中文摘要：

元胞自动机（cellular automaton,CA）方法能够有效地描述凝固过程中显微组织形貌的复杂演化过程,且计算效率较高,展现出良好的实际应用潜力.近20年来,CA模型取得了很大的进展.本文简要综述几种模拟凝固组织的CA模型,包括纯扩散和对流作用下的枝晶生长、共晶凝固、多元合金中的热力学和动力学耦合、枝晶耦合凝固气孔的生长、以及多尺度的耦合模拟.最后,对今后CA模型的发展提出作者的几点思考.

英文摘要：

Microstructure evolution during solidification is a complex process controlled by the interplay of heat, solute, capillary, thermodynamics and kinetics. Computational modeling can provide detailed information about the interactions between transport phenomena and phase transformation. Thus, it has emerged as an important and indispensable tool in studying the underlying physics of microstructural formation in solidification. During the last two decades, extensive efforts have been dedicated to explore the numerical models based on the methods of phase field（PF）, cellular automaton（CA）, front tracking（FT）, and level set（LS）, for the simulation of solidification microstructures. The CA approach can reproduce various realistic microstructure features with an acceptable computational efficiency, indicating the considerable potential for practical applications. It has, therefore, drawn great interest in academia and achieved remarkable advances in the simulation of microstructures. This paper gives an overview of CA based models, spanning from the meso-scale to the micro-scale, for the prediction of microstructure evolution during alloy solidification. The governing equations and numerical algorithms of CA based models and derived coupling models are summarized, including the calculations of nucleation, growth kinetics, interface curvature, surface tension anisotropy and crystallographic orientation, thermal and solutal transport, melt convection utilizing the lattice Boltzmann method（LBM）, the coupling of CA with control volume（CV） method, the coupling of CA with CALPHAD approach for multi-component alloy systems, as well as the approaches for eliminating the artificial anisotropy caused by the CA square cells. The main achievements in this field are addressed by presenting examples encompassing a wide variety of problems involving dendritic growth in pure diffusion and with melt convection, eutectic solidification, microstructure formation in multi-component alloys, dendritic growth with gas