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

To extend the range of applicability of continuum formulations into the continuum-transition regime, an extended set of fluid dynamic equations has been derived. These equations, termed as the Bhatnagar-Gross-Krook (BGK)-Burnett equations, have been derived by taking moments of the Boltzmann equation by using the BGK model for the collision integral. The second-order distribution function that forms the basis of this derivation is formulated by considering the first three terms of the Chapman-Enskog expansion. It is shown 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 these computations are compared with the augmented Burnett and Navier-Stokes solutions. The second-order distribution function does not violate Boltzmann's H-theorem; as a consequence the BGK-Burnett equations are entropy consistent for the range of Knudsen numbers for which computations have been performed.