Steady base states for Navier-Stokes granular hydrodynamics with boundary heating and shear

TL;DR

This paper classifies and explicitly describes steady states of a granular gas under boundary shear and heating, validated by simulations, and discusses their physical origins and hydrodynamic validity.

Contribution

It provides a comprehensive classification and explicit expressions for steady states in granular hydrodynamics with boundary conditions, including new states not previously reported.

Findings

Identification of new steady states with linear temperature profiles.

Validation of theoretical profiles through simulations.

Conditions for the applicability of Navier-Stokes hydrodynamics.

Abstract

We study the Navier-Stokes steady states for a low density monodisperse hard sphere granular gas (i.e, a hard sphere ideal monatomic gas with inelastic interparticle collisions). We present a classification of the uniform steady states that can arise from shear and temperature (or energy input) applied at the boundaries (parallel walls). We consider both symmetric and asymmetric boundary conditions and find steady states not previously reported, including sheared states with linear temperature profiles. We provide explicit expressions for the hydrodynamic profiles for all these steady states. Our results are validated by the numerical solution of the Boltzmann kinetic equation for the granular gas obtained by the direct simulation Monte Carlo method, and by molecular dynamics simulations. We discuss the physical origin of the new steady states and derive conditions for the validity of Navier-Stokes hydrodynamics.