It is well known that the fluid and interface motion due to electromagnetic forces have a huge impact on the stability and productivity of aluminum cells.

In order to improve the design of existing cells and to create more efficient ones, numerical simulations of those phenomena can be very useful, allowing to study many configurations at lower cost. On the other hand, due to extreme conditions surronding the cells (temperature, current, magnetic field, bath corrosivity), direct observations and in situ measurements are particularly difficult to achieve.

Within the chair, several models have been developed to address and reproduce the magnetohydrodynamic instabilities (MHD) :

**Dynamical approach**: one solution is to simulate the full dynamics of the fluids by solving the multifluid Navier-Stokes equations, coupled to the Maxwell equations for electrical current and magnetic induction. Our model can also take into account the ferromagnetic screen effect due to the metallic structure in which the cells are are built.The following animation illustrates the time evolution of the interface between the fluids in an unstable configuration for a realistic cell.

**Linear approach**: Another approach consist in the linearization of the equations that describe the cell evolution around a stationary solution, in order to obtain a new problem for the perturbations of this solution as unknowns. Assuming an exponential behaviour over time for the perturbations leads to the resolution an eigenvalue problem. This approach has been introduced by Jean Descloux, Michel Flück and Michel Romerio and allows to make a parallel between the cell stability and the position of eigenvalues in the complex plane. The more negative the imaginary of eigenvalues, the more unstable the cell is.