Paper Info
Title
Study of conservation and recurrence of Runge---Kutta discontinuous Galerkin schemes for Vlasov---Poisson systems
Abstract
In this paper we consider Runge---Kutta discontinuous Galerkin (RKDG) schemes for Vlasov---Poisson systems that model collisionless plasmas. One-dimensional systems are emphasized. The RKDG method, originally devised to solve conservation laws, is seen to have excellent conservation properties, be readily designed for arbitrary order of accuracy, and capable of being used with a positivity-preserving limiter that guarantees positivity of the distribution functions. The RKDG solver for the Vlasov equation is the main focus, while the electric field is obtained through the classical representation by Green's function for the Poisson equation. A rigorous study of recurrence of the DG methods is presented by Fourier analysis, and the impact of different polynomial spaces and the positivity-preserving limiters on the quality of the solutions is ascertained. Several benchmark test problems, such as Landau damping, the two-stream instability, and the Kinetic Electro static Electron Nonlinear wave, are given.
Year
DOI
Venue
2013
10.1007/s10915-012-9680-x
J. Sci. Comput.
Keywords
Field
DocType
kutta discontinuous galerkin scheme,poisson system,dg method,fourier analysis,conservation law,poisson equation,excellent conservation property,rkdg solver,vlasov equation,positivity-preserving limiter,rkdg method
Discontinuous Galerkin method,Runge–Kutta methods,Order of accuracy,Mathematical optimization,Nonlinear system,Poisson's equation,Vlasov equation,Landau damping,Mathematical analysis,Conservation law,Mathematics
Journal
Volume
Issue
ISSN
56
2
1573-7691
Citations 
PageRank 
References 
8
0.59
7
Authors
3
Name
Order
Citations
PageRank
Yingda Cheng120120.27
Irene M. Gamba28612.52
Philip J. Morrison3191.53