Oberseminar Mathematical Fluid Dynamics - Gudrun Grünwald: "A split-step Active Flux method for the Vlasov-Poisson system"

Active Flux is a finite volume method that besides cell avaerages has additional degrees of freedom for each cell. These are point values located on the cell interface. The point values are updated by a high order non-conservative method. These are used to compute the numerical fluxes through the cell interface which allow to evolve the cell-average in a conservative way.

In this talk, we apply the method to the Vlasov-Poisson system describing the time evolution of the time-dependent distribution function of a collisionless plasma. In particular, we consider the evaluation of the flux integrals in higher dimensions. We propose a dimensional splitting and three types of formulations of the flux integral: a one-dimensional reconstruction of second order, a third-order reconstruction based on information along each dimension, and a third-order reconstruction based on a discrepancy formulation of the Active Flux method. Numerical results in 1 dim. - 1 velocity phase-space compare the properties of the various methods.

This is joint work with R. Grauer, L. Hensel and K. Kormann.

All information can be found in the announcement.