基于自适应有限元枝晶自由生长相场模型模拟

Simulation of dendrite free growth with phase-field model based on adaptive finite element method

利用相场模型模拟了过冷熔体中单个完整等轴枝晶在凝固过程中的生长和形貌演化,采用自适应有限元方法求解相场模型的控制方程,研究了在计算域较大、界面层厚度较薄的情况下各向异性和过冷度等物理参数对枝晶形状和生长的影响.结果表明:过冷度越大,枝晶间竞争越激烈,生长速度越慢;各向异性系数越大,枝晶沿选定方向生长的趋势越强,生长速度越快,二次枝晶间距越小,侧向分枝越发达.与有限差分方法(FDM)相比,采用自适应有限元法(AFM)在CPU计算时间和存储空间均降低了一个数量级,并且系统尺寸越大,自适应有限元法优势越明显,便于更大尺度多场耦合相场模型的数值模拟.通过比较均匀网格法和以往的晶体生长数值模拟实验,证明了自适应有限元法的准确性、高效性和鲁棒性.

Phase-field model is used to simulate the growth and morphological evolution of single intact equiaxed dendrite during its solidification in supercooled melt,the governing equations of the phase-field model are solved with adaptive finite element method,and the influence of physical parameters such as anisotropy and supercooling degree on the dendrite shape and growth under condition of larger computational domain and less interfacial layer thickness.The result shows that a competition will occur more intensively among the dendrites and their growth speed will be less when the supercooling degree is greater.However,the greater the anisotropy coefficient is,the stronger the dendrite growth tendency along a chosen direction will be,the faster the growth speed will be,the less the secondary dendrite spacing will be,and the more developed the lateral branch will be.Compared with the finite difference method(FDM),the adaptive finite element method(AFM)will reduce CPU time and storage space by one order of magnitude,and the larger the system size is,the more obvious the superiority of adaptive finite element method will be,which will facilitate the numeric simulation of greater dimensional and multi-field coupled phase field.By means of comparing to FDM and previous numerical simulation of crystal growth,the AFM is proved to be accurate,efficient and robust.