Nonequilibrium Brownian dynamics simulations are applied to model a highly concentrated dispersion of charged particles at high ionic strength. Through the use of hydrodynamic preaveraging, as applied to the overdamped Langevin equation, and correlations appropriate for hard spheres, good predictions are obtained for the suspension shear viscosity at low to moderate shear rates. At higher shear rates, the influence of near-field hydrodynamic interactions on the suspension microstructure invalidates the preaveraging approach.