Stability and Conservation properties of Hermite-based approximations of the Vlasov-Poisson System

Technical Report · Fri Jun 11 04:00:00 EDT 2021

DOI:https://doi.org/10.2172/1788400· OSTI ID:1788400

Funaro, Daniele ^[1]; Manzini, Gianmarco ^[2]

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1. Univ. of Modena and Reggio Emilia (Italy); Institute of Applied Mathematics and Information Technologies Imati Pavia (Italy)
2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Spectral approximation based on Hermite-Fourier expansion of the Vlasov-Poisson model for a collisionless plasma in the electro-static limit is provided by adding high-order artificial collision operators of Lenard-Bernstein type. These differential operators are suitably designed in order to preserve the physically-meaningful invariants (number of particles, momentum, energy). In view of time-discretization, stability results in appropriate norms are presented. In this study, necessary conditions link the magnitude of the artificial collision term, the number of spectral modes of the discretization, as well as the time-step. The analysis, carried out in full for the Hermite discretization of a simple linear problem in one-dimension, is then partly extended to cover the complete nonlinear Vlasov-Poisson model.

• Research Organization: Univ. of Modena and Reggio Emilia (Italy); Institute of Applied Mathematics and Information Technologies Imati Pavia (Italy); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
• DOE Contract Number: 89233218CNA000001
• OSTI ID: 1788400
• Report Number(s): LA-UR--21-25536
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Hermite polyomials
Vlasov equation
conservation laws
spectral methods