Accurate Implementation of Rotating Magneto-Hydrodynamics in a Channel Geometry Using an Influence Matrix Method

We numerically study wall-bounded convectively driven magneto-hydrodynamic (MHD) flows subject to rotation in a Cartesian periodic channel. For the accurate treatment of the rotating MHD equations, we develop a pseudo-spectral simulation code with accurate treatment of boundary conditions for both velocity and magnetic fields. The solenoidal condition on the magnetic field is enforced by the addition of a fictitious magnetic pressure. This allows us to employ an influence matrix method with tau correction for the treatment of velocity and magnetic fields subject to Robin boundary conditions at the confining walls. We validate the developed method for the specific case of no slip velocity and perfectly conducting magnetic boundary conditions. The validation includes the accurate reproduction of linear stability thresholds and of turbulent statistics. The code shows favorable parallel scaling properties.