The first fully three-dimensional solution flow and solute transport simulations are performed to model the potassium titanyl phosphate(KTP) growth system of Bordui et al. Steady flows and supersaturation fields for two crystal mounting geometries are computed using a stabilized finite element method implemented on a data-parallel supercomputer. Our results present a mechanistic picture of solute transport which is consistent with inclusion formation patterns obtained in experiments. The simulations also explain beneficial outcomes, in terms of better global mixing and more uniform surface supersaturation, observed for a crystal mounting geometry which strongly breaks cylindrical symmetry in the system.