Numerical analysis of two partitioned methods for uncoupling evolutionary MHD flows

Magnetohydrodynamics (MHD) studies the dynamics of electrically conducting fluids, involving Navier-Stokes (NSE) equations in fluid dynamics and Maxwell equations in eletromagnetism. The physical processes of fluid flows and electricity and magnetism are quite different and numerical simulations of each subprocess can require different meshes, time steps, and methods. In most terrestrial applications, MHD flows occur at low-magnetic Reynold numbers. We introduce two partitioned methods to solve evolutionary MHD equations in such cases. The methods we study allow us at each time step to call NSE and Maxwell codes separately, each possibly optimized for the subproblem's respective physics. Complete error analysis and computational tests supporting the theory are given.