Fluid dynamics at arbitrary Knudsen on a base of Alexeev-Boltzmann equation: sound in a rarefied gas

Abstract

The system of hydrodynamic-type equations is derived from Alexeev's generalized Boltzmann kinetic equation by two-side distribution function for a stratified gas in gravity field. It is applied to a problem of ultrasound propagation and attenuation. The linearized version of the obtained system is studied and compared with the Navier-Stokes one at arbitrary Knudsen numbers. The problem of a generation by a moving plane in a rarefied gas is explored and used as a test while compared with experiment. It is good agreement between predicted propagation speed, attenuation factor and experimental results for a wide range of Knudsen numbers.