A recently developed mesoscopic solvent model with multiparticle-collision dynamics is applied to three-dimensional solvent flows in a channel with and without a spherical obstacle. The advantage of a gravitationally driven flow of the solvent over the flow induced by a pressure gradient in the calculation of the solvent viscosity is demonstrated. Three different algorithms for stochastic collision steps are investigated and compared. In particular, we have examined an alternative algorithm with relative velocities drawn from a Maxwell-Boltzmann distribution at each collision step. This algorithm increases the numerical efficiency of the mesoscopic model for solvent flows with low and intermediate Reynolds numbers. Our simulation results for the recirculation length of stationary vortices behind a spherical obstacle are in good agreement with the previous experimental measurements.