Cellular automata-lattice Boltzmann simulation of multi-dendrite motion under convection based on dynamic grid technology

Abstract

A cellular automata-lattice Boltzmann coupling model with dynamic grids for simulating the preferential growth and movement of multiple dendrites under convection of binary alloy melt. In this model, dendritic growth is computed using the cellular automata method, and flow of the melt is computed using the lattice Boltzmann method, and the motion of the dendrite is described by solving the equation of motion. To deal with the motion of the dendrite, each dendrite is given a local dynamic grid, which can move with the motion of the dendrite. The correctness of this model in dealing with the motion of solids in fluids by simulating the settlement of a cylinder in a vertical channel. Then, dendrites of three different preferred growth directions grow under pure diffusion are simulated to prove that the model can also solve the grid dependence of dendritic growth in the Cartesian grid. Finally, this model is used to stimulate the growth of a single dendrite under Couette flow, and the settlement of multiple dendrites under gravity, and the growing motion of multiple dendrites under Poiseuille flow. The simulation results show that the dendritic morphology can be well maintained when this model is used to deal with dendritic movement, and the melt convection and motion will promote the dendritic growth in the direction of motion.