A New Approach to Numerical Simulation of Melt Flows and Interface Instability in Hall-Héroult Cells

A new approach to numerical analysis of magnetohydrodynamic phenomena in aluminum reduction cells is proposed. The flows of aluminum and cryolite, as well as the instability of the interface between the two layers, are described using a nonlinear two-dimensional model based on the shallow-water approximation. There are two principal distinctive properties of our model. First, the background melt flow and instability are considered as coupled fully nonlinear parts of one nonsteady process. Second, while capturing the main physical mechanisms operating in the system, the model is computationally very efficient and allows simulations in a "real-time" regime.