On the velocity space discretization for the Vlasov-Poisson system: comparison between Hermite spectral and Particle-in-Cell methods. Part 2: fully-implicit scheme
Abstract
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. This paper concludes the study presented in Camporeale et al. (2013) where the same method has been described for a semi-implicit time discretization, and was compared against an explicit PIC.
Keywords
Cite
@article{arxiv.1312.4991,
title = {On the velocity space discretization for the Vlasov-Poisson system: comparison between Hermite spectral and Particle-in-Cell methods. Part 2: fully-implicit scheme},
author = {E. Camporeale and G. L. Delzanno and B. K. Bergen and J. D. Moulton},
journal= {arXiv preprint arXiv:1312.4991},
year = {2013}
}
Comments
submitted to Journal of Computational Physics 16 pages, 7 figures. arXiv admin note: text overlap with arXiv:1311.2098