Hydrodynamic simulations of mesoscopic solvent have been performed by multi-particle collision algorithm in a real dimensional system without and with the random shifting of the grid. A systematic conversion of the dimensionless units to a real dimensional system was confirmed by jump rates of solvent particles. Speed distributions of solvent particles obtained from the simulations agreed very well with the Maxwell-Boltzmann distributions. Solvent viscosities obtained from the simulations and from the conversion of units are exactly the same which confirmed the correct conversion of the units once again. The calculation of the friction coefficient of a massive Brownian particle in a mesoscopic solvent as a function of Brownian particle diameter was examined as an example.