Three-Dimensional MHD on Cubed-Sphere Grids: Parallel Solution-Adaptive Simulation Framework

and scalable cubed-sphere grid framework is described for simulation of magnetohydrodynamic (MHD) space-physics ows in domains between two concentric spheres. The unique feature of the proposed formulation compared to existing cubed-sphere codes lies in the design of a cubed-sphere framework that is based on a genuine and consistent multi-block implementation, leading to ux calculations, adaptivity, implicit solves, and parallelism that are fully transparent to the boundaries between the six grid root blocks that correspond to the six sectors of the cubed-sphere grid. Crucial elements of the proposed approach that facilitate this exible design are: an unstructured connectivity of the six root blocks of the grid, multi-dimensional k-exact reconstruction that automatically takes into account information from neighbouring cells, and adaptive division of the six root blocks into smaller blocks of varying resolution that are all treated exactly equally for ghost cell information transfers, ux calculations, adaptivity, implicit solves and parallel distribution. The approach requires signicant initial investment in developing a general and sophisticated adaptive multi-block implementation, with the added complexity of unstructured root-block connectivity, but once this infrastructure is in place, a simulation framework that is uniformly accurate and easily scalable can be developed naturally, since blocks that are adjacent to sector boundaries or sector corners are not treated specially in any way. The general design principles of the adaptive multi-block approach are described and, in particular, how they are used in the implementation of the cubed-sphere framework. The nite-volume discretization, parallelization, and implicit solves are also described. The adaptive mesh renement (AMR) algorithm uses an upwind spatial discretization procedure in conjunction with limited linear solution reconstruction and Riemann-solver based ux functions to solve the governing equations on multi-block