Stability of partitioned methods for magnetohydrodynamics flows at small magnetic Reynolds number

MHD flows are governed by the Navier-Stokes equations coupled with the Maxwell equations. Broadly, MHD flows in astrophysics occur at large magnetic Reynolds numbers while those in terrestrial applications, such as liquid metals, occur at small magnetic Reynolds numbers, the case considered herein. The physical processes of fluid flows and electricity and magnetism are quite different and numerical simulations of non-model problems can require different meshes, time steps and methods. We introduce implicit-explicit (IMEX) methods where the MHD equations can be evolved in time by calls to the NSE and Maxwell codes, each possibly optimized for the subproblem’s respective physics.