Year: 2011
Communications in Computational Physics, Vol. 10 (2011), Iss. 4 : pp. 1001–1026
Abstract
In this report, a charge preserving numerical resolution of the 1D Vlasov-Ampère equation is achieved, with a forward Semi-Lagrangian method introduced in [10]. The Vlasov equation belongs to the kinetic way of simulating plasmas evolution, and is coupled with the Poisson's equation, or equivalently under charge conservation, the Ampère's one, which self-consistently rules the electric field evolution. In order to ensure having proper physical solutions, it is necessary that the scheme preserves charge numerically. B-spline deposition will be used for the interpolation step. The solving of the characteristics will be made with a Runge-Kutta 2 method and with a Cauchy-Kovalevsky procedure.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.210410.211210a
Communications in Computational Physics, Vol. 10 (2011), Iss. 4 : pp. 1001–1026
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
-
Energy-conserving discontinuous Galerkin methods for the Vlasov–Ampère system
Cheng, Yingda | Christlieb, Andrew J. | Zhong, XinghuiJournal of Computational Physics, Vol. 256 (2014), Iss. P.630
https://doi.org/10.1016/j.jcp.2013.09.013 [Citations: 45] -
Energy-conserving discontinuous Galerkin methods for the Vlasov-Ampère system with Dougherty-Fokker-Planck collision operator
Ye, Boyang | Hu, Jingwei | Shu, Chi-Wang | Zhong, XinghuiJournal of Computational Physics, Vol. 514 (2024), Iss. P.113219
https://doi.org/10.1016/j.jcp.2024.113219 [Citations: 0] -
Numerical simulations of one laser-plasma model based on Poisson structure
Li, Yingzhe | Sun, Yajuan | Crouseilles, NicolasJournal of Computational Physics, Vol. 405 (2020), Iss. P.109172
https://doi.org/10.1016/j.jcp.2019.109172 [Citations: 5] -
Hamiltonian splitting for the Vlasov–Maxwell equations
Crouseilles, Nicolas | Einkemmer, Lukas | Faou, ErwanJournal of Computational Physics, Vol. 283 (2015), Iss. P.224
https://doi.org/10.1016/j.jcp.2014.11.029 [Citations: 61] -
Numerical Solution of the Vlasov–Ampère Equations
Chizhonkov, E. V.
Computational Mathematics and Mathematical Physics, Vol. 64 (2024), Iss. 7 P.1537
https://doi.org/10.1134/S0965542524700714 [Citations: 0] -
Hamiltonian Particle-in-Cell methods for Vlasov–Poisson equations
Gu, Anjiao | He, Yang | Sun, YajuanJournal of Computational Physics, Vol. 467 (2022), Iss. P.111472
https://doi.org/10.1016/j.jcp.2022.111472 [Citations: 4] -
An asymptotic preserving scheme for the relativistic Vlasov–Maxwell equations in the classical limit
Crouseilles, Nicolas | Einkemmer, Lukas | Faou, ErwanComputer Physics Communications, Vol. 209 (2016), Iss. P.13
https://doi.org/10.1016/j.cpc.2016.08.001 [Citations: 8] -
Numerical study of the two-species Vlasov–Ampère system: Energy-conserving schemes and the current-driven ion-acoustic instability
Cheng, Yingda | Christlieb, Andrew J. | Zhong, XinghuiJournal of Computational Physics, Vol. 288 (2015), Iss. P.66
https://doi.org/10.1016/j.jcp.2015.02.020 [Citations: 6] -
An energy-conserving Fourier particle-in-cell method with asymptotic-preserving preconditioner for Vlasov-Ampère system with exact curl-free constraint
Li, Zhuoning | Xu, Zhenli | Yang, ZhiguoJournal of Computational Physics, Vol. 495 (2023), Iss. P.112529
https://doi.org/10.1016/j.jcp.2023.112529 [Citations: 1]