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A lattice Boltzmann (LB)–cellular automaton (CA) model is employed to study the dendrite growth of Al-4.0 wt％Cu–1.0 wt％Mg alloy. The effects of melt convection, solute diffusion, interface curvature, and preferred growth orientation are incorporated into the coupled model by coupling the LB–CA model and the CALPHAD-based phase equilibrium solver, PanEngine. The dendrite growth with single and multiple initial seeds was numerically studied under the conditions of pure diffusion and melt convection. Effects of initial seed number and melt convection strength were characterized by new-defined solidification and concentration entropies. The numerical result shows that the growth behavior of dendrites, the final microstructure, and the micro-segregation are significantly influenced by melt convection during solidification of the teary alloys. The proposed solidification and concentration entropies are useful characteristics bridging the solidification behavior and the microstructure evolution of alloys.