Description
To study near-Earth plasma environments without assuming a given velocity distribution function, kinetic models are required. Vlasiator [1] is a 6D hybrid-Vlasov solver which treats ions kinetically using a semi-Lagrangian method [2], while electrons are modeled as a charge-neutralizing fluid, enabling global simulations of the interaction between the solar wind and the Earth’s magnetosphere.
Solving the evolution of a six-dimensional distribution function over such a large domain with the required accuracy would require excessive computational resources. Vlasiator addresses this challenge by using a sparse velocity space grid to reduce the computational cost by up to 98%, together with spatial mesh refinement [1]. Initially, the mesh refinement was static and based on predefined regions of interest (e.g. the magnetopause and magnetotail); however, it has recently evolved towards an adaptive mesh refinement (AMR) strategy that targets regions with strong dimensionless spatial gradients and magnetic reconnection sites [3].
One of the next major developments for Vlasiator is the implementation of a velocity-space AMR. This enhancement aims to further reduce computational costs while accurately capturing filamentation of the velocity distribution function, which plays a key role in plasma instabilities [4]. We present the possible refinement strategy and discuss its associated technical challenges.
[1] U. Ganse et al., « Enabling technology for global 3D + 3V hybrid-Vlasov simulations of near-Earth space », PoP, 2023.
[2] M. Zerroukat and T. Allen, « A three-dimensional monotone and conservative semi-Lagrangian scheme (SLICE-3D) for transport problems», Q. J. R. Meteorol. Soc., 2012.
[3] L. Kotipalo et al., « Physics-motivated cell-octree adaptive mesh refinement in the Vlasiator 5.3 global hybrid-Vlasov code », Geosci. Model Dev., 2024.
[4] M. Antoine et al., « Embedded grid refinement for Semi-Lagrangian parallelized relativistic Vlasov-Maxwell solver », PoP, 2025.