A s one of the most important solidification patterns, eutectic microstructure has been recognized for its significant influence on the ultimate mechanical properties of the materials [1,2] . Since the classical mathematical analysis for the steady-state growth of eutectic alloy was presented by Jackson and Hunt [3] , theoretical studies on eutectic solidification have attracted increasing attention.However, the influence of convection on eutectic growth still lacks sufficient research. Generally, there are two main types of convection considered during the directional solidification of eutectic alloys, i.e., forced convection caused by imposed external fields, and natural convection driven by the solute (or density) difference. Considering that there are many uncertainties in experiments, numerical simulation has become an indispensable way to accurately recover the underlying physics during solidification [4][5][6][7] . Wang et al. [8] performed a Monte-Carlo simulation of eutectic growth with weak convection and found that convection made Abstract: In the present study, the influence of natural convection on the lamellar eutectic growth is determined by a phase-field-lattice Boltzmann study for Al-Cu eutectic alloy. The mass difference resulting from concentration difference led to the fluid flow, and a robust parallel and adaptive mesh refinement algorithm was employed to improve the computational efficiency without any compromising accuracy. Results show that the existence of natural convection would affect the growth undercooling and thus control the interface shape by adjusting the lamellar width. In particular, by alternating the magnitude of the solute expansion coefficient, the strength of the natural convection is changed. Corresponding microstructure patterns are discussed and compared with those under no-convection conditions. the distribution of lamellar spacing more scattered. But beyond that, to the best of our knowledge, there has been no more numerical case to study the effect of convection on eutectic growth. Encouragingly, a robust parallel-adaptive mesh refinement algorithm (Para-AMR) has been developed to efficiently solve the phase field equations including the dendritic [9] and eutectic transitions [10] . The lattice Boltzmann method (LBM) has also emerged with great potential to numerically solve the energy, momentum and mass transport problems by a relaxation to a local equilibrium [11][12][13] . Therefore, it seems reasonable to couple the LBM into eutectic phase-field models to retrieve the interaction of eutectic microstructure and flows.In this work, we coupled the LBM into the developed Para-AMR algorithm to reveal the effect of natural convection on eutectic growth. The phase field model was employed to simulate eutectic evolution while the LBM was for the simultaneous calculation of melt convection. The velocity field near the solid/liquid (S/ L) interface was explored and several key mechanisms were highlighted. In particular, by alternating the magnitude of solute expansion coe...