Abstract:

On the basis of simulating the phase field method of dendritic growth, this work combined the multi-relaxation format of lattice Boltzmann method of the phase field method, established the phase field-lattice dynamic coupling model, and numerically simulated the microstructure of dendrite growth occurred in the process of polymer crystallization. This coupling model circumvented difficulties of traditional phase field method that needed resolve solid liquid interface accurately in high resolution which would severely impact the option of time steps. Using lattice Boltzmann method (LBM), this work came up the adaptive time stepping, that allowed changing time step expect sizing grid correspondingly, in other words, time step can be large, however, the results of numerical simulation will not emerge the phenomenon of dispersion, avoid the using of high precision differential formats. Using FORTRAN to accomplish the coupling model's establishment and simulating the crystallization of isotactic polystyrene, this work researched the crystallization of isotactic polystyrene at different experimental temperature, and compared the simulated results with the reality experimental results, to determine the feasibility of the coupling model.

摘要：

在模拟枝晶生长的相场方法上，耦合多松弛格式的格子Boltzmann方法，建立了相场-格子动力学耦合模型，对聚合物结晶过程中出现的枝晶生长形貌进行了数值模拟。耦合模型规避了传统相场法需要高分辨率场精确解决固液界面的难点，其中高精确的解析度会严重影响时间步长的选取。运用LBM方法，提出了一种自适应的时间步长计算方法，允许在改变时间步长的同时不需要相应地改变网格大小，时间步长允许设置得较大而数值模拟结果不会出现发散现象，也避免了高精度差分格式的使用。使用FORTRAN语言对相场-格子动力学耦合模型进行了求解，通过对聚合物等规聚苯乙烯结晶的数值模拟，研究了在不同实验温度下等规聚苯乙烯晶体的数值模拟形貌，并与实验结果进行了比较，验证了模型的有效性。