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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