Regularization of the Chapman–Enskog expansion and its description of shock structure

Abstract

In the continuum transition flow regime, we propose to truncate the Chapman–Enskog expansion of the Boltzmann equation to the Navier–Stokes order without going to the Burnett or super Burnett orders. However, the particle collision time has to be generalized to depend not only on the local macroscopic flow variables, but also their gradients in the rarefied gas regime. In other words, a generalized constitutive relation for the stress and heat flux 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.