A numerical study that aims to analyze the thermal mechanisms of unsteady, supersonic granular flow by means of hydrodynamic simulations of the Navier-Stokes granular equation is reported in this paper. For this purpose, a paradigmatic problem in granular dynamics such as the Faraday instability is selected. Two different approaches for the Navier-Stokes transport coefficients for granular materials are considered, namely the traditional Jenkins-Richman theory for moderately dense quasi-elastic grains and the improved Garzó-Dufty-Lutsko theory for arbitrary inelasticity, which we also present here. Both the solutions are compared with event-driven simulations of the same system under the same conditions, by analyzing the density, temperature and velocity field. Important differences are found between the two approaches, leading to interesting implications. In particular, the heat transfer

A granular gas in gravity heated from below develops a certain stationary density profile. When the heating is switched off, the granular gas collapses. We investigate the process of sedimentation using computational hydrodynamics, based on the Jenkins-Richman theory, and find that the process is significantly more complex than generally acknowledged. In particular, during its evolution, the system passes several stages which reveal distinct spatial regions of inertial (supersonic) and diffusive (subsonic) dynamics. During the supersonic stages, characterized by Mach>1, the system develops supersonic shocks which are followed by a steep front of the hydrodynamic fields of temperature and density, traveling upward.

An inelastic hard ball bouncing repeatedly off the ground comes to rest in finite time by performing an infinite number of collisions. Similarly, a granular gas under the influence of external gravity, condenses at the bottom of the confinement due to inelastic collisions. By means of hydrodynamical simulations, we find that the condensation process of a granular gas reveals a similar dynamics as the bouncing ball. Our result is in agreement with both experiments and particle simulations, but disagrees with earlier simplified hydrodynamical description. Analyzing the result in detail, we find that the adequate modeling of pressure plays a key role in continuum modeling of granular matter.

A determining form for the two-dimensional Navier-Stokes equations: The Fourier modes case J. Math. Phys. 53, 115623 (2012) Ill-posedness for subcritical hyperdissipative Navier-Stokes equations in the largest critical spaces J. Math. Phys. 53, 115620 (2012) Lower bounds on blow up solutions of the three-dimensional Navier-Stokes equations in homogeneous Sobolev spaces J. Math. Phys. 53, 115618 (2012) A new boundary condition for the three-dimensional Navier-Stokes equation and the vanishing viscosity limit J. Math. Phys. 53, 115617 (2012) Additional information on AIP Conf. Proc. Abstract. We perform two-dimensional hydrodynamic simulations on a paradigmatic problem of granular dynamics, the Faraday instability, using two different approximations to the Navier-Stokes granular equations: the constitutive equations and kinetic coefficients derived from the assumption of vanishing inelasticity (Jenkins-Richman approach) obtained by solving the Enskog equation disks by means of Grad's method, and the ones obtained by solving the Enskog equation with the ChapmanEnskog method (Garzó-Dufty-Lutsko approach). The comparison reveals important qualitative and quantitative differences with respect to the hydrodynamic fields obtained by averaging results from particle simulations of the same system.

Abstract. The evolution of a force-free granular gas with a constant restitution coefficient is studied by means of granular hydrodynamics. We numerically solve the hydrodynamic equations and analyze the mechanisms of cluster formation. According to our findings, the presently accepted mode-enslaving mechanism may not be responsible for the latter phenomenon. On the contrary, we observe that the cluster formation is mainly driven by shock-waves, which spontaneously originate and develop in the system. This agrees with a previously suggested mechanism of formation of density singularities in one-dimensional granular gases.