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

Abstract

This paper presents a two‐dimensional Lagrangian–Eulerian finite element approach of non‐steady state turbulent fluid flows with free surfaces. The proposed model is based on a velocity–pressure finite element Navier–Stokes solver, including an augmented Lagrangian technique and an iterative resolution of Uzawa type. Turbulent effects are taken into account with the k–ε two‐equation statistical model. Mesh updating is carried out through an arbitrary Lagrangian–Eulerian (ALE) method in order to describe properly the free surface evolution. Three comparisons between experimental and numerical results illustrate the efficiency of the method. The first one is turbulent flow in an academic geometry, the second one is a mould filling in effective casting conditions and the third one is a precise confrontation to a water model. Copyright © 2000 John Wiley & Sons, Ltd.

Free Surface and Buoyancy Driven Flows

“…These methods are generally complex to implement and we shall give further description of these methods later [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. Such methods are known as ALE methods.…”

Numerical simulation of three dimensional non-Newtonian free surface flows in injection molding using ALE finite element method

“…The ALE method was originally developed in the finite difference context by Hirt et al [18], the subsequent applications in the finite element context were done by Belytschko et al [19], Hughes et al [20] and Huerta et al [21], and the review paper has been presented by Donea et al [23]. As deemed to be a promising approach to handle the free surface problem, the ALE method has been applied to the simulation of liquid bridge [24], tank sloshing [25], broken dam [26] and mold filling [15,27].…”

“…Consequently mesh regeneration is inevitably required to maintain the mesh quality. As shown in the literatures [15,[24][25][26][27], global remeshing strategy is usually adopted for the mesh regeneration for moving free surface flow problems. However, the global remeshing strategy is computationally expensive and time-consuming especially for the three dimensional case, which also introduces the errors due to the re-interpolations between the two meshes associated with the two successive time steps.…”

Model of Flow Over Rippled Bed Using Arbitrary Lagrangian Eulerian Approach With Mapping Technique

“…The standard k-ε turbulence model was used to calculate the eddy viscosity time. Gaston and Camara [10] presented a two-dimensional Lagrangian-Eulerian finite element approach for non-steady state turbulent fluid flows with free surfaces. Lo and Young [11] described the application of velocity-vorticity formulation of the Navier-Stokes equations for twodimensional free surface flow using an arbitrary Lagrangian-Eulerian method.…”