Anti-symmetric and positivity preserving formulation of a spectral method for Vlasov-Poisson equations

We analyze the anti-symmetric properties of a spectral discretization for the one-dimensional Vlasov-Poisson equations. The discretization is based on a spectral expansion in velocity with the symmetrically weighted Hermite basis functions, central finite differencing in space, and an implicit Runge...

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational physics 2024-10, Vol.514, p.113263, Article 113263
Main Authors: Issan, Opal, Koshkarov, Oleksandr, Halpern, Federico D., Kramer, Boris, Delzanno, Gian Luca
Format: Article
Language:English
Subjects:
Anti-symmetry
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Conservation laws
Heliospheric and Magnetospheric Physics
Mathematics
Spectral methods
Vlasov-Poisson equations
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We analyze the anti-symmetric properties of a spectral discretization for the one-dimensional Vlasov-Poisson equations. The discretization is based on a spectral expansion in velocity with the symmetrically weighted Hermite basis functions, central finite differencing in space, and an implicit Runge Kutta integrator in time. The proposed discretization preserves the anti-symmetric structure of the advection operator in the Vlasov equation, resulting in a stable numerical method. We apply such discretization to two formulations: the canonical Vlasov-Poisson equations and their continuously transformed square-root representation. The latter preserves the positivity of the particle distribution function. We derive analytically the conservation properties of both formulations, including particle number, momentum, and energy, which are verified numerically on the following benchmark problems: manufactured solution, linear and nonlinear Landau damping, two-stream instability, bump-on-tail instability, and ion-acoustic wave.
ISSN:0021-9991
DOI:10.1016/j.jcp.2024.113263