  We present a direct numerical simulation method for investigating the
dynamics of dispersed particles in a compressible solvent fluid. The validity
of the simulation is examined by calculating the velocity relaxation of an
impulsively forced spherical particle with a known analytical solution. The
simulation also gives information about the fluid motion, which provides some
insight into the particle motion. Fluctuations are also introduced by random
stress, and the validity of this case is examined by comparing the calculation
results with the fluctuation-dissipation theorem.
