This paper reviews methods and applications of the phase field technique, one of the fastest
growing areas in computational materials science. The phase field method is used as a …

Dendritic growth is one of the most common microstructures in metal and solution
solidification. The subject of dendritic growth has received much attention from both scientific …

In this paper we present a phase-field model to describe isothermal phase transitions
between ideal binary-alloy liquid and solid phases. Governing equations are developed for …

This book is about adaptive mesh generation and moving mesh methods for the numerical
solution of time-dependent partial differential equations. It presents a general framework and …

In an effort to unify the various phase-field models that have been used to study
solidification, we have developed a class of phase-field models for crystallization of a pure …

A simple level set method for solving Stefan problems is presented. This method can be
applied to problems involving dendritic solidification. Our method consists of an implicit finite …

A phase field model is used to numerically simulate the solidification of a pure material. We
employ it to compute growth into an undercooled liquid for a one-dimensional spherically …

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 …

We present a front-tracking method to simulate time dependent two-dimensional dendritic
solidification of pure substances. The method is based on a finite difference approximation …

This research work presents an experimental and numerical study of the coupled thermo-
hydro-mechanical (THM) processes that occur during soil freezing. With focusing on the …