Extended Boltzmann kinetic equation for turbulent flows

Science

Volumn 301, Issue 5633, 2003, Pages 633-636

  Chen, Hudong ^a   Kandasamy, Satheesh ^a   Orszag, Steven ^b   Shock, Rick ^a   Succi, Sauro ^c   Yakhot, Victor ^d  

^a EXA CORPORATION   (United States)

^b YALE UNIVERSITY   (United States)

^c CNR   (Italy)

^d BOSTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; HYDRAULIC MODELS; KINETIC THEORY; NAVIER STOKES EQUATIONS;

BOLTZMANN EQUATIONS;

TURBULENT FLOW;

EQUATION; KINETICS; TURBULENT FLOW;

ARTICLE; BOLTZMANN EQUATION; FLOW KINETICS; LIQUID; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MODEL; NAVIER STOKES EQUATION; PHYSICS; PRIORITY JOURNAL; TURBULENT FLOW;

EID: 0041489950     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.1085048     Document Type: Article

References (38)

1. L. Boltzmann, Sitzungber. Kais. Akad. Wiss. Wien Math. Naturwiss. Classe 66, 275 (1872).
2. C. Cercignani, Theory and Application of the Boltzmann Equation (Elsevier, New York, 1975).
3. S. Chapman, T. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge Univ. Press, Cambridge, 1952).
4. L. Landau, E. Lifshitz, Fluid Mechanics (Pergamon, Oxford, 1987).
5. U. Frisch, Turbulence, The Legacy of A. Kolmogorov (Cambridge Univ. Press, Cambridge, 1996).
6. U. Frisch, S. Orszag, Phys. Today 43, 24 (1990).
7. K. R. Sreenivasan, Rev. Mod. Phys. 71, S383 (1999).
8. A. Kolmogorov, Dokl. Akad. Nauk. SSSR 30, 9 (1941).
9. J. Boussinesq, C. R. Acad. Sci. Paris 71, 389 (1870).
10. B. Launder, D. Spalding, Comp. Mech. Appl. Mech. Eng. 3, 269 (1974).
11. V. Yakhot, S. Orszag, J. Sci. Comput. 1, 3 (1986).
12. V. Yakhot, S. Orszag, S. Thangam, T. Gatski, C. Speziale, Phys. Fluids A 4, 1510 (1992).
13. P. Bhatnagar, E. Gross, M. Krook, Phys. Rev. A 94, 511 (1954).
14. G. Wannier, Statistical Physics (Dover, New York, 1966).
15. A. V. Bobylev, Sov. Phys. Dokl. 27, 29 (1982).
16. I. V. Karlin, A. N. Gorban, Ann. Phys. 11, 783 (2002).
17. S. Succi, I. Karlin, H. Chen, S. Orszag, Physica A 280, 92 (2000).
18. H. Chen, S. Succi, S. Orszag, Phys. Rev. E 59, R2527 (1999).
19. S. Succi, O. Filippova, H. Chen, S. Orszag, J. Stat. Phys. 107, 261 (2002).
20. S. Ansumali, I. V. Karlin, Phys. Rev. E 62, 7999 (2000).
21. B. M. Boghosian, J. Yepez, P. V. Coveney, A. J. Wagner, Proc. R. Soc. London Ser. A 457, 717 (2001).
22. S. Ansumali, I. V. Karlin, Phys. Rev. E 65, 056312 (2002).
23. S. Succi, I. Karlin, H. Chen, Rev. Mod. Phys. 74, 1203 (2002).
24. O. Pashko, Y. Oono, Int. J. Mod. Phys. B 14, 555 (2000).
25. R. Benzi, S. Succi, M. Vergassola, Phys. Rep. 222, 145 (1992).
26. S. Chen, G. Doolen, Annu. Rev. Fluid Mech. 30, 329 (1998).
27. S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (Oxford Univ. Press, Oxford, 2001).
28. G. McNamara, G. Zanetti, Phys. Rev. Lett. 61, 2332 (1988).
29. F. Higuera, S. Succi, R. Benzi, Europhys. Lett. 9, 345 (1989).
30. H. Chen, S. Chen, W. Matthaeus, Phys. Rev. A 45, 5339 (1992).
31. Y. Qian, D. d'Humieres, P. Lallemand, Europhys. Lett. 17, 479 (1992).
32. H. Chen, C. Teixeira, K. Molvig, Int. J. Mod. Phys. C 9, 1281 (1998).
33. See www.exa.com/newsite/frames/powerflowmaster. html.
34. R. Shock et al., J. Aircraft 39, 434 (2002).
35. D. P. Lockard, L. S. Luo, S. D. Milder, B. A. Singer, J. Stat. Phys. 107, 423 (2002).
36. W. Bartelheimer, SAE Paper 20015332 (2001).
37. R. Lietz, S. Mallick, S. Kandasami, H. Chen, SAE Paper 20020154 (2002).
38. We thank R. Benzi, B. Boghosian, S. Chen, U. Frisch, J, Hoch, I. Karlin, A. Karpikov, S. Mallick, H. C. Oettinger, Y. Qian, S. Remondi, K. Sreenivasan, I. Staroselsky, R. Zhang, and B. Alder for discussions. Supported by NSF grant DHS9974289.