Phase-field modelling of solidification microstructures

Phase-field models have become the most popular method for the numerical simulation of solidification microstructures. This is due to several reasons: (i) they are based on thermodynamic principles, which facilitate their application in metallurgy, (ii) they are numerically simple, and standard mathematical methods for the solution of partial differential equations can be employed, and (iii) they can be very accurate, which has been demonstrated by number of benchmark simulations. In order to be both accurate and efficient, the dynamics of the interfaces in the model has to be precisely controlled. This is achieved by the construction of the model, and demonstrated by matched asymptotic expansion methods. Here, some fundamentals of phase-field modelling will be introduced, and several examples of their application in the modelling of solidification microstructures will be reviewed.