Higher-order distribution functions, BGK-burnett equations and Boltzmann’s H-theorem

In order 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 BGK-Burnett equations, have been derived by taking moments of the Boltzmann equations 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. The BGK-Burnett equations have been used to compute the hypersonic shock structure and hypersonic flows past blunt bodies. The results of these computations are compared with the augmented Burnett and Navier-Stokes solutions. It has been shown that the second-order distribution function does not violate Boltzmann's H-theorem as a consequence of which the BGK-Burnett equations are entropy consistent for the range of Knudsen numbers for which computations have been performed.