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Mean-Field Model Beyond Boltzmann-Enskog Picture for Dense Gases

Published online by Cambridge University Press:  20 August 2015

S. Ansumali
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Scientific Research, 560064 Bangalore, India
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Abstract

This work proposes an extension to Boltzmann BGK equation for dense gases. The present model has an H-theorem and it allows choice of the Prandtl number as an independent parameter. I show that similar to Enskog equation this equation can reproduce dynamics of dense gases.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2011

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References

[1]Cercignani, C., The Boltzmann Equation and Its Applications, Springer, Berlin, 1988.CrossRefGoogle Scholar
[2]Oran, E. S., Oh, C. K., and Cybyk, B. Z., Direct simulation monte carlo: recent advances and applications, An. Rev. Fluid. Mech., 30 (1998), 403441.CrossRefGoogle Scholar
[3]Chen, H., Kandasamy, S., Orszag, S., Shock, R., Succi, S., and Yakhot, V., Extended Boltzmann kinetic equation for turbulent flows, Science., 301 (2003), 633636.CrossRefGoogle ScholarPubMed
[4]Succi, S., The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University, 2001.Google Scholar
[5]Ansumali, S., Karlin, I. V., Arcidiacono, S., Abbas, A., and Prasianakis, N. I., Hydrodynamics beyond Navier-Stokes: exact solution to the lattice Boltzmann hierarchy, Phys. Rev. Lett., 98 (2007), 124502.CrossRefGoogle ScholarPubMed
[6]Gorban, A. N., and Karlin, I. V., General approach to constructing models of the Boltzmann equation, Phys. A., 206 (1994), 401420.CrossRefGoogle Scholar
[7]Ansumali, S., Arcidiacono, S., Chikatamarla, S. S., Prasianakis, N. I., Gorban, A. N., and Karlin, I. V., Quasi-equilibrium lattice Boltzmann method, EuroPhys. J. B., 56 (2007), 135139.Google Scholar
[8]Chapman, S., and Cowling, T. G., The Mathematical Theory of Non-uniform Gases, Cambridge University Press, New York, 1991.Google Scholar
[9] H. van Beijeren, and Ernst, M. H., The modified Enskog equation, Phys., 68 (1973), 437456.Google Scholar
[10]Résibois, P., H-theorem for the (modified) nonlinear Enskog equation, Phys. Rev. Lett., 40 (1978), 14091411.CrossRefGoogle Scholar
[11]Alexander, F. J., Garcia, A. L., and Alder, B. J., A consistent Boltzmann algorithm, Phys. Rev. Lett., 74 (1995), 52125215.CrossRefGoogle ScholarPubMed
[12]Dufty, J. W., Santos, A., and Brey, J. J., Practical kinetic model for hard sphere dynamics, Phys. Rev. Lett., 77 (1996), 12701273.CrossRefGoogle ScholarPubMed
[13]Lutsko, J. F., Approximate solution of the Enskog equation far from equilibrium, Phys. Rev. Lett., 78 (1997), 243246.CrossRefGoogle Scholar
[14]Liboff, R. L., Kinetic Theory: Classical, Quantum, and Relativistic Descriptions, Springer, Berlin, 2003.Google Scholar
[15]Luo, L. S., Unified theory of the lattice Boltzmann models for nonideal gases, Phys. Rev. Lett., 81 (1998), 16181621.CrossRefGoogle Scholar
[16]Helbing, D., and Molnár, P., Social force model for pedestrian dynamics, Phys. Rev. E., 51 (1995), 42824286.CrossRefGoogle ScholarPubMed
[17]Goldhirsch, I., and Ronis, D., Theory of thermophoresis. I. general considerations and mode-coupling analysis, Phys. Rev. A., 27 (1983), 16161634.CrossRefGoogle Scholar
[18]Grmela, M., and Garcia-Colin, L. S., Compatibility of the Enskog kinetic theory with thermodynamics. I, Phys. Rev. A., 22 (1980), 12951304.CrossRefGoogle Scholar
[19]Ottinger, H. C., Beyond Equilibrium Thermodynamics, Wiley-Interscience, Hoboken, NJ 2005.Google Scholar

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