Validation Test Cases for Multi-Physic Problems: Application to Magneto-Hydrodynamic Numerical Simulations

The present paper is concerned with the numerical simulation of magneto-hydrodynamic (MHD) problems with industrial tools. MHD has received attention some thirty to twenty years ago as a possible alternative in propulsion applications; MHD propelled ships have even been designed to that purpose. However such propulsion systems have been proved of low efficiency and fundamental researches in the area have progressively received much less attention over the past decades. Numerical simulation of MHD problem could however provide interesting solutions in the field of turbulent flow control. The development of recent efficient numerical techniques for multi-physic applications provide promising tool for the engineer for that purpose. In the present paper, some elementary test cases in laminar flow with magnetic forcing terms are analyzed; equations of the coupled problem are exposed and analytical solutions are derived in each case, highlighting the relevant non-dimensional number which drives the physics of the problem. Several analytical calculations are then proposed and discussed. The present work will serve as basis for validation of numerical tools (based on the finite element method) for academic as well as industrial application purposes.