Numerical simulation of three-dimensional augmented Burnett equations for hypersonic flow in continuum-transition regime

For the computation of hypersonic flowfields about space vehicles in low earth orbits, where the local Knudsen numbers (Kn) lie in 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 thesis, the three-dimensional augmented Burnett equations are derived from the Chapman-Enskog expansion of the Boltzmann equation to O(Kn 2) and adding the augmented terms (linear third-order 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-Warming 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 comparisons show that the difference between the 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.