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Role of Molecular Chaos in Granular FluctuatingHydrodynamics

Published online by Cambridge University Press:  18 July 2011

G. Costantini  and
A. Puglisi
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Abstract

We perform a numerical study of the fluctuations of the rescaled hydrodynamic transversevelocity field during the cooling state of a homogeneous granular gas. We are interestedin the role of Molecular Chaos for the amplitude of the hydrodynamic noise and itsrelaxation in time. For this purpose we compare the results of Molecular Dynamics (MD,deterministic dynamics) with those from Direct Simulation Monte Carlo (DSMC, randomprocess), where Molecular Chaos can be directly controlled. It is seen that the large timedecay of the fluctuation’s autocorrelation is always dictated by the viscosity coefficientpredicted by granular hydrodynamics, independently of the numerical scheme (MD or DSMC).On the other side, the noise amplitude in Molecular Dynamics, which is known toviolate the equilibrium Fluctuation-Dissipation relation, is not alwaysaccurately reproduced in a DSMC scheme. The agreement between the two models improves ifthe probability of recollision (controlling Molecular Chaos) is reduced by increasing thenumber of virtual particles per cells in the DSMC. This result suggests that DSMC is notnecessarily more efficient than MD, if the real number of particles is small(~103 ± 104) and if one is interested in accurately reproducefluctuations. An open question remains about the small-times behavior of theautocorrelation function in the DSMC, which in MD and in kinetic theory predictions is nota straight exponential.

Keywords

granular gasfluctuationshydrodynamicsnumerical simulations
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 4: Granular hydrodynamics , 2011 , pp. 2 - 18
Copyright
© EDP Sciences, 2011

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