Analytical Solutions of Shock Structure Thickness and Asymmetry in Navier-Stokes/Fourier Framework

摘要

Closed-form analytical formulas (12-19) and (A1-A4) for the shock wave structure in monatomic gases are derived within the Navier-Stokes/Fourier framework. In particular, the shock thickness and asymmetry requiring the spatial differentiation and integral of density profile, respectively, are presented in elementary function form. In the derivation, the only major assumption introduced is a special value of a Prandtl number of three-fourths. These fully analytical results are expected to benefit the better understanding of the shock inner structure physics for all Mach numbers and the verification of the numerical scheme.