Finite element analysis of interfacial instability in aluminium reduction cells in a uniform, vertical magnetic field

In this paper the interfacial instability in aluminium reduction cells under a uniform, vertical magnetic field is investigated by means of numerical simulation. Shallow-water equations governing the wave motion and the electric field at the interface between two electrically conducting fluids are discretized using a finite element scheme which employs quadratic interpolation functions. For a sufficiently high magnetic field, it is observed that one global maximum and one global minimum of the interface elevation are formed in closed symmetrical and asymmetrical domains irrespective of shape. By taking account of this, an asymptotic expression for the evaluation of the growth rate and the frequency of instability is constructed. The effectiveness of the proposed model is validated through comparison with the numerical results.