Physics-motivated Cell-octree Adaptive Mesh Refinement in the Vlasiator 5.3 Global Hybrid-Vlasov Code

Automatically adaptive grid resolution is a common way of improving simulation accuracy while keeping the computational efficiency at a manageable level. In space physics adaptive grid strategies are especially useful as simulation volumes are extreme, while the most accurate physical description is based on electron dynamics and hence requires very small grid cells and time steps. Therefore, many past global simulations encompassing e.g. the near-Earth space have made tradeoffs in terms of the physical description and used laws of magnetohydrodynamics (MHD) that require less accurate grid resolutions. Recently, using supercomputers, it has become possible to model the near-Earth space domain with an ion-hybrid scheme going beyond the MHD-based fluid dynamics. These simulations, however, must develop a new adaptive mesh strategy beyond what is used in MHD simulations.

We developed an automatically adaptive grid refinement strategy for ion-hybrid Vlasov schemes, and implemented it within the Vlasiator global solar wind – magnetosphere – ionosphere simulation Vlasiator. This method automatically adapts the resolution of the Vlasiator grid using two indices: one formed as a maximum of dimensionless gradients measuring the rate of spatial change in selected variables, and the other derived from the ratio of the current density to the magnetic field density perpendicular to the current. Both these indices can be tuned independently to reach a desired level of refinement and computational load. We test the indices independently and compare the results to a control run using static refinement.

The results show that adaptive refinement highlights relevant regions of the simulation domain and keeps the computational effort at a manageable level. We find that the refinement shows some overhead in rate of cells solved per second. This overhead can be large compared to the control run without adaptive refinement, possibly due to resource utilisation, grid complexity and issues in load balancing. These issues lay a development roadmap for future optimisations.