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A simulation of the motion of molten aluminium inside an electrolytic cell is presented. Since the driving term of the aluminium motion is the Lorentz (j × B) body force acting within the fluid,this problem involves the solution of the magneto‐hydro‐dynamic equations. Different solver modules for the magnetic field computation and for the fluid motion simulation are coupled together. The interactions of all these are presented and discussed.

In this paper, a hybrid formulation for solving time harmonic eddy current problems in terms of magnetic field h is considered. In particular, we discuss some properties of the implicit boundary condition on the discrete level and the computation of the integral operator exploited in this context. An iterative technique is confirmed to be efficient in solving the arising, partly dense, complex linear system of equations. Furthermore, some test results, including timings for linear solvers are presented.

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.