Shock-wave structure according to the Navier--Stokes--Fourier constitutive relations

The Navier--Stokes--Fourier constitutive equations are used to study plane shock--waves in dilute gases. We use the soft sphere model in which the viscosity and thermal conductivity are proportional to a power of the local temperature: $\eta, \kappa \sim T^\sigma$, $\sigma$ being the viscosity index . We show that the experimental normalized density profiles for argon can be fit with the viscosity index. Results form the direct simulation Monte Carlo method and with transport coefficients obtained from ab initio potentials are also considered.