  This paper studies the dynamics of relaxation phenomena in the standard
dissipative particle dynamics (DPD) model [Groot and Warren, JCP, 107:4423
(1997)]. Using fluctuating hydrodynamics as the framework of the investigation,
we focus on the collective transverse and longitudinal dynamics. It is shown
that classical hydrodynamic theory predicts the transverse dynamics at relative
low temperatures very well when compared to simulation data, however, the
theory predictions are, on the same length scale, less accurate for higher
temperatures. The agreement with hydrodynamics depends on the definition of the
viscosity, and here we find that the transverse dynamics are independent of the
dissipative and random shear force contributions to the stress. For high
temperatures, the spectrum for the longitudinal dynamics is dominated by the
Brillouin peak for large length scales and the relaxation is therefore governed
by sound wave propagation and is athermal. This contrasts the results at lower
temperatures and small length scale, where the thermal process is clearly
present in the spectra. The Landau-Placzek ratio is lower than the classical
model Lennard-Jones liquid, especially at higher temperatures. The DPD model,
at least qualitatively, re-captures the underlying hydrodynamical mechanisms,
and quantitative agreement is excellent at intermediate temperatures for the
transverse dynamics.
