High resolution finite volume method for kinetic equations with Poisson brackets

Simulation of plasmas in electromagnetic fields requires numerical solution of a kinetic equation that describes the time evolution of the particle distribution function. In this paper we propose a finite volume scheme based on integral relation for Poisson brackets to solve the Liouville equation, the most fundamental kinetic equation. The proposed scheme conserves the number of particles, maintains the total-variation-diminishing (TVD) property, and provides high-quality numerical results. Other types of kinetic equations may be also formulated in terms of Poisson brackets and solved with the proposed method including the transport equations describing the acceleration and propagation of Solar Energetic Particles (SEPs), which is of practical importance, since the high energy SEPs produce radiation hazards. The proposed scheme is demonstrated to be accurate and efficient, which makes it applicable to global simulation systems analyzing space weather. (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by-nc -nd /4 .0/).

Automated summary

In this paper, a finite volume scheme based on integral relation for Poisson brackets is proposed to solve the Liouville equation, which conserves the number of particles, maintains the total-variation-diminishing (TVD) property, and provides high-quality numerical results. The proposed scheme can be used to solve other types of kinetic equations, including the transport equations describing the acceleration and propagation of Solar Energetic Particles (SEPs), which is of practical importance due to radiation hazards. The scheme is demonstrated to be accurate and efficient, making it applicable to global simulation systems analyzing space weather.