Journal of Fluid Mechanics

Papers

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

FRANCISCO VEGA REYESa1 c1 and JEFFREY S. URBACHa2

a1 Departamento de Física, Universidad de Extremadura, 06071 Badajoz, Spain

a2 Department of Physics, Georgetown University, Washington, DC 20057, USA

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 inter-particle 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.

(Received July 30 2008)

(Revised April 28 2009)

(Accepted April 29 2009)

Correspondence:

c1 Email address for correspondence: fvega@physics.georgetown.edu

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