中文摘要：

基于自适应有限元方法,通过求解表征纯物质相场模型的非线性抛物型方程,研究镍过冷熔体中不同起伏情况下单个完整等轴枝晶的演化过程.模拟结果表明：采用自适应有限元方法求解相场模型时结果更接近真实物理模型,在计算终止时整个计算域节点数仅为2.79×10^5个,远小于采用相同网格间距普通方法的1.6×10^6个,较大不同计算域对枝晶尖端速度的平衡值影响不大;随着起伏强度的增大,枝晶尖端获得更高的温度梯度,等温线波动更大,一次枝晶臂表面失稳,二次枝晶臂向过冷溶液中凸起的趋势越强,二次枝晶臂越发达.

英文摘要：

Based on adaptive finite element method, the pure substance phase-field model characterized by the non-linear parabolic partial differential equations were solved. A single complete isometric crystal evolution process in nickel supercooled melt was investigated under different fluctuation intensity. The simulation result showed that the phase field model employing adaptive finite element method was closer to the actual physical model. The number of system grid nodes were just 2. 79 ×10^5, which was far less than 1.6 ×10^6 when the common method was used. When the computation domain was larger enough, the domain size had little influence on the dendrite tip speed. With the increase of fluctuation intensity, the dendrite tips would obtain a higher temperature gradient that made the surface of primary crystalline arms lose and isothermal curves would fluctuate dramatically surface stability and the secondary arms become developed, protruding into the suppercooled melt.