  In this work we study the effect of the Enskog collision terms on the steady
shock transitions in the supersonic flow of a hard sphere gas. We start by
examining one-dimensional, nonlinear, nondispersive planar wave solutions of
the Enskog-Navier-Stokes equations, which move in a fixed direction at a
constant speed. By further equating the speed of the reference frame with the
speed of such a wave, we reduce the Enskog-Navier-Stokes equations into a more
simple system of two ordinary differential equations, whose solutions depend on
a single scalar spatial variable. We then observe that this system has two
fixed points, which are taken to be the states of the gas before and after the
shock, and compute the corresponding shock transition in the form of the
heteroclinic orbit connecting these two states. We find that the Enskog
correction affects both the difference between the fixed points, and the
thickness of the transition. In particular, for a given state of the gas before
the shock transition, the difference between the fixed points is reduced, while
the shock thickness is increased, with the relative impact on the properties of
transition being more prominent at low Mach numbers. We also compute the speed
of sound in the Enskog-Navier-Stokes equations, and find that, for the same
thermodynamic state, it is somewhat faster than that in the conventional
Navier-Stokes equations, with an additional dependence on the density of the
gas.
