Asymptotic Solutions of the Kinetic Boltzmann Equation, Multicomponent Non-equilibrium Gas Dynamics and Turbulence

TL;DR

This paper develops an asymptotic solution method for the kinetic Boltzmann equation, derives multicomponent non-equilibrium gas dynamics equations, and interprets turbulent gas flow as a stratified component flow.

Contribution

It formulates a correct asymptotic solution method, derives new multicomponent gas dynamics equations, and offers a novel interpretation of turbulence as stratified component flow.

Findings

Velocity distribution functions are equivalent up to first order terms.

Derived equations describe multicomponent non-equilibrium gas dynamics.

Turbulent flow interpreted as stratified component flow.

Abstract

In the article correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert's and Enskog's methods are discussed. The equations system of multicomponent non-equilibrium gas dynamics is derived, that corresponds to the first order in the approximate (asymptotic) method for solution of the system of kinetic Boltzmann equations. It is shown, that the velocity distribution functions of particles, obtained by the proposed method and by Enskog's method, within Enskog's approach, are equivalent up to the infinitesimal first order terms of the asymptotic expansion, but, generally speaking, differ in the next order. Interpretation of turbulent gas flow is proposed, as stratified on components gas flow, which is described by the derived equations system of multicomponent non-equilibrium gas dynamics.