**Yu Bai, Yingming Wang, Shijie Zhang, Qi Wang and Ri Li \***

Simulation Laboratory, School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300132, China; 201721803007@stu.hebut.edu.cn (Y.B.); 201731804057@stu.hebut.edu.cn (Y.W.); 201821803012@stu.hebut.edu.cn (S.Z.); 201831804007@stu.hebut.edu.cn (Q.W.)

**\*** Correspondence: sdzllr@163.com

Received: 27 December 2019; Accepted: 25 January 2020; Published: 27 January 2020

**Abstract:** In this paper, a new method is proposed to solve the solute field of moving grains, and a Cellular automaton (CA)-Lattice Boltzmann method (LBM)-Semi rebound format(Ladd) coupling model which can accurately simulate the motion behavior of multiple dendrites is established. The growth process of microstructure in the solidification process of Al-4.7% Cu alloy ingot was calculated by Cellular automaton (CA) method, the momentum, heat, and mass transfer processes were calculated by Lattice Boltzmann method (LBM), and the melt-dendrite sharp interface interaction was treated by Ladd method. The reliability of the model is verified, and then the growth and movement of single dendrite and multiple dendrites under the action of gravity field are simulated. The simulation results show that the growth and movement mode of multiple dendrites are quite different from that of single dendrite, which is shown in two aspects: (1) the original motion state of dendrites is changed by the combination of flow field, which slows down the falling speed of dendrites to a certain extent; (2) the fusion of solute field between dendrites changed the original growth mode of boundary dendrites and increased their rotation speed.

**Keywords:** multi-dendrite motion; CA-LBM model; dendritic growth; natural convection; numerical simulation
