▪ Abstract The phase-field method has recently emerged as a powerful computational
approach to modeling and predicting mesoscale morphological and microstructure evolution …

This is the first account of the history of our understanding of, and ability to model,
solidification microstructures. Its objective is to retrace the scientific steps made, from the …

Additive manufacturing (AM) processes are receiving widespread attention due to the ability
to create or repair precision engineering components without use of any die or mold …

We report the results of quantitative phase-field simulations of the dendritic crystallization of
a pure melt in two and three dimensions. These simulations exploit a recently developed …

We present a phase-field model (PFM) for solidification in binary alloys, which is found from
the phase-field model for a pure material by direct comparison of the variables for a pure …

The phase-field method has become an important and extremely versatile technique for
simulating microstructure evolution at the mesoscale. Thanks to the diffuse-interface …

A phase-field formulation is introduced to simulate quantitatively microstructural pattern
formation in alloys. The thin-interface limit of this formulation yields a much less stringent …

We present a detailed derivation and thin interface analysis of a phase-field model that can
accurately simulate microstructural pattern formation for low-speed directional solidification …

A novel diffuse interface model is presented for the direct numerical simulation of
microstructure evolution in solidification processes involving convection in the liquid phase …

A comprehensive model is developed for solving the heat and solute diffusion equations
during solidification that avoids tracking the liquid—solid interface. The bulk liquid and solid …