# Role of Molecular Chaos in Granular Fluctuating Hydrodynamics

Mathematical Modelling of Natural Phenomena (2011)

- Volume: 6, Issue: 4, page 2-18
- ISSN: 0973-5348

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topCostantini, G., and Puglisi, A.. "Role of Molecular Chaos in Granular Fluctuating Hydrodynamics." Mathematical Modelling of Natural Phenomena 6.4 (2011): 2-18. <http://eudml.org/doc/222326>.

@article{Costantini2011,

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

author = {Costantini, G., Puglisi, A.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {granular gas; fluctuations; hydrodynamics; numerical simulations},

language = {eng},

month = {7},

number = {4},

pages = {2-18},

publisher = {EDP Sciences},

title = {Role of Molecular Chaos in Granular Fluctuating Hydrodynamics},

url = {http://eudml.org/doc/222326},

volume = {6},

year = {2011},

}

TY - JOUR

AU - Costantini, G.

AU - Puglisi, A.

TI - Role of Molecular Chaos in Granular Fluctuating Hydrodynamics

JO - Mathematical Modelling of Natural Phenomena

DA - 2011/7//

PB - EDP Sciences

VL - 6

IS - 4

SP - 2

EP - 18

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

LA - eng

KW - granular gas; fluctuations; hydrodynamics; numerical simulations

UR - http://eudml.org/doc/222326

ER -

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