Linear versus nonlinear approaches for the stability analysis of aluminium production cells

The modelling of magnetohydrodynamics (MHD) phenomena in aluminium electrolysis cells is a challenging problem. The basic equations are the MHD equations in parabolic form, for two immiscible fluids. Among the various nonlinearities in the model, one is due to the moving interface between the two fluids. The basic question that numerical simulations contribute to solve is the study of the stability of the cell. In previous works, we have developed and implemented a fully nonlinear approach to solve the two-fluid MHD system. On the other hand, many approaches rely on a simplified version of the equations, and linear stability analysis. The present study compares and discusses the results obtained in the two approaches