Computation of Complex Solidification Morphologies Using a Phase-Field Model

摘要

An anisotropic phase-field model is used to calculate numerically thesolidification patterns of a pure material into an undercooled liquid in a two-dimensional rectangular region. In the phase-field approach, the solid-liquid interface is treated as diffuse, and a dynamic equation for the phase variable is introduced in addition to the equation for heat flow. The phase-field model equations are solved using finite-difference techniques on a uniform mesh. Calculations for dendritic growth are presented for both four-fold and six-fold anisotropy, and the effect of the level of anisotropy on the growth of a dendrite is investigated. A previous study has shown that performing computations with an interface that is sufficiently thin for the numerical solution to accurately represent a sharp interface model is computationally demanding. However, even with a relatively thick interface, the computations using the phase-field model show many of the qualitative features of dendritic growth, and the method is well suited for handling the evolution of very complex, realistic interface shapes.