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, emphasizing the thermomechanical simulation package REM3D®, which was initially developed for modeling Stokes’ flow in polymer injection. The solver employs a Eulerian velocity-pressure formulation, utilizing P1/P1 tetrahedral elements for spatial discretization. Additionally, a front tracking module resolves a transport equation through a space-time discontinuous Galerkin formulation, enabling mesh adaptation for dynamic refinement at the fluid front, thereby controlling numerical diffusion. Specific adaptations for treating Navier-Stokes flow are discussed, with a detailed explanation of the inertia treatment and the implementation of sliding conditions at the mold surface using conservative normals. The methodology addresses the complexity of simulating non-steady state three-dimensional flows in the mold filling stage of casting processes, highlighting the limitations of conventional VOF methods that are commonly used in existing software. The paper concludes with an overview of industrial applications demonstrating the solver’s capabilities.