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Two-dimensional Ostwald ripening of an Al-4% Cu alloy solid/liquid mush in the presence of melt convection, and the influence of ripening on the flow, is studied numerically using a recent extension of the phase-field method that accounts for flow in the liquid phase. Through a parametric study, the ripening kinetics are investigated and compared for cases with and without melt convection. The cases without convection show good agreement with available coarsening theories for a finite fraction of solid. In the cases with how the mean radius of the solid particles increases at a faster rate than without convection. The ripening exponent changes from 1/3 to 1/2, while the rate constant depends on the fraction of solid. Comparisons are made with the convective ripening theory of Ratke and Thieringer. Although the present analysis of coarsening is hampered by the limited number of particles in the domain, some qualitative results are presented for the effect of convection on the particle radius distribution. Finally, the present simulations allow for a determination of the permeability of the mush as :a function of the fraction of solid, and the dependence of the permeability on the ripening kinetics is shown to be scalable using the specific surface area or the mean radius. (C) 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.