Mesoscopic modeling of columnar solidification and comparisons with phase-field simulations

We use two complementary modeling approaches for the simulation of columnar growth in directional solidification of organic alloys: a phase field model and a mesoscopic envelope model of dendritic growth. While the phase-field method captures the details of the dendritic structure and of the growth dynamics, the mesoscopic model approximates the complex dendritic morphology by its envelope. The envelope growth is deduced from the velocities of the dendrite tips, calculated by an analytical LGK-type tip model that is matched to the temperature and concentration fields in the stagnant film around the envelope. The computational cost of the mesoscopic model is several orders of magnitude lower and can bridge the gap between phase-field and macroscopic models. We demonstrate the applicability of the mesoscopic model to columnar growth and we discuss in particular its capabilities to predict the primary dendrite arm spacing.