论文标题
对相位场方法的树突固化和数值分析的建模，以建模合金中的复杂形态
Modeling of dendritic solidification and numerical analysis of the phase-field approach to model complex morphologies in alloys
论文作者
论文摘要
树突是自然界中最广泛观察到的模式之一，并且发生在各种物理现象中。在金属和晶体中的凝固和生长模式中，树突的多级分支结构构成了建模挑战，并且对这些结构的全面分辨率在计算上是要求的。在文献中，树突形成和进化的理论模型本质上是因为存在经典移动边界史蒂芬问题的扩展。这种理解的大部分来自对金属合金固化过程中发生的树突的分析。通过在MAM期间纯金属和合金液体进行微结构进化的问题的激励，我们开发了一个全面的数值框架，用于对与金属固化相关的各种树突结构进行建模。在这项工作中，我们提出了一个数值框架，其中包含使用相位场方法和有限元方法实现的Stefan问题制定与树突发展相关的建模。使用此框架，我们对许多与纯熔体和二元合金的凝固在物理上相关的复杂树突形态进行了建模。这项工作的区别是 - 对纯属和合金的统一处理；树突状尖端速度的新型数值误差估计；与数值离散化有关的原始温度场和顺序参数的误差的收敛性。据我们所知，这是对有限元方法设置中树突状生长相相位方程数的数值收敛的首个研究。此外，我们对2D和3D计算域中的各种物理相关的树突固化模式进行了建模。
Dendrites are one of the most widely observed patterns in nature and occur across a wide spectrum of physical phenomena. In solidification and growth patterns in metals and crystals, the multi-level branching structures of dendrites pose a modeling challenge, and a full resolution of these structures is computationally demanding. In the literature, theoretical models of dendritic formation and evolution, essentially as extensions of the classical moving boundary Stefan problem exist. Much of this understanding is from the analysis of dendrites occurring during the solidification of metallic alloys. Motivated by the problem of modeling microstructure evolution from liquid melts of pure metals and alloys during MAM, we developed a comprehensive numerical framework for modeling a large variety of dendritic structures that are relevant to metal solidification. In this work, we present a numerical framework encompassing the modeling of Stefan problem formulations relevant to dendritic evolution using a phase-field approach and a finite element method implementation. Using this framework, we model numerous complex dendritic morphologies that are physically relevant to the solidification of pure melts and binary alloys. The distinguishing aspects of this work are - a unified treatment of both pure metals and alloys; novel numerical error estimates of dendritic tip velocity; and the convergence of error for the primal fields of temperature and the order parameter with respect to numerical discretization. To the best of our knowledge, this is a first-of-its-kind study of numerical convergence of the phase-field equations of dendritic growth in a finite element method setting. Further, we modeled various types of physically relevant dendritic solidification patterns in 2D and 3D computational domains.
