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

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.

16 pages, 4 figures. Changes in the final version respect to first version: Title slightly changed; the structure of the paper has substantially changed; one new figure; molecular dynamics simulations added. To appear in J. Fluid Mech

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• Modified Sonine approximation for granular binary mixtures
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• Hydrodynamics of inelastic Maxwell models
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• Diffusion transport coefficients for granular binary mixtures at low density. Thermal diffusion segregation
• Steady base states for non-Newtonian granular hydrodynamics
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• Zero-gravity thermal convection in granular gases
• Dissipative lateral walls are sufficient to trigger convection in vibrated granular gases
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