Conservative and non-conservative methods based on Hermite Weighted Essentially Non Oscillatory reconstruction for Vlasov equations.

Chang Yang (1) , Francis Filbet (2, 3)

1 ICJ - Institut Camille Jordan
2 MMCS - Modélisation mathématique, calcul scientifique
3 KALiFFE - Kinetic models AppLIed for Future of Fusion Energy

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]

Chang Yang, Francis Filbet. Conservative and non-conservative methods based on Hermite Weighted Essentially Non Oscillatory reconstruction for Vlasov equations.. Journal of Computational Physics, 2014, 279, pp.18-36. ⟨hal-00918077⟩