Energy conserving discrete Boltzmann equation for nonideal systems

International Journal of Modern Physics C

Volumn 10, Issue 7, 1999, Pages 1367-1382

  Martys, Nicos S ^a  

^a NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

Author keywords

BBGKY; BGK; Discrete Boltzmann Methods; Hydrodynamic Fluctuations; Lennard Jones Fluid; Nonideal Systems; Thermal Lattice Boltzmann

Indexed keywords

EID: 0033262074     PISSN: 01291831     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129183199001121     Document Type: Article

References (36)

1. G. D. Doolen (ed.), Lattice Gas Methods for Partial Differential Equations (Addison-Wesley, Redwood City, California, 1990); Lattice Gas Methods: Theory, Applications, and Hardware (MIT, Cambridge, 1991).
2. G. D. Doolen (ed.), Lattice Gas Methods for Partial Differential Equations (Addison-Wesley, Redwood City, California, 1990); Lattice Gas Methods: Theory, Applications, and Hardware (MIT, Cambridge, 1991).
3. J. Stat. Phys. 81(1/2), (1995).
4. A. K. Gunstensen, D. H. Rothman, S. Zaleski, and G. Zanetti, Phys. Rev. A 43, 4320 (1991); A. K. Gunstensen, Ph.D. thesis, M.I.T. (1992); A. K. Gunstensen and D. H. Rothman, Europhys. Lett. 18, 157 (1992); J. Geophys. Res. 98, 6431 (1993).
5. A. K. Gunstensen, D. H. Rothman, S. Zaleski, and G. Zanetti, Phys. Rev. A 43, 4320 (1991); A. K. Gunstensen, Ph.D. thesis, M.I.T. (1992); A. K. Gunstensen and D. H. Rothman, Europhys. Lett. 18, 157 (1992); J. Geophys. Res. 98, 6431 (1993).
6. A. K. Gunstensen, D. H. Rothman, S. Zaleski, and G. Zanetti, Phys. Rev. A 43, 4320 (1991); A. K. Gunstensen, Ph.D. thesis, M.I.T. (1992); A. K. Gunstensen and D. H. Rothman, Europhys. Lett. 18, 157 (1992); J. Geophys. Res. 98, 6431 (1993).
7. A. K. Gunstensen, D. H. Rothman, S. Zaleski, and G. Zanetti, Phys. Rev. A 43, 4320 (1991); A. K. Gunstensen, Ph.D. thesis, M.I.T. (1992); A. K. Gunstensen and D. H. Rothman, Europhys. Lett. 18, 157 (1992); J. Geophys. Res. 98, 6431 (1993).
8. X. Shan and H. Chen, Phys. Rev. E 47, 1815 (1992); ibid. 49, 2941 (1994).
9. X. Shan and H. Chen, Phys. Rev. E 47, 1815 (1992); ibid. 49, 2941 (1994).
10. M. R. Swift, W. R. Osborn, and J. M. Yeomans, Phys. Rev. Lett. 75, 830 (1995); W. R. Osborn, E. Orlandini, M. R. Swift, J. M. Yeomans, and J. R. Banavar, ibid. 75, 4031 (1995); E. Orlandini, M. R. Swift, and J. M. Yeomans, Europhys. Lett. 32, 463 (1995).
11. M. R. Swift, W. R. Osborn, and J. M. Yeomans, Phys. Rev. Lett. 75, 830 (1995); W. R. Osborn, E. Orlandini, M. R. Swift, J. M. Yeomans, and J. R. Banavar, ibid. 75, 4031 (1995); E. Orlandini, M. R. Swift, and J. M. Yeomans, Europhys. Lett. 32, 463 (1995).
12. M. R. Swift, W. R. Osborn, and J. M. Yeomans, Phys. Rev. Lett. 75, 830 (1995); W. R. Osborn, E. Orlandini, M. R. Swift, J. M. Yeomans, and J. R. Banavar, ibid. 75, 4031 (1995); E. Orlandini, M. R. Swift, and J. M. Yeomans, Europhys. Lett. 32, 463 (1995).
13. N. S. Martys and H. Chen, Phys. Rev. E 53, 743 (1996).
14. N. S. Martys, X. Shan, and H. Chen, Phys. Rev. E to appear Oct. 1998.
15. B. T. Nadiga, Euro. J. Mech. B: Fluids 15, 885 (1996).
16. J. H. Irving and J. G. Kirkwood, J. Chem. Phys. 18, 817 (1950).
17. F. Mohling, Statistical Mechanics: Methods and Applications (John Wiley and Sons, Inc., New York, 1982).
18. P. L. Bhatnagar, E. P. Gross, and M. Krook, Phys. Rev. 94, 511 (1954).
19. X. Shan and X. He, Phys. Rev. Lett. 90, 65 (1998).
20. Most of the results described in this section can be found, or are minor extensions of that, in Refs. 9 and 10.
21. T. M. Reed and K. E. Gubbins, Applied Statistical Mechanics (Butterworth-Heinemann, Stoneham, MA, 1991).
22. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases, 3rd edition (Cambridge University Press, London, 1970).
23. W. E. Alley, B. J. Alder, and S. Yip, Phys. Rev. A 27, 3174 (1983).
24. W. E. Alley and B. J. Alder, Physical Rev. A 27, 3158 (1983).
25. C. Cercignani, Theory and Application of the Boltzmann Equation (Elsevier, New York, 1975).
26. H. Grad, Commun. Pure Appl. Math. 2, 325 (1949).
27. A. Santos, J. M. Montanero, J. Dufty, and J. J. Brey, Phys. Rev. E 57, 1644 (1983).
28. As an alternative approach, W, the contribution to the stress tensor due to nonlocal interactions may be derived from a free energy. For instance see: R. Evans, Adv. in Phys. 28, 143 (1979) and L. M. Lust, O. T. Valls, and C. Dasgupta, Phys. Rev. E 48, 1787 (1993).
29. As an alternative approach, W, the contribution to the stress tensor due to nonlocal interactions may be derived from a free energy. For instance see: R. Evans, Adv. in Phys. 28, 143 (1979) and L. M. Lust, O. T. Valls, and C. Dasgupta, Phys. Rev. E 48, 1787 (1993).
30. G. McNamara and B. Alder, Physica A 194, 218 (1993).
31. Y. Chen, H. Ohashi, and M. Akiyama, Phys. Rev. E 50, 2776 (1994).
32. See for instance, M. R. Swift, E. Orlandini, W. R. Osborn, and J. M. Yeomans, Phys. Rev. E 54, 5041 (1996); X. He, X. Shan and G. Doolen, Phys. Rev. E 57, R13 (1998).
33. See for instance, M. R. Swift, E. Orlandini, W. R. Osborn, and J. M. Yeomans, Phys. Rev. E 54, 5041 (1996); X. He, X. Shan and G. Doolen, Phys. Rev. E 57, R13 (1998).
34. H. Chen, C. Teixera, and K. Molvig, Int. J. Mod. Phys. C 8, 675 (1997).
35. J. A. Leegwater, Ph.D. Thesis, Utrecht Univ. (1991).
36. J. P. Boon and S. Yip, Molecular Hydrodynamics (Dover Publications, Inc., New York, 1980).