publication status | Published - 10 Aug 2007 |

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### Keywords

- Vlasov-Maxwell system
- numerical method
- Fourier method

### Cite this

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*Journal of Computational Physics*, vol. 225, no. 2, pp. 1508-1532. https://doi.org/10.1016/j.jcp.2007.02.005

**Outflow boundary conditions for the Fourier transformed three-dimensional Vlasov–Maxwell system.** / Eliasson, Bengt.

Research output: Contribution to journal › Article

TY - JOUR

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

AU - Eliasson, Bengt

PY - 2007/8/10

Y1 - 2007/8/10

N2 - 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.

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

UR - http://www.sciencedirect.com/science/article/pii/S0021999107000666

U2 - 10.1016/j.jcp.2007.02.005

DO - 10.1016/j.jcp.2007.02.005

M3 - Article

VL - 225

SP - 1508

EP - 1532

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 2

ER -