A quasi-conservative dynamical low-rank algorithm for the Vlasov equation
For researchers using low-rank methods for kinetic plasma simulations, this work provides a more conservative algorithm, though it is an incremental improvement over existing approaches.
The paper proposes a quasi-conservative dynamical low-rank algorithm for the Vlasov equation that improves mass and momentum conservation, addressing a key limitation of existing low-rank methods for intermediate and long time integration.
Numerical methods that approximate the solution of the Vlasov-Poisson equation by a low-rank representation have been considered recently. These methods can be extremely effective from a computational point of view, but contrary to most Eulerian Vlasov solvers, they do not conserve mass and momentum, neither globally nor in respecting the corresponding local conservation laws. This can be a significant limitation for intermediate and long time integration. In this paper we propose a numerical algorithm that overcomes some of these difficulties and demonstrate its utility by presenting numerical simulations.