High Resolution Finite Volume Method for Kinetic Equations with Poisson Brackets

TL;DR

This paper introduces a high-resolution finite volume method based on Poisson brackets for solving the Liouville equation in plasma physics, ensuring conservation and stability for accurate space weather simulations.

Contribution

The paper presents a novel finite volume scheme utilizing integral Poisson brackets for kinetic equations, enhancing accuracy and conservation in plasma simulations.

Findings

Scheme conserves particle number and is TVD

Provides high-quality numerical results

Applicable to space weather modeling

Abstract

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.