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

This chapter surveys recent numerical advances in the phase field method for geometric
surface evolution and related geometric nonlinear partial differential equations (PDEs) …

This comprehensive and self-contained, one-stop source discusses phase-field
methodology in a fundamental way, explaining advanced numerical techniques for solving …

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

How to develop efficient numerical schemes while preserving energy stability at the discrete
level is challenging for the three-component Cahn–Hilliard phase-field model. In this paper …

We report the results of an extensive phase-field study of the growth competition of columnar
dendritic grains in two dimensions. We investigate the influence of the temperature gradient …

A general formulation of phase-field models for nonisothermal solidification in
multicomponent and multiphase alloy systems is derived from an entropy functional in a …

Hot tearing in castings is closely related to the difficulty of bridging or coalescence of
dendrite arms during the last stage of solidification. The details of the process determine the …

A phase-field model that allows for quantitative simulations of low-speed eutectic and
peritectic solidification under typical experimental conditions is developed. Its cornerstone is …

This paper describes a phase field method for the optimization of multimaterial structural
topology with a generalized Cahn–Hilliard model. Similar to the well-known simple isotropic …