A comparative study of augmented burnett and BGK-burnett equations for computing hypersonic blunt body flow

In this paper two different forms of Burnett equations are studied which have been designated as ‘Augmented Burnett Equations’ and ‘BGK-Burnett Equations’. The augmented Burnett equations were developed by Zhong to stabilize the solution of the conventional Burnett equations which were derived in 1935 by Burnett from the Boltzmann equation using the second-order Chapman-Enskog expansion. In this formulation, The conventional Burnett equations are augmented by adding ad hoc thirdorder derivatives to stress and heat transfer terms so that the augmented equations are stable to small wavelength disturbances. The BGK-Burnett equations have been recently derived by Agarwal and Balakrishnan from the Boltzmann equation using the Bhatnagar-Gross-Krook (BGK) approximation for the collision integral. These equations have been shown to be entropy consistent and satisfy the Boltzmann H-Theorem in contrast to the conventional Burnett equations which violate the second law of thermodynamics. In this paper, both sets of Burnett equations are applied to compute a 2- D hypersonic flow over a circular cylinder at Knudsen numbers 0.001 to 0.1. The radius of the cylinder, which is the characteristic length of the body, determines the Knudsen number. The Steger- Warming flux-vector splitting scheme is applied to the convective inviscid flux terms. Stress and heat transfer terms are simply second-order centraldifferenced. Comparison is made between the augmented and BGK-Burnett equations solutions and with the Navier-Stokes calculations. Comparison of the solutions from the augmented Burnett equations with the Navier-Stokes solutions shows that the difference is significant at high Knudsen number (Kn=0.1). The solutions from the BGKBurnett equations are matched well with those from the Navier-Stokes equations and the augmented Burnett equations at lower Knudsen numbers (Kn=0.001, 0.01). BGK-Burnett solutions are currently underway at higher Knudsen numbers.