Dynamics of Generalized Hydrodynamics: Hyperbolic and Pseudohyperbolic Burgers Equations

Abstract

The equations of continuum hydrodynamics can be derived from the Boltzmann equation, which describes rarefied gas dynamics at the kinetic level, by means of the Chapman-Enskog expansion. This expansion assumes a small Knudsen number, and as a consequence, the hydrodynamics equations are able to successfully describe sound propagation when the frequency of a sound wave is much higher than the collision frequency of the particles. When both frequencies become comparable, these equations give a poor account of the experimental measurements. A series of generalized hydrodynamic equations has been introduced in the literature along the years in order to improve the continuous description of small scale properties of fluid flow, as ultrasound propagation. We will describe herein some of the simplified models that has been proposed so far.