Adaptive phase-field computations of dendritic crystal growth

Abstract

Phase-field models have been the subject of much interest in the last several years for the investigation of phase transitions with complicated morphology, such as dendritic growth. The phase-field method introduces a continuous transition between the two phases across a thin layer of finite thickness; the advantage of this approach is that the location of the interface does not have to be explicitly determined as part of the solution but is obtained from the solution of an additonal field equation representing the evolution of the phase-field variable over the entire domain. A brief overview is presented of the phase-field model development for a pure material using irreversible thermodynamics. The computational model includes four-fold anisotropy both in surface energy and interfacial kinetics. Numerical solutions are obtained using a general-purpose adaptive finite-difference algorithm. Adaptivity in space and time is found to extend somewhat the parameter regime where computations can be carried out. Good convergence to sharp-interface models is achieved for dimensionless undercoolings of 0.25, but a relatively small amount of solid phase grows before the thermal field is affected by the size of the computational domain. Further progress to smaller undercoolings will have to be aided by more sophisticated modeling.