Computational methods for a phase-field model of grain growth kinetics

Abstract

An apriori understanding of micro structures and its linkage to material properties is possible through the use of workable models. In this thesis, we explore a variety of computational algorithms for solving partial differential equations that govern the kinetics of grain growth. To start with, we employ the emerging phase-field approach to model the micro structural evolutions. In the model we have to design the appropriate energy functional. Then, solve the Allen-Cahn equations or the Complex Ginzhburg Landau equations (CGLE).Following computational schemes are devised for the phase-field equations: (i) Solve the equations by Finite difference method with a simple explicit time marching scheme. (ii) Solve the Allen-Cahn equations using operator splitting method, where the equation is divided into a Poisson part and a cubic equation. (iii) A simple observation that only the interfaces have more than one active phase-field variables at every grid point was successfully exploited by devising AIA-PT approach.