  We present a full investigation into shock wave profile description using
hydrodynamics models. We identified constitutive equations that provide better
agreement for all parameters involved in testing hydrodynamic equations for the
prediction of shock structure in a monatomic gas in the Mach number range
$1.0-11.0$. The constitutive equations are extracted from a previously derived
thermomechanically consistent Burnett regime continuum flow model. The
numerical computations of the resulting hydrodynamic equations along with
classical ones are performed using a finite difference global solution (FDGS)
scheme. Compared to previous studies that focussed mainly on the density
profile across the shock, here we also include temperature profiles as well as
non-negativity of entropy production throughout the shock. The results obtained
show an improvement upon those obtained previously in the bi-velocity (or
volume/mass diffusion) hydrodynamics and are more accurate than in the
hydrodynamic models from expansions method solutions to the Boltzmann equation.
