Phase-field Simulation For Ternary Dendritic Growth Using Adaptive Finite Element Method

The phase-field model as a method of quantitatively simulating solidification mi-crostructures emerged in recent years. Since the solidification process involves differentphysical scales ranging from 10?9m to 10?3 m,the numerical simulation for the phasefield model is extraordinary time consuming, greatly limiting its application in practice.So how to reduce the capacity of computation and memory and extend it to solve highdimensional models comes into being the main problem.Based on the construction of a reliable,efficient algorithm -adaptive finite ele-ment method(AFEM)-for solving the phase-field equations,the crystal growth in theundercooled melts is quantitatively simulated. And the main factors such as undercool-ing,anisotropy of interfacial energy and kinetics have been discussed thoroughly. Themain research results in this thesis reads as follows:1) Based on the entropy function, a nonisothermal phase field model for alloyswith multiple phases and components is derived.2) AFEM methods are employed to simulate the dendritic growth of the ternaryCu-Ni-Cr alloys.3) The in?uence of anisotropy of interfacial energy and kinetics, surfacial energy,undercooling temperature and the initial nuclei on the dendritic growth are studied.