Numerical Investigation of Crystallization Process in One Phase-Field Model

The results of a numerical study of the crystallization of melts in the framework of the mesoscopic theory are given in the article. This model is based on the system of Plotnikov equations with the initial condition of Showalter–Sidorov and the boundary condition of Robin. This model describes the interaction of the phase field, temperature field and time. The physical meaning of the model is the restoration of the relationship between the phase field, the temperature field and time. The results, obtained in article, can be used for modeling and forecasting the process of crystallization and for the development of the automatic control system of technological processes of continuous casting machines. Based on the theoretical results, an algorithm for the numerical solution of the problem has been developed, the result of the computational experiment has been developed, and the graphs have been constructed to analyze the crystallization of the melt at a certain time and describe the parameters, characterizing the process. The changes in the parameters of a given model are investigated with the help of mathematical modeling methods.