Reducing numerical diffusion in magnetospheric simulations

Physics‐based global magnetosphere modeling requires large computational resources. It is still impractical to resolve the computational domain to the point where numerical errors become negligible. One possible way of reducing numerical diffusion is the “Boris correction”: the semirelativistic magnetohydrodynamics equations are solved with an artificially reduced speed of light. Here we introduce a new alternative approach, an Implicit Scheme with Limited Numerical Dissipation (ISLND). The fully implicit time stepping provides stability, and the wave speeds are limited in the dissipative numerical fluxes only. This limiting only affects the numerical scheme, and it does not modify the equations being solved. This approach can be employed for most total variation diminishing schemes. The differences between the Boris and ISLND schemes are demonstrated in simple numerical tests. We also perform several simulations for two magnetic storms using the global magnetosphere, the ionosphere electrodynamics, and the inner magnetosphere models of the Space Weather Modeling Framework, and we compare the Boris scheme with the limited numerical dissipation method and also with the unmodified base scheme at various grid resolutions. We find that for these particular simulations the Boris scheme and the ISLND scheme produce comparable results, both being significantly less diffusive than the unmodified scheme.