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We study the response of an infinite system of point particles on the lineinitially at rest on the instantaneous release of energy in a localized region.We make a detailed comparison of the hydrodynamic variables predicted by Eulerequations for non-dissipative ideal compressible gas and the results of directmicroscopic simulations. At long times the profiles of the three conservedvariables evolve to self-similar scaling forms, with a scaling exponent aspredicted by the Taylor-von Neumann-Sedov (TvNS) blast-wave solution. Thescaling functions obtained from the microscopic dynamics show a remarkableagreement with the TvNS predictions, except at the blast core, where the TvNSsolution predicts a diverging temperature which is not observed in simulations.We show that the effect of heat conduction becomes important and presentresults from a numerical solution of the full Navier-Stokes-Fourier equations.A different scaling form is observed in the blast core and this is carefullyanalyzed. Our microscopic model is the one-dimensional alternate masshard-particle gas which has the ideal gas equation of state but isnon-integrable and known to display fast equilibration.

The Taylor-von Neumann-Sedov blast-wave solution: comparisons with microscopic simulations of a one-dimensional gas