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This review presents the development of quantitative phase-field models for simulating the formation processes of solidification microstructures, with particular attention to the theoretical foundation and progress in modeling. The symmetry of interpolating functions required to reproduce the free-boundary problem in the thin-interface limit and the necessity of antitrapping current in the diffusion equation are discussed. In addition, new cross-coupling in the phase-field equation for two-sided asymmetric diffusion is briefly described. Recent achievements of large-scale simulations using high-performance computing techniques are explained. Furthermore, some important applications of quantitative phase-field simulations such as investigations of cellular and dendritic growth, microsegregation, and peritectic reaction in carbon steel are discussed.
Munekazu Ohno (Tue,) studied this question.