For increasingly rarefied flowfields, the predictions from continuum formulation, such as the Navier–Stokes equations lose accuracy. These inaccuracies are attributed primarily to the linear approximations of the stress and heat flux terms in the Navier–Stokes equations. The inclusion of higher order terms, such as Burnett, or high-order moment equations, could improve the predictive capabilities of such continuum formulations, but there has been limited success in the shock structure calculations, especially in the high Mach number case. Here, after reformulating the viscosity and heat conduction coefficients appropriate for the rarefied flow regime, we will show that the extended Navier–Stokes-type continuum formulation may still be properly used. The equations with generalized dissipative coefficients based on the closed solution of the Bhatnagar–Gross–Krook (BGK) model of the Boltzmann equation, are solved using the gas-kinetic numerical scheme.
