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Publikationen

Lukas Hensel, Gudrun Grünwald, Katharina Kormann, Rainer Grauer


A split-step Active Flux method for the Vlasov-Poisson system


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.

J. Comp. Phys. 540 (2025) 114294 https://doi.org/10.1016/j.jcp.2025.114294 https://doi.org/10.1016/j.jcp.2025.114294 https://arxiv.org/abs/2412.06525

G. Grünwald, L. Hensel, M. Deisenhofer, S. Lautenbach, K. Kormann, R. Grauer


Solving the six-dimensional Vlasov–Maxwell System with Active Flux and Splitting Methods


Active Flux (AF) is a modified Finite Volume method that evolves additional Degrees of Freedom (DoF) located on the cell interfaces to compute high-order approximations to the numerical fluxes through the respective interface. We present an AF-based scheme for the simulation of collisionless plasmas described by the Vlasov equation coupled with Maxwell’s equations. In order to limit the DoF in high dimensional settings we employ operator splitting. The resulting one-dimensional advection equations can be solved efficiently and with low implementation complexity, making it a very fast alternative to standard Finite Volume methods. We compare our scheme’s performance with a related finite-volume method based on the semi-Lagrangian approach. We find that, as a consequence of its compact stencil, the AF scheme has significantly lower dissipation and reduced anisotropy, and thus produces results on par with or even superior to the benchmark for standard test cases reproducing important kinetic phenomena, while also offering lower computational cost.

submitted (2025) https://arxiv.org/abs/2511.22440