Vlasov methods in space physics and astrophysics

This paper reviews Vlasov-based numerical methods used to model plasma in space physics and astrophysics. Plasma consists of collectively behaving charged particles that form the major part of baryonic matter in the Universe. Many physical concepts ranging from our own planetary environment to the Solar system and beyond can be understood in terms of kinetic plasma physics, represented by the Vlasov equation. We introduce the physical basis for the Vlasov systems, and then outline the associated numerical methods that are typically used. A particular application of the Vlasov system is Vlasiator, the world’s first global hybrid-Vlasov simulation for the Earth’s magnetic domain, the magnetosphere. We introduce the design strategies for Vlasiator and outline its numerical concepts ranging from solvers to coupling schemes. We review Vlasiator’s parallelisation methods and introduce the used high-performance computing (HPC) techniques. A short review of verification, validation, and physical results is included. The purpose of the paper is to present the Vlasov equation and its use in numerical modelling, introduce an example implementation, and to illustrate that even with massive computational challenges, an accurate description of physics is highly rewarding as it allows to significantly advance our understanding of complex plasma systems. As an update to the previous paper in this series, we especially highlight latest trends in HPC including graphics processing units (GPUs) and emerging applications in astrophysical plasmas.