A level set approach to simulate magnetohydrodynamic instabilities in aluminum reduction cells

Magnetohydrodynamic instabilities at the metal-bath interface in aluminum reduction cells is an important and not fully understood topic. To simulate the two-fluid three-dimensional unstationary flow subject to a background magnetic field, a level set approach is proposed. It features a formulation in terms of the magnetic vector potential to avoid a numerical growth of the divergence of the magnetic field. The same exact projection scheme (with staggered grids) is used for both the velocity field and the magnetic vector potential. Test simulations show that the overall method behaves well in purely hydrodynamic as well as in fully magnetohydrodynamic regimes, in both cases with a single fluid and with two fluids. We also simulate with our technique the metal pad roll instability and trace the behavior of coupled interfacial modes.