Modeling and simulation of the industrial production of aluminium : the nonlinear approach

Jean-Frédéric Gerbeau (1) , Tony Lelièvre (2, 3) , Claude Le Bris (2, 3)

1 BANG - Nonlinear Analysis for Biology and Geophysical flows
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
3 MICMAC - Methods and engineering of multiscale computing from atom to continuum

We report on the numerical simulation of the industrial production of aluminium. The motion of the two nonmiscible conducting fluids is modeled through the incompressible Navier-Stokes equations coupled with the (parabolic) Maxwell equations. Stabilized finite elements techniques and an arbitrary Lagrangian Eulerian formulation (for the motion of the interface separating the two-fluids) are used in the numerical simulation. The industrial problem and the modeling strategy are presented in details. An outline of the numerical analysis of the problem, with a special emphasis on conservation and stability properties is provided. Examples of numerical simulations of the industrial case are eventually presented.

Domaines: Analyse numérique [math.NA]

Jean-Frédéric Gerbeau, Tony Lelièvre, Claude Le Bris. Modeling and simulation of the industrial production of aluminium : the nonlinear approach. Computers and Fluids, 2004, 33 (5-6), pp.801-814. ⟨10.1016/j.compfluid.2003.06.013⟩. ⟨hal-00695952⟩