Forward simulations for free boundary reconstruction in magnetic fluid dynamics

In many industrial applications of magnetic fluid dynamics it is important to control the motion of the surface of liquids. In aluminium electrolysis cells, large surface deformations of the molten aluminium are undesired, and it would be useful to have the possibility to recognize the surface deviation. This includes the problem of reconstructing a free boundary between the conducting fluids. We have investigated how the interface between two fluids of different conductivity assumed in a highly simplified model of an aluminium electrolysis cell could be reconstructed by means of external magnetic field measurements. Forward simulations of the magnetic field generated by the impressed current are done by applying the FEM software code FEMLAB. Several interface shapes which can be realized in experiments are investigated and a strategy for identifying the main interface characteristics using magnetic field measurements as an initial guess to the solution of the inverse problem is proposed.