Hydrodynamic Modes for a Granular Gas from Kinetic Theory
J. Javier Brey, J.W. Dufty
TL;DR
This paper derives hydrodynamic modes for a low-density granular gas using kinetic theory, showing their agreement with Chapman-Enskog results and discussing conditions for their dominance.
Contribution
It provides a detailed kinetic theory analysis of hydrodynamic excitations in granular gases, including eigenvalues and eigenvectors at Navier-Stokes order.
Findings
Hydrodynamic eigenvalues match Chapman-Enskog results.
Conditions for dominance of hydrodynamic modes are discussed.
Eigenvectors are explicitly calculated at Navier-Stokes order.
Abstract
Small perturbations of the homogeneous cooling state (HCS) for a low density granular gas are described by means of the linearized Boltzmann equation. The spectrum of the generator for this dynamics is shown to contain points corresponding to hydrodynamic excitations. The corresponding eigenvectors and eigenvalues are calculated to Navier-Stokes order and shown to agree with those obtained by the Chapman-Enskog method. The conditions for the hydrodynamic excitations to dominate all other excitations are discussed.
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