Development, implementation and application of a Stochastic Rotation Dynamics algorithm for granular matter

In this work we present an extension of the well-known particle based stochastic rotation dynamics method for the simulation of hydrodynamics of granular gases. We use an effective local coefficient of restitution to render energy dissipation dependent on local macroscopic observables, while locally conserving density and momentum. We derive the granular Boltzmann equation and demonstrate that our model obeys linear granular hydrodynamic equations. Furthermore, we derive a formula for the kinematic viscosity of the model fluid in two dimensions. We present results from simulations with a software implementation for general purpose graphics cards, that we successfully test and benchmarked with analytical predictions for standard stochastic rotation dynamics. For the granular system we observe that our prediction of the kinematic viscosity compares well with the results obtained from simulations. In this context we find that for low shear driving the fluid becomes unstable and develops shear bands. In the simulations of a freely cooling granular gas the temperature evolution follows the prediction of Haff’s law over several orders of magnitude in both time and temperature. Furthermore, we observe clustering for lower coefficients of restitution. The emergence and dynamics of the cluster compare well with expectations based on theory, experiments and simulations. The clustering sets in as the global Mach number exceeds one. Subsequently, density fluctuations grow while we observe a change in the power law of the temperature evolution. The clusters exhibit a higher cooling rate than dilute regions, hence, density and temperature become anti-correlated. This locally leads to supersonic flow. After their emergence, clusters move, collide and thus grow further. The velocity distribution function compares well with theoretical predictions. The shape of the reduced velocity distribution function changes with time as predicted, and the evolution of the second Sonine coefficient qualitative matches with analytical predictions. In our discussion we provide criteria for the selection of model parameters, and identify the effects of the finite system size