Development of a parallel multi-scale model of dendritic growth coupling the FEM (Finite Element Method) and CAPTN (Cellular Automaton Parabolic Thick Needles) ; Modélisation multi-échelle parallélisée pour la prédiction de structures de grains dendritiques couplant les éléments finis, un automate cellulaire et un réseau de paraboles

Multiscale modelling of solidification processes is of great interest for industries. However coupling the multiple scale phenomena to reach quantitative large simulations is challenging. This is achieved using a combination of three methods : the Finite Element (FE), the Cellular Automaton (CA) and the Parabolic Thick Needle (PTN). The FE method provides a solution of the conservation equations, written for volume average quantities, that is suitable for large domain size computations. It serves for macroscopic description of heat and mass transfers. Additionally, the CA method tracks the development of the envelope of each individual dendritic grain at a mesoscopic scale. The coupling of these two methods is the CAFE model and was demonstrated to provide efficient and quantitative simulations of the columnar-to-equiaxed transition for instance. The Dendritic Needle Network (DNN) is another mesoscopic method recently introduced. It uses solute mass balance considerations in the vicinity of the tip of the dendrites to compute accurately the growth kinetics. Because it relies on adirect estimation of the composition gradient at the solid-liquid interface, steady state growth regime is no longer assumed. We introduce the Parabolic Thick Needle (PTN) method inspired from the DNN’s computed growth idea for one dendritetip. Its implementation with a FE method to solve the solute flow is extensively validated against analytical results given by the Ivantsov solution. Coupling CAFE with PTN computed growth kinetics provides a unique solidification model. The CA grid handles both the shape of the grain envelopes and branching mechanisms. The FE mesh is used to solve flux and conservation of mass and energy at both the scale of the dendrite tip solute layer and the domain dimensions. It is possible thanks to adaptive remeshing strategies. Various simulations demonstrate the capabilities of the model. The improvement areas are being developed in order to hope, in the long term, for 3D simulation laboratory experiments. ...