An arbitrary Lagrangian-Eulerian finite element approach to non-steady state turbulent fluid flow with application to mould filling in casting

This paper presents a two-dimensional Lagrangian-Eulerian finite element ap proach of non-steady state turbulent fluid flows with free surfaces. The pr oposed model is based on a velocity-pressure finite element Navier-Stokes s olver, including an augmented Lagrangian technique and an iterative resolut ion of Uzawa type. Turbulent effects are taken into account with the k-epsi lon two-equation statistical model. Mesh updating is carried out through an arbitrary Lagrangian-Eulerian (ALE) method in order to describe properly t he free surface evolution. Three comparisons between experimental and numer ical results illustrate the efficiency of the method. The first one is turb ulent flow in an academic geometry, the second one is a mould filling in ef fective casting conditions and the third one is a precise confrontation to a water model. Copyright (C) 2000 John Wiley & Sons, Ltd.