A 3D-Fem Solver for Non-Steady State Navier-Stokes Equations with Free Surface. Application to Mold Filling Simulation in Casting Processes

"The paper presents a 3D finite element solver for non-steady state fluid flow. The thermomechanical simulation package REM3D® has been initially developed to model Stokes' flow for polymer injection. The mechanical module is based on a Eulerian velocitypressure formulation. The spatial discretization uses P 1+IP1 tetrahedral elements. The front tracking module consists of the resolution of a transport equation, thanks to a space-time discontinuous Galerkin formulation. It includes mesh adaptation, which permits a dynamic refinement at the front, thus controling the numerical diffusion. The same approach is used to solve heat transfer. In this paper, we focus on the specific adaptations done to treat Navier Stokes flow. The treatment of inertia is detailed, as well as the implementation of sliding conditions at mould surface, using conservative normals. Industrial applications are presented.IntroductionThe study of the mould filling stage in casting processes requires the ability to simulate complex non steady-state three-dimensional flows. Most commercial software use the volume of fluid (VOF) method, associated with a Eulerian formulation, see for instance the series of conferences ""Modelling of Casting, Welding and Advanced Solidification Processes"" [1-3]. The VOF method [4] consists in solving the conservation equation dF / dt = 0 for a variable F - the volumic fraction of fluid - whose value is 1 in filled regions and 0 elsewhere. Two fluids are actually considered: the molten alloy and a gas in the empty regions. This method suffers generally from numerical diffusion in the resolution of the free surface tracking equation, which is of pure advective type. The precision of the computation is then strongly dependent on the mesh density. Since the mesh is fixed (Eulerian formulation) this implies that in case of complex flow the user must have a priori a fairly good idea of the flow characteristics in order to capture properly the critical features of the flow. In addition, the method can hardly handle the discontinuity of the material viscosity at the interface. To prevent this difficulty, the viscosity value is smoothed around the interfuce, adding once again some inaccuracy. Since the value F = ½ is supposed to represent the free surface, it results in a smeared fluid surface. An alternative to the fixed mesh methods are the methods in which the mesh covers the fluid domain only, as proposed by Navti and Lewis [5-6], or Gaston and Bellet [7]. Based on updated Lagrangian schemes, they must be associated with an ALE formulation (arbitrary LagrangianEulerian) in order to reduce the number of full remeshing operations."