A quasi-conservative dynamical low-rank algorithm for the Vlasov equation

TL;DR

This paper introduces a quasi-conservative low-rank numerical algorithm for the Vlasov equation that improves mass and momentum conservation over existing low-rank methods, enhancing long-term simulation accuracy.

Contribution

The paper presents a novel low-rank algorithm that conserves mass and momentum locally and globally for the Vlasov equation, addressing limitations of previous methods.

Findings

The new algorithm demonstrates improved conservation properties in numerical simulations.

Numerical results show enhanced accuracy over long time integrations.

The method is computationally efficient compared to traditional Eulerian solvers.

Abstract

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.