Blast in the one-dimensional cold gas: Comparison of microscopic simulations with hydrodynamic predictions

We study the response of an infinite system of point particles on the line initially at rest to the instantaneous release of energy in a localized region. The blast generates shock waves, and we make a detailed comparison of the density, velocity, and temperature in the growing region between the shock waves predicted by Euler equations for the ideal nondissipative compressible gas and the results of direct microscopic simulations. At long times, the hydrodynamic variables acquire self-similar forms with scaling functions 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 Navier-Stokes-Fourier equations. A different scaling form is observed in the blast core. Our microscopic model is the one-dimensional hard-point gas with binary mass distribution and alternating masses. This infinitely dilute gas has the ideal gas equation of state and is nonintegrable and known to display fast equilibration.