A structure and asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck model

Blaustein, Alain; Filbet, Francis

doi:10.1016/j.jcp.2023.112693

Journal of Computational Physics

2024

DOI: 10.1016/j.jcp.2023.112693

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A structure and asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck model

Alain Blaustein,

Francis Filbet

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2024

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Cited by 2 publications

References 33 publications

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On a discrete framework of hypocoercivity for kinetic equations

Blaustein

Filbet

2023

Math. Comp.

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We propose and study a fully discrete finite volume scheme for the linear Vlasov-Fokker-Planck equation written as an hyperbolic system using Hermite polynomials in velocity. This approach naturally preserves the stationary solution and the weighted L 2 L^2 relative entropy. Then, we adapt the arguments developed in Dolbeault, Mouhot, and Schmeiser [Trans. Amer. Math. Soc. 367 (2015), pp. 3807–3828] based on hypocoercivity methods to get quantitative estimates on the convergence to equilibrium of the discrete solution. Finally, we prove that in the diffusive limit, the scheme is asymptotic preserving with respect to both the time variable and the scaling parameter at play.

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On a discrete framework of hypocoercivity for kinetic equations

Blaustein

Filbet

2023

Math. Comp.

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Discrete hypocoercivity for a nonlinear kinetic reaction model

Bessemoulin-Chatard,

Laidin,

Rey

2024

IMA Journal of Numerical Analysis

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In this article we propose a finite-volume discretization of a one-dimensional nonlinear reaction kinetic model proposed in Neumann & Schmeiser (2016), which describes a two-species recombination-generation process. Specifically, we establish the long-time convergence of approximate solutions towards equilibrium, at exponential rate. The study is based on an adaptation for a discretization of the linearized problem of the $L^{2}$ hypocoercivity method introduced in Dolbeault et al. (2015). From this we can deduce a local result for the discrete nonlinear problem, in the sense that small initial perturbations from the steady state are considered. As in the continuous framework this result requires the establishment of a maximum principle, which necessitates the use of monotone numerical fluxes.

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A structure and asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck model

Cited by 2 publications

References 33 publications

On a discrete framework of hypocoercivity for kinetic equations

On a discrete framework of hypocoercivity for kinetic equations

Discrete hypocoercivity for a nonlinear kinetic reaction model

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