Improvements to 6D Grid Optimisation in Vlasiator

Vlasiator is a global hybrid-Vlasov space plasma simulation, modeling the velocity distribution of ions in a large region of near-Earth space. Due to the high memory and computation demands of the kinetic method as well as the large physical scale, optimisations are required to make simulation feasible. This presentation explores optimisations used in the spatial and velocity grids.

We first consider the spatial dimension. For this, Vlasiator utilises cell-based octree adaptive mesh refinement (AMR). Essentially, each spatial cell may be split in all three spatial dimensions to create eight smaller children in order to improve simulation accuracy in relevant regions. This can be repeated if necessary, with runs typically using four levels of refinement. Refinement may be done statically at the start of the simulation, or dynamically based on the plasma parameters.

Vlasiator uses a combination of several parameters for dynamic runtime refinement. These include scaled gradients of macroscopic variables to detect steep changes, the ratio of the current density to perpendicular magnetic field for current sheets and reconnection, as well as pressure anisotropy and vorticity for foreshock refinement.

For the velocity grid we use a somewhat similar method of stretching. In order to simplify translation, the velocity grid is static and identical in each spatial cell. To eliminate splitting of acceleration pencils, the size of cells in each coordinate direction is a function of that coordinate. Thus if we consider a grid with higher resolution around some point, the grid appears stretched along the coordinate axes when moving away from that point. The main purpose of the stretched grid is to enable modeling of colder distributions requiring a higher resolution without increasing resolution for the entire velocity grid.

Combining these optimisations enables simulation on modern supercomputers with scale and resolution which would be unfeasible without them. This is achieved by limiting resources expended on regions where they are less critical for simulation accuracy and the scientific focus of a given run, while allowing higher fidelity in more important regions. These methods are applicable to other kinetic simulations, as well as grid-based simulations in general.