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Title: A Semi-Lagrangian Spectral Method for the Vlasov–Poisson System Based on Fourier, Legendre and Hermite Polynomials

Abstract

In this study, we apply a semi-Lagrangian spectral method for the Vlasov–Poisson system, previously designed for periodic Fourier discretizations, by implementing Legendre polynomials and Hermite functions in the approximation of the distribution function with respect to the velocity variable. We discuss second-order accurate-in-time schemes, obtained by coupling spectral techniques in the space–velocity domain with a BDF time-stepping scheme. The resulting method possesses good conservation properties, which have been assessed by a series of numerical tests conducted on some standard benchmark problems including the two-stream instability and the Landau damping test cases. In the Hermite case, we also investigate the numerical behavior in dependence of a scaling parameter in the Gaussian weight. Confirming previous results from the literature, our experiments for different representative values of this parameter, indicate that a proper choice may significantly impact on accuracy, thus suggesting that suitable strategies should be developed to automatically update the parameter during the time-advancing procedure.

Authors:
 [1];  [2]; ORCiD logo [3]
  1. Univ. degli Studi di Camerino, Camerino (Italy)
  2. Univ. degli Studi di Modena e Reggio Emilia, Modena (Italy)
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1569732
Report Number(s):
LA-UR-18-25332
Journal ID: ISSN 2096-6385
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Accepted Manuscript
Journal Name:
Communications on Applied Mathematics and Computation
Additional Journal Information:
Journal Volume: 1; Journal Issue: 3; Journal ID: ISSN 2096-6385
Publisher:
Springer Nature
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Mathematics; Spectral methods; Semi-Lagrangian methods; High-order; Hermite functions; Vlasov–Poisson equations; Mass conservation

Citation Formats

Fatone, Lorella, Funaro, Daniele, and Manzini, Gianmarco. A Semi-Lagrangian Spectral Method for the Vlasov–Poisson System Based on Fourier, Legendre and Hermite Polynomials. United States: N. p., 2019. Web. doi:10.1007/s42967-019-00027-8.
Fatone, Lorella, Funaro, Daniele, & Manzini, Gianmarco. A Semi-Lagrangian Spectral Method for the Vlasov–Poisson System Based on Fourier, Legendre and Hermite Polynomials. United States. doi:10.1007/s42967-019-00027-8.
Fatone, Lorella, Funaro, Daniele, and Manzini, Gianmarco. Wed . "A Semi-Lagrangian Spectral Method for the Vlasov–Poisson System Based on Fourier, Legendre and Hermite Polynomials". United States. doi:10.1007/s42967-019-00027-8.
@article{osti_1569732,
title = {A Semi-Lagrangian Spectral Method for the Vlasov–Poisson System Based on Fourier, Legendre and Hermite Polynomials},
author = {Fatone, Lorella and Funaro, Daniele and Manzini, Gianmarco},
abstractNote = {In this study, we apply a semi-Lagrangian spectral method for the Vlasov–Poisson system, previously designed for periodic Fourier discretizations, by implementing Legendre polynomials and Hermite functions in the approximation of the distribution function with respect to the velocity variable. We discuss second-order accurate-in-time schemes, obtained by coupling spectral techniques in the space–velocity domain with a BDF time-stepping scheme. The resulting method possesses good conservation properties, which have been assessed by a series of numerical tests conducted on some standard benchmark problems including the two-stream instability and the Landau damping test cases. In the Hermite case, we also investigate the numerical behavior in dependence of a scaling parameter in the Gaussian weight. Confirming previous results from the literature, our experiments for different representative values of this parameter, indicate that a proper choice may significantly impact on accuracy, thus suggesting that suitable strategies should be developed to automatically update the parameter during the time-advancing procedure.},
doi = {10.1007/s42967-019-00027-8},
journal = {Communications on Applied Mathematics and Computation},
number = 3,
volume = 1,
place = {United States},
year = {2019},
month = {5}
}

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