Behavior analyses of two-phase Stefan problems with anisotropy modeled by the stochastic phase field model

The purpose of this paper is to study a Stefan problem with anisotropy under a random disturbance. The Stefan problem is a typical example of a free boundary problem. Some mathematical models of the Stefan problem have been proposed in the past, which are generally classified into a Stefan type and a phase field one. The classical Stefan model ignores some of basic physical phenomena such as supercooling, superheating and surface tension, so we adopt the phase field model, which can include such basic physical phenomena and anisotropy in the model. In this paper, taking consideration of the influence of the random fluctuation of the temperature on the crystal growth, we propose the stochastic phase field model. And the crystal growth processes in the Stefan problem are numerically analyzed using the proposed stochastic phase field model.