Numerical modeling of the magnetic field generation in a precessing cube with a conducting melt

Precession driven flow is one of the possible causes for the magnetic field generation in planets. However, recreation of the magnetic field generation in a spherical laboratory model is problematic due to weak coupling between the vessel shell and the fluid. Therefore, it is proposed to use a cube as a vessel because it has a stronger coupling. In this work, generation of the magnetic field in a rotating precessing cube of 1 m size with ferromagnetic walls is numerically modeled. The Navier-Stokes for laminar flow and Maxwell equations were solved, and the EM field influence on the flow was discarded. An artificially high kinematic viscosity value was chosen for the melt. The rotation parameters of the cube corresponded to Re = 200, 500, 1000 flow regime. The electrical conductivity σ of the melt was chosen so that the ratio between the Reynolds number and the magnetic Reynolds number was equal to unity. The melt flow and the EM field equations were solved using the OpenFOAM open source program library.