Some Aspects of the Boltzmann Equation for a Granular Gas

Abstract

The Boltzmann equation for a gas of smooth, inelastic hard spheres is introduced and its homogeneous solution for an isolated system is discussed. The possibility of hydrodynamic excitations is explored using the linearized Boltzmann equation for small spatial perturbations of the homogeneous state. It is shown that the spectrum of the generator for this linear dynamics contains five points at long wavelengths that are the origin of hydrodynamic excitations. With this knowledge, response functions are introduced that allow the formal derivation of linear hydrodynamic equations and associated Green-Kubo expressions for the transport coefficients at Navier-Stokes order.

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Document Details

Document Type
Technical Report
Publication Date
Jul 13, 2005
Accession Number
ADA446043

Entities

People

  • James W. Dufty

Organizations

  • University of Florida

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boltzmann Equation
  • Collisions
  • Computational Science
  • Dispersion Relations
  • Distribution Functions
  • Dynamics
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Gas Dynamics
  • Hierarchies
  • Liouville Equation
  • Long Wavelengths
  • Low Density
  • Mean Free Path
  • Notation
  • Rarefied Gas Dynamics

Fields of Study

  • Physics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Computational Fluid Dynamics (CFD)
  • Fluid Dynamics.