Vlasov simulations using velocity-scaled Hermite representations
type: Item
instance of: scholarly article
title: Vlasov simulations using velocity-scaled Hermite representations
zbMATH Open document ID: 0936.76061
author: Joseph W. Schumer
author: James Paul Holloway
published in: Journal of Computational Physics
publication date: 2000-05-18T00:00:00Z
review text: The authors investigate the efficiency, accuracy, and stability of two different pseudo-spectral methods using scaled Hermite basis and weight functions, applied to the nonlinear Vlasov-Poisson equations in one dimension \((1d-1v)\). A variable velocity scale \(U\) is introduced into the Hermite basis and is shown to yield orders of magnitude reduction in errors, as compared to linear kinetic theory, with no increase in workload. A set of Fourier-Hermite coefficients, representing a periodic Gaussian distribution function, are advanced through time with an \(O(\Delta t^2)\)-accurate splitting method. Within this splitting scheme, the advection and acceleration terms of the Vlasov equation are solved separately using an \(O(\Delta t^4)\)-accurate Runge-Kutta method. Damping and growth rates, oscillation frequencies, \(E\)-field saturation levels, and phase-space evolution are seen to be qualitatively correct during simulations.
Mathematics Subject Classification ID: 76M22
Mathematics Subject Classification ID: 76X05
zbMATH DE Number: 1282701
zbMATH Keywords: pseudo-spectral methods
zbMATH Keywords: scaled Hermite basis
zbMATH Keywords: weight functions
zbMATH Keywords: Vlasov-Poisson equations
zbMATH Keywords: Fourier-Hermite coefficients
zbMATH Keywords: periodic Gaussian distribution function
zbMATH Keywords: splitting scheme
zbMATH Keywords: Runge-Kutta method
MaRDI profile type: Publication
full work available at URL: jcph.1998.5925
OpenAlex ID: W2072022733
cites work: Q5844186
cites work: Vlasov–Maxwell and Vlasov–Poisson equations as models of a one-dimensional electron plasma
cites work: A novel technique for the numerical simulation of hot collision-free plasma; Vlasov hybrid simulation
cites work: A method for overcoming the velocity space filamentation problem in collisionless plasma model solutions
cites work: Q4039908
cites work: A splitting algorithm for Vlasov simulation with filamentation filtration
cites work: Numerical integration of the Vlasov equation
cites work: Q3661894
cites work: A multistep technique for the numerical solution of a two-dimensional Vlasov equation
cites work: Asymptotic coefficients of Hermite function series
cites work: The Hermite Spectral Method for Gaussian-Type Functions
cites work: Spectral velocity discretizations for the Vlasov-Maxwell equations
cites work: Numerical integration methods of the Vlasov equation
cites work: Q4692890
cites work: On numerical methods for Hamiltonian PDEs and a collocation method for the Vlasov-Maxwell equations
DOI: 10.1006/JCPH.1998.5925
description: scientific article; zbMATH DE number 1282701