A Charge Preserving Scheme for the Numerical Resolution of the Vlasov-Ampère Equations

A Charge Preserving Scheme for the Numerical Resolution of the Vlasov-Ampère Equations

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

Keywords:   

  1. Energy-conserving discontinuous Galerkin methods for the Vlasov–Ampère system

    Cheng, Yingda | Christlieb, Andrew J. | Zhong, Xinghui

    Journal of Computational Physics, Vol. 256 (2014), Iss. P.630

    https://doi.org/10.1016/j.jcp.2013.09.013 [Citations: 45]
  2. Energy-conserving discontinuous Galerkin methods for the Vlasov-Ampère system with Dougherty-Fokker-Planck collision operator

    Ye, Boyang | Hu, Jingwei | Shu, Chi-Wang | Zhong, Xinghui

    Journal of Computational Physics, Vol. 514 (2024), Iss. P.113219

    https://doi.org/10.1016/j.jcp.2024.113219 [Citations: 0]
  3. Numerical simulations of one laser-plasma model based on Poisson structure

    Li, Yingzhe | Sun, Yajuan | Crouseilles, Nicolas

    Journal of Computational Physics, Vol. 405 (2020), Iss. P.109172

    https://doi.org/10.1016/j.jcp.2019.109172 [Citations: 5]
  4. Hamiltonian splitting for the Vlasov–Maxwell equations

    Crouseilles, Nicolas | Einkemmer, Lukas | Faou, Erwan

    Journal of Computational Physics, Vol. 283 (2015), Iss. P.224

    https://doi.org/10.1016/j.jcp.2014.11.029 [Citations: 61]
  5. 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]
  6. Hamiltonian Particle-in-Cell methods for Vlasov–Poisson equations

    Gu, Anjiao | He, Yang | Sun, Yajuan

    Journal of Computational Physics, Vol. 467 (2022), Iss. P.111472

    https://doi.org/10.1016/j.jcp.2022.111472 [Citations: 4]
  7. An asymptotic preserving scheme for the relativistic Vlasov–Maxwell equations in the classical limit

    Crouseilles, Nicolas | Einkemmer, Lukas | Faou, Erwan

    Computer Physics Communications, Vol. 209 (2016), Iss. P.13

    https://doi.org/10.1016/j.cpc.2016.08.001 [Citations: 8]
  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, Xinghui

    Journal of Computational Physics, Vol. 288 (2015), Iss. P.66

    https://doi.org/10.1016/j.jcp.2015.02.020 [Citations: 6]
  9. 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, Zhiguo

    Journal of Computational Physics, Vol. 495 (2023), Iss. P.112529

    https://doi.org/10.1016/j.jcp.2023.112529 [Citations: 1]