中文摘要：

基于高性能计算特性的自适应有限元方法,较大尺度地求解三维相场模型,定量模拟纯物质三维枝晶的凝固过程,研究过冷度、各向异性系数等相场参数对三维枝晶的影响.结果表明：过冷度和各向异性系数越大,三维枝晶生长速度越大,侧向分枝越发达,二次枝晶间距越小,并得到与结晶理论相一致的枝晶生长规律.此外,在CPU耗费时间上自适应有限元方法比均匀网格方法降低一个数量级,并且当系统尺寸越大时越能体现出自适应有限元方法的优越性,为大尺度多场耦合相场模型的模拟提供便利.

英文摘要：

On the basis of adaptive finite element method with high-performance computing feature, the three-dimensional phase-field model with larger scale is solved, the solidification process of the dendrite growth of pure material is simulated quantitatively, and the influence of the phase-field parameters such as supercooling degree and anisotropy coefficient on the growth of three-dimensional dendrite is investigated. The results showed that the greater the supercooling degree and anisotropy coefficient were, the greater the rate of three-dimensional dendrite growth would be, the more the side-branching was developed, the smaller the arm spacing of secondary dendrite would be, and thus the dendrite growth pattern is obtained, which is consistent with the crystailine theory. In addition, the adaptive finite element method can be used to reduce CPU time consuming by one order of magnitude when compared with uniform grid approach, and the larger the system size was, the better the superiority of adaptive finite element method would be manifested, offering convenience for simulating the dendrite growth phase-field model coupled with multi-field in large-scale domain.