Comparison of shock structure solutions using independent continuum and kinetic theory approaches

A vehicle traversing the atmosphere will experience flight regimes at high altitudes in which the thickness of a hypersonic shock wave is not small compared to the shock standoff distance from the hard body. When this occurs, it is essential to compute accurate flow field solutions within the shock structure. In this paper, one-dimensional shock structure is investigated for various monatomic gases from Mach 1.4 to Mach 35. Kinetic theory solutions are computed using the Direct Simulation Monte Carlo method. Steady-state solutions of the Navier-Stokes equations and of a slightly truncated form of the Burnett equations are determined by relaxation to a steady state of the time-dependent continuum equations. Monte Carlo results are in excellent agreement with published experimental data and are used as bases of comparison for continuum solutions. For a Maxwellian gas, the truncated Burnett equations are shown to produce far more accurate solutions of shock structure than the Navier-Stokes equations.