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Zusammenfassung:
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.
