Virtual front tracking model for the quantitative modeling of dendritic growth in solidification of alloys

A computationally efficient quantitative virtual front tracking model for the two-dimensional simulation of dendritic growth in the low Peclet number regime is developed. The kinetics of dendritic growth is driven by the difference between the local equilibrium composition, calculated from the local temperature and curvature, and the local actual liquid composition, obtained by solving the solutal transport equation. The dynamics of dendrite growth from the initial unstable stage to the steady-state stage is accurately described. Side branching develops without the need to introduce local noise. The model adopts the previously proposed solutions for the evaluation of local curvature and interface capturing rules with a virtual interface tracking scheme, which make the model virtually mesh-independent. To decrease the computational time, dendrite growth is calculated directly from fraction solid, eliminating the need to first calculate the growth velocity. Extensive model analysis and validation are presented.