Continuum simulations of fluidized granular materials

A successful hydrodynamic theory of granular media could allow scientists and engineers to exploit the powerful techniques of fluid dynamics to describe granular phenomena. We use computer simulations to test a set of continuum hydrodynamic equations for granular media which were proposed by Jenkins and Richman nearly twenty years ago [59]. We use these continuum simulations as well as molecular dynamics (MD) simulations to investigate phenomena in vertically shaken layers of grains. When a layer of grains is shaken vertically by a plate with maximum acceleration greater than the acceleration of gravity, the layer will be thrown off the plate with each cycle of the plate. Continuum and MD simulations show that normal shocks form in the layer upon contact with the plate later in the cycle. We show that increasing the coefficient of restitution of the particles increases the speed of the shock in the layer, and that the limit of perfectly elastic particles is not singular. In addition, deeper layers of particles exhibit denser packing fractions near the plate and higher shock speeds than shallow layers. Pressure gradients produced by these shocks play an important role in the dynamics of standing wave patterns formed in oscillated granular layers. Both continuum and molecular dynamics simulations produce standing waves with wavelengths which agree with previous experiments. Continuum simulations reproduce stripe patterns found in MD simulations of frictionless particles, but do not reproduce square or hexagonal patterns found in experiments and MD simulations of frictional particles. Finally, we show that fluctuations present in molecular dynamics simulations are not captured by our current continuum model. By fit to Swift-Hohenberg theory, we find these fluctuations in MD simulations to be several orders of magnitude larger than fluctuations found in ordinary fluids. Differences between patterns in continuum and MD simulations near onset are found to be consistent with the presence of fluctuations in MD simulations without friction.