Computational Treatment of Interface Dynamics via Phase-Field Modeling

This chapter describes the phase-field approach to modeling interface dynamics, with particular emphasis on the mathematical formulation and computational aspects. We describe to approaches to derive a phase-field model. The first one can be understood as a regularization approach: We start with a sharp interface model which is later replaced by a diffuse interface. The second approach starts with a free energy functional and balance laws for mass, linear momentum and energy; the final governing equations are derived using the second law of thermodynamics and the Coleman-Noll procedure. We finish by illustrating how the phase-field method can be used to solve problems on complicated geometries using cartesian grids only. Some of the opportunities opened by the phase-field approach are illustrated with numerical simulations.