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Preprints, Working Papers, ... Year : 2023

Hyperbolic reduced model for Vlasov-Poisson equation with Fokker-Planck collision

Abstract

This paper proposes a reduced model to simulate the one-dimensional Vlasov-Poisson equation with the non-linear Fokker-Planck operator. The model provides the space-time dynamics of a few macroscopic quantities constructed following the Reduced Order Method (ROM) in the velocity variable: the compression is thus applied to the semi-discretization of the Vlasov equation. To gain efficiency, a Discrete Empirical Interpolation Method (DEIM) is applied to the compressed non-linear Fokker-Planck operator. The size of the resulting reduced model is chosen empirically according to the Knudsen number. Furthermore, we propose a correction to the reduced collision operator that ensures the reduced moments to satisfy an Euler-type system. Numerical simulations of the reduced model show that the model can capture the plasma dynamics in different collisional regimes and initial conditions at a low cost.
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Dates and versions

hal-04099697 , version 1 (17-05-2023)
hal-04099697 , version 2 (12-04-2024)
hal-04099697 , version 3 (15-04-2024)

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  • HAL Id : hal-04099697 , version 3

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Emmanuel Franck, Ibtissem Lannabi, Youssouf Nasseri, Laurent Navoret, Giuseppe Parasiliti Rantone, et al.. Hyperbolic reduced model for Vlasov-Poisson equation with Fokker-Planck collision. 2024. ⟨hal-04099697v3⟩
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