Influence of convection on crystalline pattern formation - improving diffuse-interface models and sharp-interface models via comparative studies

从液体到固体的相变是广泛的制造和自然过程的特征现象，其可以通过潜热的释放、溶质的排斥和凝固时的密度变化来驱动熔体中的对流。解决这一问题的一种方法是发展“范式问题”，试图分析关键的物理机制。在过去的几年里，尽管没有找到令人满意的解决方案，但受到极大关注的一个范例问题是对流对凝固枝晶形态的影响。处理这个问题的数值模拟可以基于尖锐界面或扩散界面模型，它们都显示出一定的不足。本研究项目的目标是通过将它们应用于与强制外部流存在下的树突选择机制相关的问题来交互地改进这两种模型类型。

The phase transformation from liquid to solid is a phenomenon characteristic of a wide range of manufacturing and natural processes, which can drive convection in the melt through release of latent heat, the rejection of solute and the change of density upon solidification. One approach to this issue is to develop "paradigm problems" which attempt to analyse key phyical mechanisms. A paradigm problem which has received great attention albeit a satisfying solution has not been found over the last years is that of the influence of convection on a solidifying dendritic morphology. Numerical simulations dealing with this problem can be based on either sharp-interface or diffuse-interface models, both of them displaying certain deficiencies. The goal of this research project is to improve both model types interactively by applying them to questions connected with the selection-mechanism of dendrites in the presence of a forced external flow.