Vlasov methods in space physics and astrophysics
Abstract 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.
Authors
- Markku Alho (ORCID: https://orcid.org/0000-0001-9762-6795)
- Joonas Nättilä (ORCID: https://orcid.org/0000-0002-3226-4575)
- Urs Ganse (ORCID: https://orcid.org/0000-0003-0872-1761)
- Minna Palmroth (ORCID: https://orcid.org/0000-0003-4857-1227)
- Hongyang Zhou (ORCID: https://orcid.org/0000-0003-4571-4501)
- Markus Battarbee (ORCID: https://orcid.org/0000-0001-7055-551X)
- Sanni Hoilijoki (ORCID: https://orcid.org/0000-0001-5709-2346)
- Leo Kotipalo (ORCID: https://orcid.org/0009-0001-5298-0747)
- Maxime Grandin (ORCID: https://orcid.org/0000-0002-6373-9756)
- A. Sandroos
- Lucile Turc (ORCID: https://orcid.org/0000-0002-7576-3251)
- Giulia Cozzani (ORCID: https://orcid.org/0000-0001-5515-1998)
- Sebastian von Alfthan
- Yann Pfau‐Kempf (ORCID: https://orcid.org/0000-0001-5793-7070)
- Konstantinos Papadakis (ORCID: https://orcid.org/0000-0002-3307-6015)
- Ivan Zaitsev (ORCID: https://orcid.org/0000-0002-0640-0123)
- Lauri Pänkäläinen (ORCID: https://orcid.org/0009-0003-1804-5952)
Institutions
- Boston University (US)
- Université d'Orléans (FR)
- Finnish Meteorological Institute (FI)
- Centre National de la Recherche Scientifique (FR)
- University of Helsinki (FI)
- CSC - IT Center for Science (Finland) (FI)
- Laboratoire de Physique et Chimie de l’Environnement et de l’Espace (FR)
- Cadence Design Systems (United States) (US)
Publication Details
- Journal
- Living Reviews in Computational Astrophysics
- Published
- 2025-11-14
- DOI
- https://doi.org/10.1007/s41115-025-00024-0
- Primary Topic
- Ionosphere and magnetosphere dynamics
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Helsingin Yliopisto
- European Commission
- Partnership for Advanced Computing in Europe AISBL
- China Scholarship Council
- Studium Loire Valley-Institute for Advanced Studies