Uniform shear flow in dissipative gases. Computer simulations of inelastic hard spheres and (frictional) elastic hard spheres

Abstract

In the preceding paper (cond-mat/0405252), we have conjectured that the main transport properties of a dilute gas of inelastic hard spheres (IHS) can be satisfactorily captured by an equivalent gas of elastic hard spheres (EHS), provided that the latter are under the action of an effective drag force and their collision rate is reduced by a factor $(1+\alpha )/2$ (where $\alpha$ is the constant coefficient of normal restitution). In this paper we test the above expectation in a paradigmatic nonequilibrium state, namely the simple or uniform shear flow, by performing Monte Carlo computer simulations of the Boltzmann equation for both classes of dissipative gases with a dissipation range $0.5\le \alpha \le 0.95$ and two values of the imposed shear rate $a$. The distortion of the steady-state velocity distribution from the local equilibrium state is measured by the shear stress, the normal stress differences, the cooling rate, the fourth and sixth cumulants, and the shape of the distribution itself. In particular, the simulation results seem to be consistent with an exponential overpopulation of the high-velocity tail. The EHS results are in general hardly distinguishable from the IHS ones if $\alpha \gtrsim 0.7$, so that the distinct signature of the IHS gas (higher anisotropy and overpopulation) only manifests itself at relatively high dissipations

arXiv comment23 pages; 18 figures; Figs. 2 and 9 include new simulations; two new figures added; few minor changes; accepted for publication in PRE

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Cited by in corpus (18)

• Transport coefficients for an inelastic gas around uniform shear flow: Linear stability analysis
• A Rescaling Velocity Method for Dissipative Kinetic Equations - Applications to Granular Media
• Non-Newtonian granular hydrodynamics. What do the inelastic simple shear flow and the elastic Fourier flow have in common?
• Non-Newtonian hydrodynamics for a dilute granular suspension under uniform shear flow
• System of elastic hard spheres which mimics the transport properties of a granular gas
• Granular mixtures modeled as elastic hard spheres subject to a drag force
• Shear-rate dependent transport coefficients for inelastic Maxwell models
• Class of dilute granular Couette flows with uniform heat flux
• Aging to non-Newtonian hydrodynamics in a granular gas
• Mass transport of an impurity in a strongly sheared granular gas
• Steady base states for non-Newtonian granular hydrodynamics
• Unsteady non-Newtonian hydrodynamics in granular gases
• Computer simulations of an impurity in a granular gas under planar Couette flow
• Influence of a drag force on linear transport in low-density gases. Stability analysis
• Kinetic Theory for Binary Granular Mixtures at Low-Density
• Rheological effects in the linear response and spontaneous fluctuations of a sheared granular gas
• Shear-rate dependent transport coefficients in granular suspensions
• Exact Rheology of Uniform Shear Flow in a Gas of Inelastic and Rough Maxwell Particles