Research in the crystal growth modeling and numerical simulation includes building physical and mathematical models of the physical phenomena, such as fluid flow, heat and mass transfer, stress field, dopant distribution and defect generation in the crystal growth process, and conducting numerical simulations. Reinforcement of the research in this field is an effective way to enhance the research level in the crystal growth field in our country and to minimize the lagging in the semiconductor materials behind the developed countries. The research group lead by Professor Qi-Sheng Chen in the institute of Mechanics of CAS developed a growth kinetics theory model for the growth of silicon carbide crystals by the physical vapor transport method, which was originally published in J. Crystal Growth 224(1-2): 101-110, 2001, and proposed that the growth rate of SiC is proportional to the supersaturation of the silicon carbide vapor species. The transport of SiC vapor species is dominated by the diffusion and the Stefan flow, which is caused by the expansion of the SiC from the solid phase to vapor phase. The vapor pressure drop of SiC species from the charge to seed overcomes the resistance by the advection and diffusion of the SiC species and the resistance in the Knudsen layer. Based on the growth theory, the research group conducted the modeling work in the 2-inch SiC crystal growth system, and modeled the magnetic field and temperature distribution in the whole system with complex geometry and many components. They investigated the vapor advection problems coupled with the crystal growth kinetics, and found that the heating frequency has great effects on the temperature field and growth rate. They predicted the growth rate and the crystal interface shape as a function of the vertical temperature gradient and the inert vapor pressure. By using the proposed kinetics theory of the SiC crystal growth, the group grew high quality 6H-SiC single crystal with 2-inch in diameter and 1-inch in height. Through the accurate computer simulation of the growth furnace and growth process, the group rapidly solved the technique problems occurred in the SiC growth process. The group also conducted modeling research on the growth process of GaN using the ammonothermal technique, and found that the baffle opening can affect the flow field oscillation and the temperature oscillation near the baffle. The conclusions can provide theoretical guidance to the crystal growth experimental research. A series of research papers on the crystal growth kinetics and modeling have been published by the group in the Journal of Crystal Growth, such as the ones in J. Crystal Growth 266(1-3): 320-326, 271-277, 2004.