We investigate the impact of the convective transport of inoculant particles on the distribution of the final microstructure (grain size) in grain-refined aluminum-alloy castings. We carry out numerical simulations of a casting experiment, considering the solidification of an Al–22 wt.%Cu alloy inoculated with Al–Ti–B in a side-cooled 76 × 76 × 254 mm sand mold. We use a fully coupled multiscale volume-averaged two-phase model. At the macroscopic scale the transport of mass, heat and solute, as well as the transport of globular equiaxed grains and of inoculant particles are described by volume averaged transport equations. At the microscopic scale, nucleation and grain growth are accounted for. Nucleation is considered to be heterogeneous and athermal. Grains nucleate on polydisperse inoculant particles at an undercooling inversely proportional to the particle size. The growth of the globular solid grains is controlled by solute diffusion. We analyze the individual roles of the phenomena of transport of inoculant particles and of equiaxed grains for a range of process parameters (initial superheat, cooling rate, growth-restriction parameter). We show that the consideration of the transport of polydisperse inoculant particles has a strong impact on the prediction of the heterogeneity of the final microstructure across the casting. The transport of the inoculant particles considerably increases the heterogeneities of the microstructure and reduces the average grain size, and the grain motion reduces the microstructure heterogeneities.