Generalized slip-flow theory and its related Knudsen-layer analysis for a slightly rarefied gas I

A systematic asymptotic analysis of the Boltzmann equation shows that the overall behavior of a gas can be described by fluid-dynamic-type equations with the appropriate slip/jump boundary condition when the Knudsen number is small [the generalized slip-flow theory (Sone, Molecular Gas Dynamics, 2007)]. Near the boundary, a non-fluid-dynamic correction (the Knudsen-layer correction) to the overall solution is required. Although the generalized slip-flow theory has been established up to the second order of the Knudsen number expansion, the data of those corrections have been completed only for the BGK model. Completing the corresponding data for the original Boltzmann equation has been demanded. In the present work, partial results of completing the data for a hard-sphere gas under the diffuse reflection condition are reported.