Dynamics of Generalized Hydrodynamics: Hyperbolic and Pseudohyperbolic Burgers Equations

TL;DR

This paper discusses the development and analysis of generalized hydrodynamic equations, including hyperbolic and pseudohyperbolic Burgers equations, to better model small-scale fluid dynamics phenomena like ultrasound propagation.

Contribution

It introduces simplified models of generalized hydrodynamics, extending classical equations to improve the description of high-frequency and small-scale fluid behaviors.

Findings

Enhanced models better capture ultrasound propagation.

Generalized equations improve upon classical hydrodynamics.

Simplified models facilitate analysis of small-scale fluid phenomena.

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.