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Pré-Publication, Document De Travail Année : 2022

Multiscale numerical schemes for the collisional Vlasov equation in the finite Larmor radius approximation regime

Schéma numérique mutli-échelles pour l'équation de Vlasov avec collisions dans le régime d'approximation du rayon de Larmor fini

Résumé

This work is devoted to the construction of multiscale numerical schemes efficient in the finite Larmor radius approximation of the collisional Vlasov equation. Following the paper of Bostan and Finot (2019), the system involves two different regimes, a highly oscillatory and a dissipative regimes, whose asymptotic limits do not commute. In this work, we consider a Particle-In-Cell discretization of the collisional Vlasov system which enables to deal with the multiscale characteristics equations. Different multiscale time integrators are then constructed and analysed. We prove asymptotic properties of these schemes in the highly oscillatory regime and in the collisional regime. In particular, the asymptotic preserving property towards the modified equilibrium of the averaged collision operator is recovered. Numerical experiments are then shown to illustrate the properties of the numerical schemes.
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Dates et versions

hal-03690427 , version 1 (08-06-2022)
hal-03690427 , version 2 (13-12-2023)

Identifiants

  • HAL Id : hal-03690427 , version 1

Citer

Anaïs Crestetto, Nicolas Crouseilles, Damien Prel. Multiscale numerical schemes for the collisional Vlasov equation in the finite Larmor radius approximation regime. 2022. ⟨hal-03690427v1⟩
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