Finite element solution of three-dimensional turbulent flows applied to mold-filling problems

This paper presents a finite element solution algorithm for three-dimension al isothermal turbulent flows for mold-filling applications. The problems o f interest present unusual challenges for both the physical modelling and t he solution algorithm. High-Reynolds number transient turbulent flows with free surfaces have to be computed on complex three-dimensional geometries. In this work, a segregated algorithm is used to solve the Navier-Stokes, tu rbulence and front-tracking equations. The streamline-upwind/ Petrov-Galerk in method is used to obtain stable solutions to convection-dominated proble ms. Turbulence is modelled using either a one-equation turbulence model or the k-epsilon two-equation model with wall functions. Turbulence equations are solved for the natural logarithm of the turbulence variables. The chang e of dependent variables allows for a robust solution algorithm and good pr edictions even on coarse meshes. This is very important in the case of larg e three-dimensional applications for which highly refined meshes result in untreatable large numbers of elements. The position of the flow front in th e mold cavity is computed using a level set approach. Finally, equations ar e integrated in time using an implicit Euler scheme. The methodology presen ts the robustness and cost effectiveness needed to tackle complex industria l applications. Copyright (C) 2000 John Wiley & Sons, Ltd.