A second-order continuum theory of fluids

We use continuum conservation equations in conjunction with the entropy inequality to obtain a theoretical model that is accurate for hypersonic flows. This is accomplished by extending the constitutive equations to second order in strain rate and gradients of density and temperature. The accuracy of the extended theory is demonstrated by computing the shock structure in argon and nitrogen gases over a large range of Mach numbers. The solutions indicate that our constitutive equations are more accurate than the classical linear ones and are also more robust and accurate than equations obtained through expansions of the Boltzmann equation or equations arising from diffusion of volume arguments.