F. Vega Reyes, A. Santos, V. Garzó
We study in this work steady laminar flows in a low density granular gas modelled as a system of identical smooth hard spheres that collide inelastically. The system is excited by shear and temperature sources at the boundaries, which consist of two infinite parallel walls. Thus, the geometry of the system is the same that yields the planar Fourier and Couette flows in standard gases. We show that it is possible to describe the steady granular flows in this system, even at large inelasticities, by means of a (non-Newtonian) hydrodynamic approach. All types of Couette-Fourier granular flows are systematically described, identifying the different types of hydrodynamic profiles and also their corresponding non-linear transport coefficients. We obtain the results by following three independent and complementary methods: (1) an analytical solution obtained from Grad's 13-moment method applied to the inelastic Boltzmann equation, (2) a numerical solution of the inelastic Boltzmann equation obtained by means of the direct simulation Monte Carlo method and (3) event-driven molecular dynamics simulations. The three procedures are shown to yield the same general classification of planar Couette-Fourier flows for the granular gas. Moreover, the analytical results exhibit a fair quantitative agreement with computer simulations.
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http://arxiv.org/abs/1203.0266
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