We describe a method for modeling aggregation in a flowing fluid. In the model, aggregation proceeds by the accumulation of a "nutrient." The nutrient is modeled using a lattice Boltzmann model of transport. The aggregate absorbs the nutrient, and the amount absorbed determines the local growth probability. This model contains some of the essential features of growth of stony corals. We find that the morphology of the aggregates changes drastically as we increase the Péclet number from a regime where nutrient transport is diffusion controlled to a regime where hydrodynamic transport dominates. This is in qualitative agreement with the morphogenesis of stony corals.