the mathematical model was used to simulate the distribution regular of the temperature field during the vacuum arc remelting (VAR) process, and it was also investigated how the regular of crystallizer cooling intensity, melting temperature, and melting rate affected the shape of the melt pool, grain growth, and grain distribution during the microstructure of the solidification in the VAR process. The findings demonstrate that when the melting temperature increasing, the melt pool's depth increasing, the width of the mushy zone decreases, its form changes from bowl-shaped to V-shaped, the average grain radius increasing, and the proportion of columnar crystals increases. The average grain size increases with increasing crystallizer cooling intensity, and these effects are also reflected in the depth of the melt pool and the width of the mushy zone, which decrease with increasing melt pool cooling intensity. When the melting rate increases, the width of the mushy zone and the depth of the melt pool increase, the temperature gradient of the melt pool decreases sharply, the average grain size decreases, and the proportion of equiaxed crystals increases.

The phase field model is established for the eutectic growth system in this paper, and the finite difference method is used to solve the model. The evolution of tilted eutectic interface morphology under isothermal solidification and directional solidification conditions, respectively, was investigated. The effects of solid-solid interface anisotropy, solid-liquid interface anisotropy, eutectic spacing and pulling speed on the evolution of the tilted eutectic structure were simulated to reveal the growth mechanism of the tilted eutectic structure. It is found that under isotropic and directional solidification conditions, eutectic growth is influenced by both of the direction of heat flow and the solid-liquid interface anisotropy. When the solid-solid interface anisotropy is small, the direction of heat flow dominates the growth direction of eutectic structure, and as the solid-solid interface anisotropy increases, the growth direction of eutectic structure starts to tilt. Two kinds of instability phenomena, bifurcation or merger and fault line, are also found in the eutectic growth.