Approximation numérique des écoulements turbulents dans des cuves d'électrolyse de l'aluminium

Aluminium is a metal extracted from bauxite ore using electrolysis process in cells of big size. A huge electric current goes in the cell through an electrolytic bath and aluminium liquid. These currents generate strong magnetic forces that allow the bath and the aluminium to move. A good knowledge of these turbulent flows is very important to optimize the process. The purpose of this thesis is to study and simulate turbulent flows in the aluminium smelting process. These flows are solved numerically with a finite element method. In particular, the Navier-Stokes equations for bifluid flows with free moving interface are solved numerically. In the first part of this work, we develop some mixing-length models that take into account the effects of the wall. A theoretical mathematical study shows the validity of these models and we give some recommendation on the choice of the parameters of the computation. In the second part we study the resolution of the Navier-Stokes equations. The study focuses on algorithms that decouple the computation of the speed and pressure, commonly called projection method or Chorin-Temam algorithm. The final section provides answers on the relevance of wall modelling and projection methods in numerical simulation of turbulent flows in the aluminium smelting process. In particular, we obtain a numerical model that produces a realistic flow with a reasonable CPU time and we discuss the choice of certain parameters involved in the different models.