  The solution for the radial distribution of pressure, density, temperature
and flow velocity fields in a blast wave propagating through a medium at rest,
following an intense explosion, starting from hydrodynamic equations, is one of
the classic problems in gas dynamics. However, there is very little direct
verification of the theory and its assumptions from simulations of microscopic
models. In this paper, we compare the results and assumptions of the
hydrodynamic theory with results from large scale event driven molecular
dynamics simulations of a hard sphere gas in three dimensions. We find that the
predictions for the radial distribution of the thermodynamic quantities do not
match well with the numerical data. We improve the theory by replacing the
ideal gas law with a more realistic virial equation of state for the hard
sphere gas. While this improves the theoretical predictions, we show that they
still fail to describe the data well. To understand the reasons for this
discrepancy, the different assumptions of the hydrodynamic theory are tested
within the simulations. A key assumption of the theory is the existence of a
local equation of state. We validate this assumption by showing that the local
pressure, temperature and density obey the equation of state for a hard sphere
gas. However, the probability distribution of the velocity fluctuations has
non-gaussian tails, especially away from the shock front, showing that the
assumption of local equilibrium is violated. This, along with neglect of heat
conduction, could be the possible reasons for the mismatch between theory and
simulations.
