Conservative and non-conservative methods based on Hermite Weighted Essentially Non Oscillatory reconstruction for Vlasov equations.
Résumé
We introduce a WENO reconstruction based on Hermite interpolation both for semi-Lagrangian and finite difference methods. This WENO reconstruction technique allows to control spurious oscillations. We develop third and fifth order methods and apply them to non-conservative semi-Lagrangian schemes and conservative finite difference methods. Our numerical results will be compared to the usual semi-Lagrangian method with cubic spline reconstruction and the classical fifth order WENO finite difference scheme. These reconstructions are observed to be less dissipative than the usual weighted essentially non- oscillatory procedure. We apply these methods to transport equations in the context of plasma physics and the numerical simulation of turbulence phenomena.
Domaines
Analyse numérique [math.NA]
Origine : Fichiers produits par l'(les) auteur(s)
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