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

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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.