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H 2 Numerical simulation of the Vlasov-Poisson model with an external magnetic field

Auteurs : Filbet, Francis (Auteur de la Conférence)
CIRM (Editeur )

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Vlasov-Poisson system asymptotic analysis of Vlasov equation guiding center model semi-Lagrangian methods WENO reconstruction boundary condition for kinetic equation inverse Lax-Wendroff procedure diocotron instability ion turbulence simulation

Résumé : We present an efficient algorithm for the long time behavior of plasma simulations. We will focus on 4D drift-kinetic model, where the plasma's motion occurs in the plane perpendicular to the magnetic field and can be governed by the 2D guiding-center model. Hermite WENO reconstructions, already proposed in [1], are applied for solving the Vlasov equation. Here we consider an arbitrary computational domain with an appropriate numerical method for the treatment of boundary conditions. Then we apply this algorithm for plasma turbulence simulations. We first solve the 2D guiding-center model in a D-shape domain and investigate the numerical stability of the steady state. Then, the 4D drift-kinetic model is studied with a mixed method, i.e. the semi-Lagrangian method in linear phase and finite difference method during the nonlinear phase. Numerical results show that the mixed method is efficient and accurate in linear phase and it is much stable during the nonlinear phase. Moreover, in practice it has better conservation properties.

Keywords: Cartesian mesh - semi-Lagrangian method - Hermite WENO reconstruction - guiding-center - drift-kinetic model

Codes MSC :
65M25 - Method of characteristics
78A35 - Motion of charged particles
65M08 - Finite volume methods

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 18/11/14
    Date de captation : 11/11/14
    Collection : Research talks ; Mathematical Physics ; Numerical Analysis and Scientific Computing
    Format : QuickTime (.mov) Durée : 00:44:32
    Domaine : Mathematical Physics ; Numerical Analysis & Scientific Computing
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2014-11-11_Filbet.mp4

Informations sur la rencontre

Nom de la rencontre : Kinetic equations / Equations cinétiques
Organisateurs de la rencontre : Bostan, Mihaï ; Hauray, Maxime ; Marra, Rossana ; Nouri, Anne
Dates : 10/11/14 - 14/11/14
Année de la rencontre : 2014

Citation Data

DOI : 10.24350/CIRM.V.18627903
Cite this video as: Filbet, Francis (2014). Numerical simulation of the Vlasov-Poisson model with an external magnetic field. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18627903
URI : http://dx.doi.org/10.24350/CIRM.V.18627903

Bibliographie

  • [1] Yang, C. and Filbet, F. Conservative and non-conservative methods based on Hermite weighted essentially non-oscillatory reconstruction for Vlasov equations, Journal of Computational Physics, vol. 279 (2014), pp. 18-36 - http://dx.doi.org/10.1016/j.jcp.2014.08.048

  • [2] Yang, C. and Filbet, F. An inverse Lax-Wendroff method for boundary conditions applied to Boltzmann type models, Journal of Computational Physics, vol. 245 (2013), pp. 43-61 - http://dx.doi.org/10.1016/j.jcp.2013.03.015

  • [3] Sonnendrücker, E. and Roche, J. The semi-Lagrangian method for the numerical resolution of the Vlasov equation, Journal of Computational physics, vol. 149 (1999), pp. 201-220 - http://dx.doi.org/10.1006/jcph.1998.6148

  • [4] Jiang, G.-S. and Shu, C.-W. Efficient implementation of weighted ENO schemes, Journal of Computational physics, vol. 126 (1996), pp. 202-228 - http://dx.doi.org/10.1006/jcph.1996.0130



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