Computational test of kinetic theory of granular media

Kinetic theory of granular media based on inelastic hard sphere interactions predicts continuum equations of motion similar to Navier–Stokes equations for fluids. We test these predictions using event-driven molecular dynamics simulations of uniformly excited inelastic hard spheres confined to move in a plane. The event-driven simulations have been previously shown to quantitatively reproduce the complex patterns that develop in shallow layers of vertically oscillated granular media. The test system consists of a periodic two-dimensional box filled with inelastic hard disks uniformly forced by small random accelerations in the absence of gravity. We describe the inelasticity of the particles by a velocity-dependent coefficient of restitution. Granular kinetic theory assumes that the velocities at collision are uncorrelated and close to a Maxwell–Boltzmann distribution. Our two-dimensional simulations verify that the velocity distribution is close to a Maxwell–Boltzmann distribution over 3 orders of magnitude in velocity, but we find that velocity correlations, of up to 40% of the temperature, exist between the velocity components parallel to the relative collision velocity. Despite the velocity correlations we find that the calculated transport coefficients compare well with kinetic theory predictions.