Numerical simulation of 3-D augmented burnett equations for hypersonic flow in continuum-transition regime

For computation of hypersonic flowfields about space vehicles in low earth orbits, where the local Knudsen munbers (Kn) lie in the continuum-transition regime, a set of extended three-dimensional hydrodynamic equations are required which are more accurate than the Navier- Stokes equations and computationally more efficient than the Direct Simulation Monte Carlo (DSMC) computations in this regime. In this paper, the three-dimensional augmented Burnett equations are derived from the Chapman-Enskog expansion of the Boltzmann equation to O(Kn²) and adding the augmented terms (linear thirdorder super Burnett terms with coefficients determined from linearized stability analysis to ensure stability of the augmented Burnett equations to small wavelength disturbances). The three-dimensional augmented Burnett equations are applied to compute the three-dimensional hypersonic blunt body flows for various range of Knudsen numbers and Mach numbers. An explicit time-stepping scheme with Steger-Warmlmg flux vector splitting is employed to discretize the convective flux terms. Stress and heat flux terms are central differenced. For the wall boundary conditions, the first-order Maxwell- Smoluchowski slip boundary conditions are employed. The computational results are compared with the Navier- Stokes solutions, the existing augmented Burnett solutions of Zhong, and the available DSMC results. The comparisonss how that the difference betweent he Navier- Stokes and the augmented Burnett solutions is very small at Knudsen numbers less than 0.01; the difference becomes significant as the Knudsen number increases. The comparisons also show that the augmented Burnett solutions are much closer to the DSMC results in the continuum-transition regime than the Navier-Stokes calculations.