Role of Molecular Chaos in Granular Fluctuating Hydrodynamics

G. Costantini; A. Puglisi

Mathematical Modelling of Natural Phenomena (2011)

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

Abstract

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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.

How to cite

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Costantini, 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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