A split-step Active Flux method for the Vlasov-Poisson system
Abstract
Active Flux is a modified Finite Volume method that evolves additional Degrees of Freedom for each cell that are located on the interface by a non-conservative method to compute high-order approximations to the numerical fluxes through the respective interface to evolve the cell-average in a conservative way. In this paper, 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 1D1V phase-space compare the properties of the various methods.
Cite
@article{arxiv.2412.06525,
title = {A split-step Active Flux method for the Vlasov-Poisson system},
author = {Lukas Hensel and Gudrun Grünwald and Katharina Kormann and Rainer Grauer},
journal= {arXiv preprint arXiv:2412.06525},
year = {2024}
}