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

A review surveying the developments in the application of the phase-field method in the
study of phase transitions and microstructure evolution in multi-component systems is …

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 …

A new diffuse interface model for a two-phase flow of two incompressible fluids with different
densities is introduced using methods from rational continuum mechanics. The model fulfills …

The Cahn–Hilliard equation involves fourth-order spatial derivatives. Finite element
solutions are not common because primal variational formulations of fourth-order operators …

A good choice of model formulation and model parameters is one of the most important and
difficult aspects in mesoscale modeling and requires a systematic and quantitative analysis …

This book aims to introduce students and scientists to the programming of the phase-field
method. The codes provided in the book will serve as a foundation and template for …

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

In this paper, we describe the derivation of a model for the simulation of phase
transformations in multicomponent real alloys starting from a grand-potential functional. We …