The free boundary problem is one which finds both a value of a state and the boundary of a domain. This paper is concerned with analyses of the Stefan problem which is the typical example of a free boundary problem. A phase field model is used as a mathematical model of the Stefan problem. The phase field model can include supercooling, superheating, the influence of surface tension and anisotropy in the model.In this paper, the stochastic phase field model is proposed and the influence of the random fluctuation on the crystal growth is numerically analized using the proposed stochastic phase field model.
