A Numerical procedure for solving 2D phase-field model problems

We present a general 2D phase-field model, but without anisotropy, applied to freezing into a supercooled melt of pure nickel. The complete numerical procedure and details of assigning the numerical parameters are provided; convergence of the numerical method is demonstrated by conducting grid function convergence tests. The physics of solidification problems such as conditions for nucleation and crystal growth rate are discussed theoretically and shown to display at least qualitative agreement numerically. In particular, comparison of the computed critical radius with the theoretical one and the consistency of the computational dendrite structure for different Stefan numbers, the relationship between the growth rate and the Stefan number, etc., with the theoretical and experimental evidence indicate that phase-field models are able to capture the physics of supercooled solidification.