ALE method for solidification modelling Original Research Article

In this paper an arbitrary Lagrangian–Eulerian (ALE) formulation has been developed for the simulation of casting processes. The method is applied both to mould filling simulation, where it can provide accurate free surface description, and to the study of thermo-mechanical phenomena occurring in the subsequent cooling down of cast parts: prediction of solute transport and of distortions and stresses. In the first three sections, all governing equations (constitutive equations, momentum, energy, solute transport) are given. Then the ALE formulation is presented: mesh updating with evolving free surfaces, using “conservative” normal vectors to enforce mass conservation; treatment of advection terms, using an original nodal upwind method; definition of Lagrangian and Eulerian–Lagrangian regions. Finally, examples of applications are given.