Vlasiator is a new massively parallel hybrid-Vlasov simulation code being developed at the Finnish Meteorological Institute with the purpose of building new global magnetospheric model going beyond magnetohydrodynamics (MHD). It solves Vlasov's equation for the ion distribution function in the full six-dimensional phase space and describes the electrons as a massless charge neutralising fluid using the MHD equations, thus including ion kinetic effects.
The Vlasov equation solver is based on a second-order, three-dimensional finite volume wave-propagation algorithm, making use of Strang splitting to separate translation in space from acceleration in velocity space. The electromagnetic fields are obtained through a second-order, finite volume upwind constrained transport method which conserves the divergence of the magnetic by construction.
This work presents the numerical and physical validation tests developed and/or run by the author for Vlasiator, without however covering the technical aspects pertaining to implementation or parallelisation. The numerical quality of the solvers is being assessed for their isotropy, their conservation of div B = 0 and their order of accuracy in space and time. The physical validation tests include an assessment of the diffusive properties of the Vlasov solver, a brief discussion of results obtained from the Riemann problem displaying kinetic effects in the shock solution and finally dispersion plots for quasiperpendicular and quasiparallel wave modes are presented and
discussed.
The conclusions are that Vlasiator performs well and in line with the expected characteristics of the methods implemented, provided the resolution is good enough. In space, ion kinetic scales should be resolved for kinetic effects going beyond an MHD description to emerge. In velocity space the resolution should yield a smooth discretisation of the ion distribution function, otherwise spurious non-physical artefacts can crop up in the results. The higher-order correction terms included in the solvers ensure good orders of accuracy even for discontinuous solutions, the conservation of div B = 0 is provided up to floating-point accuracy and dispersion plots match remarkably well analytic solutions.
