Numerical modeling of the solidification process of a metastable melt

The paper presents the model of the solidification process of a metastable melt based on the time-dependent Landau-Ginzburg equation and the equation of energy conservation (the phase-field model). The thermodynamical consistence of the model and it applicability to describe the solidification process are discussed. The comparison of exact solutions of Stefan problem of the planar-front solidification process with numerical solutions of the phase-field model obtained using the adaptive grid technique is performed. Numerical results of the steady-state solidification process of the undercooled melt are analyzed.