On the velocity space discretization for the Vlasov–Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods

On the velocity space discretization for the Vlasov–Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods

We describe a spectral method for the numerical solution of the Vlasov–Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty of our approach is an implicit time discretization that allow...

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Bibliographic Details
Published in:Computer physics communications Vol. 198; no. C; pp. 47 - 58
Main Authors: Camporeale, E., Delzanno, G.L., Bergen, B.K., Moulton, J.D.
Format: Journal Article
Language:English
Published: Netherlands Elsevier B.V 01-01-2016
Elsevier
Subjects:
Computational efficiency
Decomposition
Discretization
Fourier analysis
Mathematical models
Multiscale simulations
Particle in cell technique
Plasma physics
Spectra
Spectral methods
Vlasov equation
Plasma physics
Multiscale simulations
Vlasov equation
Spectral methods
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Summary:We describe a spectral method for the numerical solution of the Vlasov–Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty of our approach is an implicit time discretization that allows exact conservation of charge, momentum and energy. The computational efficiency and the cost-effectiveness of this method are compared to the fully-implicit PIC method recently introduced by Markidis and Lapenta (2011) and Chen et al. (2011). The following examples are discussed: Langmuir wave, Landau damping, ion-acoustic wave, two-stream instability. The Fourier–Hermite spectral method can achieve solutions that are several orders of magnitude more accurate at a fraction of the cost with respect to PIC.
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USDOE
AC52-06NA25396
ISSN:0010-4655
1879-2944
DOI:10.1016/j.cpc.2015.09.002