Mathematical and Computational Aspects of Solidification of Pure Substances

The aim of the article is to deliver an information on the state of the art in the field of modelling of microstructure growth in a solidifying pure substance with a stress on the phase-field approach. We briefly summarize the physical background of the problem. The phase-field method is then explained and its variants are mentioned. Justification and theoretical results concerning the model equations are necessary for a quantitatively correct use of the model. We give some examples of qualitative computational studies and introduce the reader into quantitative comparison techniques used for verification of the model.

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