  It is known that a gas composed of a large number of atoms following
Newtonian dynamics can be described by the continuum laws of hydrodynamics.
Proving this rigorously is one of the outstanding open problems in physics and
mathematics. Surprisingly, precise numerical demonstrations of the equivalence
of the hydrodynamic and microscopic descriptions are rare. We test this
equivalence in the context of the classic problem of the evolution of a
blast-wave, a problem that is expected to be at the limits where hydrodynamics
would work. We study a one-dimensional gas for which the hydrodynamic Euler
equations for the conserved fields of density, momentum and energy are known to
have self-similar scaling solutions. Our microscopic model consists of hard
point particles with alternate masses, which is a non-integrable system with
strong mixing dynamics. Our extensive microscopic simulations find a remarkable
agreement with hydrodynamics, with deviations in a small core region that are
understood as arising due to heat conduction.
