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Simulation of plasmas in electromagnetic fields requires numerical solutionof a kinetic equation that describes the time evolution of the particledistribution function. In this paper we propose a finite volume scheme based onintegral relation for Poisson brackets to solve the Liouville equation, themost fundamental kinetic equation. The proposed scheme conserves the number ofparticles, maintains the total-variation-diminishing (TVD) property, andprovides high-quality numerical results. Other types of kinetic equations maybe also formulated in terms of Poisson brackets and solved with the proposedmethod including the transport equations describing the acceleration andpropagation of Solar Energetic Particles (SEPs), which is of practicalimportance, since the high energy SEPs produce radiation hazards. The proposedscheme is demonstrated to be accurate and efficient, which makes it applicableto global simulation systems analyzing space weather.

High Resolution Finite Volume Method for Kinetic Equations with Poisson Brackets