A Sharp Computational Method for the Simulation of the Solidification of Binary Alloys

We present a numerical method for the simulation of binary alloys. We make use of the level-set method to capture the evolution of the solidification front and of an adaptive mesh refinement framework based on non-graded quadtree grids to efficiently capture the multiscale nature of the alloys' concentration profile. In addition, our approach is based on a sharp treatment of the boundary conditions at the solidification front. We apply this algorithm to the solidification of an Ni-Cu alloy and report results that agree quantitatively with theoretical analyses. We also apply this algorithm to show that solidification mechanism maps predicting growth regimes as a function of tip velocities and thermal gradients can be accurately computed with this method; these include the important transitions from planar to cellular to dendritic regimes.