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

Issan, Opal; Koshkarov, Oleksandr; Halpern, Federico D.; Kramer, Boris; Delzanno, Gian Luca

doi:10.1016/j.jcp.2024.113263

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

Journal Article · Tue Jul 09 00:00:00 EDT 2024 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2024.113263· OSTI ID:2406642

^[1]; ^[2]; Halpern, Federico D. ^[3]; Kramer, Boris ^[1]; ^[2]

Univ. of California, San Diego, La Jolla, CA (United States)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
General Atomics, San Diego, CA (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Fusion Energy Sciences (FES)

Grant/Contract Number:: 89233218CNA000001; FG02-95ER54309

OSTI ID:: 2406642

Report Number(s):: LA-UR--23-33819

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 514; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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

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