To understand the dendrite formation during solidification phase-field model has become a powerful numerical method of simulating crystal growth in recent years. Two phase-field models due to Wheeler et al. and Karma et al., respectively, have been employed for modeling the dendrite growth worldwidely. The comparison of the two models was performed. Then using the adaptive finite element method, both models were solved to simulate a free dendrite growing from highly undercooled melts of nickel at various undercoolings. The simulated results showed that the discrepancy between the two phase-field models is negligible. Careful comparison of the phase-filed simulations with LKT(BCT) theory and experimental data were carried out, which demonstrated that the phase-field models are able to quantitatively simulate the dendrite growth of nickel at low undercoolings, however, at undercoolings above ten percent of the melting point (around 180K), the simulated velocities by Wheeler and Karma model as well as the analytical predictions overestimated the reported experiment results.
