A comprehensive three-dimensional (3D) stochastic model for simulating the evolution of
dendritic crystals during the solidification of binary alloys was developed. The
multi-scale model takes into account all the length scales (e.g., macro, micro- and
meso-scales) required to accurately predict the evolution of dendritic morphologies during
solidification of alloys. The model includes time-dependent computations for temperature
distribution, solute redistribution in the liquid and solid phases, curvature, and growth
anisotropy. Stochastic models previously developed for simulating dendritic grains in 2D
were modified to control the nucleation and growth of dendrites in 3D. 3D mesoscopic
computations at the dendrite tip length scale were performed to simulate the evolution of
columnar and equiaxed dendritic morphologies including segregation patterns and compared
then with predictions based on 2D mesoscopic computations.