Based on the theory of numerical simulation and fluid mechanics, the equations of solidification heat transfer are established

Momentum conservation equation:

Energy conservation equation:

Where u, V and W are the velocity components (M / s) of the velocity vector in the X, y and Z directions; ρ is the density of semi-solid alloy melt (3m / kg); t is the time (s); P is the instantaneous average pressure (MPA); t is the temperature (℃); μ is the kinematic viscosity (MPA · s); K is the thermal conductivity (w / m · K); GX, Gy, GZ are the acceleration of gravity (M / S2); CP is the specific heat capacity (J · kg-1 ·℃ – 1); FS is the solid rate (%); L is the latent heat (J). When the free surface moves, it can be tracked by volume function method

Where: F is the volume fraction of liquid phase. Based on the basic equations of fluid mechanics, it needs to be discretized, including boundary conditions and initial conditions, including initial temperature and velocity parameters, solid-liquid interface conditions, temperature boundary, liquid-gas and liquid-liquid interface, so as to obtain the unique solution.