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

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