Shock Propagation in a Driven hard-sphere Gas: Molecular Dynamics Simulations and Hydrodynamics

The continuous injection of energy in a stationary gas creates a shock wave that propagates radially outwards. We study the hydrodynamics of this disturbance using event driven molecular dynamics of a hard-sphere gas in two and three dimensions, the numerical solution of the Euler equation with a virial equation of state for the gas, and the numerical solution of the Navier-Stokes equations, for the cases when the driving is localized in space and when it is uniform throughout the shock. We show that the results from the Euler equation do not agree with the data from hard-sphere simulations when the driving is uniform and has singularities when the driving is localized. Including dissipative terms through the Navier-Stokes equations results in reasonably good description of the data, when the coefficients of dissipation are chosen parametrically.