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

Abstract

The problem of shock wave structures of gases is not only important from the technological viewpoint, but it has also been a major stumbling block for theoreticians for a long time. For example, the shock wave structures have a big impact on the overall flow patterns around hypersonic aerospace vehicles flying at high altitude. The second issue is the numerical difficulty associated with the stiffness of the shock structure arising from the rapid change of physical properties in the extremely thin region. It is well known that the stiff shock structure is one of the toughest problems to solve numerically, either in the system of ordinary differential equations or in the form of partial differential equations. Closed-form analytical formulas and 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.