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一种广泛的制造过程和自然过程所特有的现象，它可以通过释放潜热、排斥溶质和凝固时密度的变化来驱动熔体中的对流。解决这个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。对流对凝固枝晶形态的影响是近年来备受关注的一个范式问题，但尚未找到令人满意的解决方案。处理这一问题的数值模拟既可以基于锐界面模型，也可以基于扩散界面模型，但这两种模型都存在一定的缺陷。本研究项目的目标是通过将这两种模型应用于与树突选择机制有关的问题，从而交互式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.