Simulation of three-dimensional dendritic growth using H-adaptive finite element method

Based on the AFEPack adaptive software package, the H-adaptive finite element method was used to solve the three-dimensional phase field model on the Linux platform. The growth of the three-dimensional dendrites in the undercooling melt was simulated numerically, and the effects of different undercooling on three-dimensional dendritic growth were studied. The real growth process of three-dimensional dendritic was reproduced. The dendritic growth pattern that we obtained was consistent with the crystallization theory. In order to verify the reliability of the simulation results, the three-dimensional dendrite tip growth rate and the tip radius were compared with the classical theory and the same conditions under the literature value. The results are compared with those obtained by Jeong et al. and obtained by finite difference method under the same conditions. It is found that the results obtained by H-adaptive finite element method are in agreement with the calculated results obtained by these two methods. It is proved that the H-adaptive finite element method is feasible to simulate the growth of three-dimensional dendrites. The method greatly reduces the computational cost of the phase field model solution and improves the efficiency of the solution.