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Pré-Publication, Document De Travail Année : 2023

Semi-Lagrangian Vlasov-Poisson solvers with a strong external uniform magnetic field

Résumé

In this article, we numerically solve the long-time Vlasov-Poisson system with a strong external magnetic field. For that, we consider a backward semi-Lagrangian method as follows: we first propose an approximation of the characteristics based on first and second order explicit numerical schemes; then, a 4-D interpolation is performed to update a numerical unknown. We show that when the magnitude of the external magnetic field becomes large while the time step is independent of the fast oscillation in time, this scheme is able to provide a consistent semi-Lagrangian discretization of the guiding center model. In order to avoid 4-D interpolation, we apply a splitting scheme suited for strong magnetic field which is inspired by J. Ameres [1] but uses the semi-Lagrangian solver instead of a Fourier spectral discretization solver. Finally, we present some numerical simulations to validate the capabilities and limits of the methods under the Kelvin-Helmholtz instability test case.
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Dates et versions

hal-04016348 , version 1 (06-03-2023)
hal-04016348 , version 2 (08-12-2023)

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  • HAL Id : hal-04016348 , version 2

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Anh-Tuan Vu, Michel Mehrenberger. Semi-Lagrangian Vlasov-Poisson solvers with a strong external uniform magnetic field. 2023. ⟨hal-04016348v2⟩
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