BGK-Burnett equations for flows in the continuum-transition regime

To extend the range of applicability of continuum formulations into the con tinuum-transition regime, an extended set of fluid dynamic equations has be en derived. These equations, termed as the Bhatnagar-Gross-Krook (BGK)-Burn ett equations, have been derived by taking moments of the Boltzmann equatio n by using the BGK model for the collision integral. The second-order distr ibution function that forms the basis of this derivation is formulated by c onsidering the first three terms of the Chapman-Enskog expansion. It Is sho wn that the BGK-Burnett equations have been used to compute the hypersonic shock structure and the hypersonic flow past a blunt body. The results of t hese computations are compared with the augmented Burnett and Navier-Stokes solutions. The second-order distribution function does not violate Boltzma nn's H-theorem; as a consequence the BGK-Burnett equations are entropy cons istent for the range of Knudsen numbers for which computations have been pe rformed.