Numerical modeling of dendrite growth in a steady magnetic field using the two relaxation times lattice Boltzmann-phase field model

A lattice Boltzmann-phase field coupled model is developed and utilized to investigate dendrite growth with melt convection in magnetic field. In this model, the two-relaxation-time scheme with D2Q9 vectors is extended to simulate the magnetofluid flow, the anisotropic scheme is developed to model dendrite growth of binary alloys, and the finite volume method is utilized to simulate the solute transport with anti-trapping current. After model validation, the growth of single dendrite and multi-dendrites of a binary alloy with magnetic field and melt flow are numerically investigated. The results show that the magnetic flow on dendrite growth cannot be ignored, the magnetic field can greatly change dendrite growth by affecting the flow field and then affecting solute transport. This work provides a numerical solution to reveal the internal mechanism of dendritic growth under external magnetic fields.