Conservative averaging-reconstruction techniques (Ring Average) for 3-D finite-volume MHD solvers with axis singularity.

Abstract In cylindrical/spherical geometries, MHD solvers using explicit finite-volume methods face restrictive time steps imposed by the CFL condition due to the clustering of cells in the azimuthal direction near the pole/axis. We use a conservative averaging-reconstruction method (Ring Average) on structured cylindrical/spherical mesh to remove this severe time step restriction for multi-dimensional curvilinear finite-volume MHD solvers. The Ring Average technique is implemented as a post-processing step and thus requires no changes to the existing data structure, grid definition or numerical methods in the original MHD solver. This paper describes the Ring Average algorithm and presents simulation results using field loop advection and MHD blast waves in cylindrical/spherical geometries for validation. The algorithm is shown to be inexpensive and easily implemented in existing curvilinear finite-volume MHD solvers. Highlights • Ring Average is a "post-processing" module without modifying the original solver. • Ring Average relaxes time-step restrictions in MHD solvers with axis singularities. • Ring Average conserves mass, momentum and energy for proper shock propagations. • Ring Average works for codes with either divergence cleaning or constrained transport. [ABSTRACT FROM AUTHOR]