  We study self-diffusion and sedimentation in colloidal suspensions of
nearly-hard spheres using the multiparticle collision dynamics simulation
method for the solvent with a discrete mesh model for the colloidal particles
(MD+MPCD). We cover colloid volume fractions from 0.01 to 0.40 and compare the
MD+MPCD simulations to Brownian dynamics simulations with free-draining
hydrodynamics (BD) as well as pairwise far-field hydrodynamics described using
the Rotne--Prager--Yamakawa mobility tensor (BD+RPY). The dynamics in MD+MPCD
suggest that the colloidal particles are only partially coupled to the solvent
at short times. However, the long-time self-diffusion coefficient in MD+MPCD is
comparable to that in BD and BD+RPY, and the sedimentation coefficient in
MD+MPCD is in good agreement with that in BD+RPY, suggesting that MD+MPCD gives
a reasonable description of the hydrodynamic interactions in colloidal
suspensions. The discrete-particle MD+MPCD approach is convenient and readily
extended to more complex shapes, and we determine the long-time self-diffusion
coefficient in suspensions of nearly-hard cubes to demonstrate its generality.
