This article presents a novel coupling of numerical techniques that enable three-dimensional convection-driven microstructure simulations to be conducted on practical time scales appropriate for small-size components or experiments. On the microstructure side, the cellular automata method is efficient for relatively large-scale simulations, while the lattice Boltzmann method provides one of the fastest transient computational fluid dynamics solvers. Both of these methods have been parallelized and coupled in a single code, allowing resolution of large-scale convection-driven solidification problems. The numerical model is validated against benchmark cases, extended to capture solute plumes in directional solidification and finally used to model alloy solidification of an entire differentially heated cavity capturing both microstructural and meso-/macroscale phenomena.