A combined scheme based on parallel and grid computing for the simulation of granular fluids

A granular gas is a large collection of (mesoscopic or macroscopic) particles which collide inelastically and are usually kept in a state of continuous agitation. Apart from their interest in industrial and technological applications, granular gases are important at a fundamental level as physical systems intrinsically out of equilibrium and thus exhibiting a wide spectrum of complex behaviour [1]. Although the number of grains in a fluidized granular system is of course much smaller than the number of atoms or molecules in a conventional gas, it is large enough as to make nonequilibrium statisticalmechanical concepts and tools applicable. In particular, a kinetic theory approach (based on the Boltzmann and Enskog equations suitably modified to account for inelastic collisions) has proven to be very useful [2]. For the simulation of a granular gas we have considered a system made of inelastic hard spheres under conditions of uniform shear flow. This flow is characterized by a constant density n, a time-dependent (but uniform) granular temperature T (t) and a flow velocity field of the form u(r) = ayx̂, where a is the constant shear rate. We have chosen this flow for studying granular gases due to three basic reasons. First, from a macroscopic point of view this flow is simple, given that there only exists one hydrodynamic gradient (a = ∂ux/∂y) that, moreover, is a constant. Second, this flow shows an intrinsic non-Newtonian [3] steady state as a consecuence of the competition between the inelastic cooling and the viscous heating. Finally, since both the density n and the flow velocity u(r) are independent of time, the possible evolution towards the hydrodynamic behaviour is governed by the temporal dependence of the granular temperature [4], this quantity precisely being the one casting more doubts on the applicability of hydrodynamics [1]. To perform the simulations we have employed the Direct Simulation Monte Carlo method [5]. From a computational point of view, two ingre-