Choosing Hydrodynamic Fields
Mathematical Modelling of Natural Phenomena (2011)
- Volume: 6, Issue: 4, page 19-36
- ISSN: 0973-5348
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topDufty, J. W., and Brey, J. J.. "Choosing Hydrodynamic Fields." Mathematical Modelling of Natural Phenomena 6.4 (2011): 19-36. <http://eudml.org/doc/222273>.
@article{Dufty2011,
abstract = {Continuum mechanics (e.g., hydrodynamics, elasticity theory) is based on the assumption
that a small set of fields provides a closed description on large space and time scales.
Conditions governing the choice for these fields are discussed in the context of granular
fluids and multi-component fluids. In the first case, the relevance of temperature or
energy as a hydrodynamic field is justified. For mixtures, the use of a total temperature
and single flow velocity is compared with the use of multiple species temperatures and
velocities. },
author = {Dufty, J. W., Brey, J. J.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {granular gas; kinetic equations equations; hydrodynamics},
language = {eng},
month = {7},
number = {4},
pages = {19-36},
publisher = {EDP Sciences},
title = {Choosing Hydrodynamic Fields},
url = {http://eudml.org/doc/222273},
volume = {6},
year = {2011},
}
TY - JOUR
AU - Dufty, J. W.
AU - Brey, J. J.
TI - Choosing Hydrodynamic Fields
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/7//
PB - EDP Sciences
VL - 6
IS - 4
SP - 19
EP - 36
AB - Continuum mechanics (e.g., hydrodynamics, elasticity theory) is based on the assumption
that a small set of fields provides a closed description on large space and time scales.
Conditions governing the choice for these fields are discussed in the context of granular
fluids and multi-component fluids. In the first case, the relevance of temperature or
energy as a hydrodynamic field is justified. For mixtures, the use of a total temperature
and single flow velocity is compared with the use of multiple species temperatures and
velocities.
LA - eng
KW - granular gas; kinetic equations equations; hydrodynamics
UR - http://eudml.org/doc/222273
ER -
References
top- J. J. Brey, J. W. Dufty, A. Santos. Dissipative dynamics for hard spheres. J. Stat. Phys., 87 (1997), 1051–1066.
- J. J. Brey, M. J. Ruiz-Montero. Hydrodynamic character of the non-equipartition of kinetic energy in binary granular gases. Phys. Rev. E, 80 (2009), 041306.
- N. Brilliantov, T. Pöschel. Kinetic Theory of Granular Gases. Oxford, New York, 2004.
- S. R. Dahl, C. M.Hrenya, V. Garzó, J. W. Dufty. Kinetic temperatures for a granular mixture. Phys. Rev. E, 66 (2006), 04301.
- J. W. Dufty. Granular Fluids. R. Meyers, ed. Encyclopedia of Complexity and Systems Science. Springer, Heidelberg, 2009. arXiv:0709.0479.
- J. W. Dufty. Nonequilibrium Statistical Mechanics and Hydrodynamics for a Granular Fluid. B. Cichocki, M. Napiorkowski, J. Piasecki, eds. 2nd Warsaw School on Statistical Physics. Warsaw University Press, Warsaw, 2008. arXiv:0707.3714.
- J. W. Dufty, A. Baskaran, J J. Brey. Linear response and hydrodynamics for granular fluids. Phys. Rev. E, 77 (2008), 031310.
- J. W. Dufty, J. J. Brey. Origins of hydrodynamics for a granular gas. L. Pareschi,G. Russo, G. Toscani eds. Modelling and Numerics of Kinetic Dissipative Systems. Nova Science, NY, 2005; arXiv:cond-mat/0410133.
- J. Ferziger, H. Kaper. Mathematical Theory of Transport Processes in Gases. North-Holland, Amsterdam, 1972.
- D. Forster. Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions. Benjamin, Reading, MA, 1975.
- V. Garzó, J. Dufty. Homogeneous cooling state for a granular mixture. Phys. Rev. E, 60 (1999), 5706–5713.
- I. Goldhirsch. Rapid Granular Flows. Annual Review of Fluid Mechanics, 35 (2003), 267–293.
- H. Grabert. Projection Operator Techniques in Nonequilibrium Statistical Mechanics. Springer, Berlin, 1982.
- T. Halsey, A. Mehta, eds. Challenges in Granular Physics. World Scientific, Singapore, 2002.
- H. Iddir and H. Arastoopour. Modeling of multitype particle flow using the kinetic theory approach. AIChe. J., 51 (2005), 1620–1632.
- J. Jenkins, F. Mancini. Balance laws and constitutive relations for plane flows of a dense binary mixture of smooth nearly elastic circular disks. J. Appl. Mech., 54 (1987), 27–34.
- D. Jou, J. Casas-Vazquez, G. Lebon. Extended Irreversible Thermodynamics. Rep. Prog. Phys., 51 (1988), 1105.
- L. P. Kadanoff. Built upon sand: Theoretical ideas inspired by granular flows. Rev. Mod. Phys., 71 (1999), 435–444.
- J. Lutsko. Approximate solution of the Enskog equation far from equilibrium. Phys. Rev. Lett., 78 (1997), 243-246.
- J. Lutsko. Rheology of dense polydisperse granular fluids under shear. Phys. Rev. E, 70 (2004), 061101.
- P. Martin, O. Parodi, P. Pershan. Unified Hydrodynamic Theory for Cristals, Liquids, and Normal Fluids. Phys. Rev. A, 6 (1972), 2401-2420.
- J. A. McLennan. Introduction to Nonequilibrium Statistical Mechanics. Prentice-Hall, New Jersey, 1989.
- J. M. Montanero, V. Garzó. Monte Carlo simulations of the homogeneous cooling state for a granular mixture. Granular Matter, 4 (2002), 17–24.
- A. Santos, J. Dufty. Strong breakdown of equipartition in uniform gas mixtures. M. S. Ivanov, A. K. Rebrov, eds. Rarefied Gas Dynamics. Publishing House of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 2007.
- R. Zwanzig. Nonequilibrium Statistical Mechanics, Oxford, NY, 2001.
- R. Zwanzig. Memory Effects in Irreversible Thermodynamics. Phys. Rev., 124 (1961), 983–992.
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