Journal of Fluid Mechanics


Steady base states for non-Newtonian granular hydrodynamics

Francisco Vega Reyesa1 c1, Andrés Santosa1 and Vicente Garzóa1

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


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 five types of Couette–Fourier granular flows are systematically described, identifying the different types of hydrodynamic profiles. Excellent agreement is found between our classification of flows and simulation results. Also, we obtain the corresponding nonlinear transport coefficients by following three independent and complementary methods: (i) an analytical solution obtained from Grad’s 13-moment method applied to the inelastic Boltzmann equation; (ii) a numerical solution of the inelastic Boltzmann equation obtained by means of the direct simulation Monte Carlo method; and (iii) event-driven molecular dynamics simulations. We find that, while Grad’s theory does not describe quantitatively well all transport coefficients, the three procedures yield the same general classification of planar Couette–Fourier flows for the granular gas.

(Received March 02 2012)

(Revised October 20 2012)

(Accepted December 11 2012)

(Online publication February 19 2013)

Key words

  • granular media;
  • kinetic theory;
  • non-Newtonian flows


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