Abstract: Simulation technologies for material microstructure evolution at the mesoscale are crucial for understanding the relationship between material microstructures and properties, and have become a prominent research direction in the fields of material processing and property studies. When metallic materials undergo processes such as casting, additive manufacturing, and welding, convection significantly influences the transformation of microstructures, such as dendrites and eutectics. Therefore, it is essential to consider multiphase nucleation and growth under convection in solidification microstructure simulations. This paper extends the solidification phase-field simulation capabilities of Phase Lab software by developing multi-parameter phase-field equations. The Navier-Stokes (N-S) equation is incorporated to describe the evolution of the flow field, and the governing equations for the flow and phase-field are coupled, enabling the simulation of solidification microstructure evolution under convection. Furthermore, by utilizing stochastic nucleation theory, the spontaneous multiphase, multi-site nucleation process during solidification is described, successfully simulating complex solidification processes. The model has been successfully applied to simulate typical phenomena, including homogeneous nucleation and dendritic growth of alloys under supercooling, the lamellar eutectic formation resulting from two-solid-phase competitive growth, and the movement of the solid phase in flow.

Key words: phase field, flow field, numerical simulation