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

Journal Article · · Communications on Applied Mathematics and Computation
 [1];  [2];  [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)
+ Show Author Affiliations
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.
Research Organization:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
89233218CNA000001
OSTI ID:
1569732
Report Number(s):
LA-UR--18-25332
Journal Information:
Communications on Applied Mathematics and Computation, Journal Name: Communications on Applied Mathematics and Computation Journal Issue: 3 Vol. 1; ISSN 2096-6385
Publisher:
Springer NatureCopyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

97 MATHEMATICS AND COMPUTING
Hermite functions
High-order
Mass conservation
Mathematics
Semi-Lagrangian methods
Spectral methods
Vlasov–Poisson equations