Regularization of the Chapman-Enskog Expansion and Its Description of Shock Structure

Abstract. In the continuum transition ow regime, we propose to truncate the Chapman-Enskog expansion of the Boltzmann equation to the Navier-Stokes order only without going to the Burnett or super Burnett orders. However, the local particle collision time has to be generalized to depend not only on the local macroscopic ow variables, but also their gradients in the rare ed gas regime. Based on the gas-kinetic BGK model, the relation between the conventional collision time and the general one is obtained. More specially, a generalized constitutive relation for stress and heat ux is proposed. This new model is applied to the study of argon gas shock structure. There is good agreement between the predicted shock structure and experimental results for a wide range of Mach numbers.