On the validity of hydrodynamics in plane Poiseuille flows

Physica A: Statistical Mechanics and its Applications

Volumn 240, Issue 1-2, 1997, Pages 255-267

  Malek Mansour, M ^a   Baras, F ^a   Garcia, Alejandro L ^b,c  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

^c SAN JOSE STATE UNIVERSITY   (United States)

Author keywords

BGK approximation; Boltzmann equation; Direct simulation Monte Carlo; Hydrodynamics; Kinetic theory; Molecular dynamics

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; GAS DYNAMIC LASERS; KINETIC THEORY OF GASES; LAMINAR FLOW; MOLECULAR DYNAMICS; MONTE CARLO METHODS; REYNOLDS NUMBER; SUBSONIC FLOW;

BOLTZMAN EQUATION; POISEUILLE FLOWS;

HYDRODYNAMICS;

EID: 0031161869     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4371(97)00149-0     Document Type: Article

References (47)

1. B.J. Alder, T.E. Wainwright, in: I. Prigogine (Ed.), Transport Processes in Statistical Mechanics, Interscience, New York, 1958; B.J. Alder, T.E. Wainwright, J. Chem. Phys. 31 (1959) 459; B.J. Alder, T.E. Wainwright, J. Chem. Phys. 33 (1960) 1439.
2. B.J. Alder, T.E. Wainwright, in: I. Prigogine (Ed.), Transport Processes in Statistical Mechanics, Interscience, New York, 1958; B.J. Alder, T.E. Wainwright, J. Chem. Phys. 31 (1959) 459; B.J. Alder, T.E. Wainwright, J. Chem. Phys. 33 (1960) 1439.
3. B.J. Alder, T.E. Wainwright, in: I. Prigogine (Ed.), Transport Processes in Statistical Mechanics, Interscience, New York, 1958; B.J. Alder, T.E. Wainwright, J. Chem. Phys. 31 (1959) 459; B.J. Alder, T.E. Wainwright, J. Chem. Phys. 33 (1960) 1439.
4. B.J. Alder, T.E. Wainwright, Phys. Rev. A 1 (1970) 18; N.H. March, M.P. Tosi, Atomic Dynamics in Liquids, Dover, New York, 1976; S. Hess, C. Aust, L. Bennett, M. Kröger, C. Pereira Borgmeyer, T. Weider, Physica A 240 (1997) 126, these proceedings.
5. B.J. Alder, T.E. Wainwright, Phys. Rev. A 1 (1970) 18; N.H. March, M.P. Tosi, Atomic Dynamics in Liquids, Dover, New York, 1976; S. Hess, C. Aust, L. Bennett, M. Kröger, C. Pereira Borgmeyer, T. Weider, Physica A 240 (1997) 126, these proceedings.
6. B.J. Alder, T.E. Wainwright, Phys. Rev. A 1 (1970) 18; N.H. March, M.P. Tosi, Atomic Dynamics in Liquids, Dover, New York, 1976; S. Hess, C. Aust, L. Bennett, M. Kröger, C. Pereira Borgmeyer, T. Weider, Physica A 240 (1997) 126, these proceedings.
7. W.G. Hoover, Computational Statistical Mechanics, Elsevier Sc. Publ., Amsterdam, 1991; D.J. Evans, G.P. Moriss, Eds., Statistical Mechanics of Non-equilibrium Liquids, Academic Press, New York, 1990.
8. W.G. Hoover, Computational Statistical Mechanics, Elsevier Sc. Publ., Amsterdam, 1991; D.J. Evans, G.P. Moriss, Eds., Statistical Mechanics of Non-equilibrium Liquids, Academic Press, New York, 1990.
9. M. Mareschal, Ed., Microscopic Simulations of Complex Flows, Plenum, Nato ASI series, vol. 236, 1990; M. Mareschal, B. Holian, Eds., Microscopic Simulations of Complex Hydrodynamic Phenomena, Plenum, Nato ASI series, vol. 292, 1992.
10. M. Mareschal, Ed., Microscopic Simulations of Complex Flows, Plenum, Nato ASI series, vol. 236, 1990; M. Mareschal, B. Holian, Eds., Microscopic Simulations of Complex Hydrodynamic Phenomena, Plenum, Nato ASI series, vol. 292, 1992.
11. D.C. Rapaport, The Art of Molecular Dynamics Simulation, Cambridge University Press, Cambridge, 1995.
12. D.C. Rapaport, E. Clementi, Phys. Rev. Lett. 57 (1987) 695; L. Hannon, G. Lie, E. Clementi, J. Sc. Comp. 1 (1986) 145; D.C. Rapaport, Phys. Rev. A 36 (1987) 3288; E. Meiburg, Phys. Fluids 29 (1986) 3107.
13. D.C. Rapaport, E. Clementi, Phys. Rev. Lett. 57 (1987) 695; L. Hannon, G. Lie, E. Clementi, J. Sc. Comp. 1 (1986) 145; D.C. Rapaport, Phys. Rev. A 36 (1987) 3288; E. Meiburg, Phys. Fluids 29 (1986) 3107.
14. D.C. Rapaport, E. Clementi, Phys. Rev. Lett. 57 (1987) 695; L. Hannon, G. Lie, E. Clementi, J. Sc. Comp. 1 (1986) 145; D.C. Rapaport, Phys. Rev. A 36 (1987) 3288; E. Meiburg, Phys. Fluids 29 (1986) 3107.
15. D.C. Rapaport, E. Clementi, Phys. Rev. Lett. 57 (1987) 695; L. Hannon, G. Lie, E. Clementi, J. Sc. Comp. 1 (1986) 145; D.C. Rapaport, Phys. Rev. A 36 (1987) 3288; E. Meiburg, Phys. Fluids 29 (1986) 3107.
16. M. Mareschal, E. Kestemont, Nature 323 (1987) 427; M. Mareschal, E. Kestemont, J. Stat. Phys. 48 (1987) 1187; D.C. Rapaport, Phys. Rev. Lett. 60 (1988) 2480.
17. M. Mareschal, E. Kestemont, Nature 323 (1987) 427; M. Mareschal, E. Kestemont, J. Stat. Phys. 48 (1987) 1187; D.C. Rapaport, Phys. Rev. Lett. 60 (1988) 2480.
18. M. Mareschal, E. Kestemont, Nature 323 (1987) 427; M. Mareschal, E. Kestemont, J. Stat. Phys. 48 (1987) 1187; D.C. Rapaport, Phys. Rev. Lett. 60 (1988) 2480.
19. D.C. Rapaport, Phys. Rev. A 43 (1991) 7046; D.C. Rapaport, Phys. Rev. A 46 (1992) R6150.
20. D.C. Rapaport, Phys. Rev. A 43 (1991) 7046; D.C. Rapaport, Phys. Rev. A 46 (1992) R6150.
21. W.G. Hoover, Phys. Rev. Lett. 42 (1979) 1531; B.L. Holian, W.G. Hoover, B. Moran, G.K. Straub, Phys. Rev. A 22 (1980) 2798; B.L. Holian, Phys. Rev. A 37 (1988) 2562.
22. W.G. Hoover, Phys. Rev. Lett. 42 (1979) 1531; B.L. Holian, W.G. Hoover, B. Moran, G.K. Straub, Phys. Rev. A 22 (1980) 2798; B.L. Holian, Phys. Rev. A 37 (1988) 2562.
23. W.G. Hoover, Phys. Rev. Lett. 42 (1979) 1531; B.L. Holian, W.G. Hoover, B. Moran, G.K. Straub, Phys. Rev. A 22 (1980) 2798; B.L. Holian, Phys. Rev. A 37 (1988) 2562.
24. M. Mareschal, M. Malek Mansour, A. Puhl, E. Kestemont, Phys. Rev. Lett. 61 (1988) 2550; A. Puhl, M. Malek Mansour, M. Mareschal, Phys. Rev. A 40 (1989) 1999.
25. M. Mareschal, M. Malek Mansour, A. Puhl, E. Kestemont, Phys. Rev. Lett. 61 (1988) 2550; A. Puhl, M. Malek Mansour, M. Mareschal, Phys. Rev. A 40 (1989) 1999.
26. J. Koplik, J.R. Banavar, Annu. Rev. Fluid Mech. 27 (1995) 257.
27. J.C. Maxwell, Philos. Trans. London 70 (1867) 231.
28. J. Koplik, J.R. Banavar, J.F. Willemsen, Phys. Fluids A 1 (1989) 781; D.L. Morris, L. Hannon, A.L. Garcia, Phys. Rev. A 46 (1992) 5279.
29. J. Koplik, J.R. Banavar, J.F. Willemsen, Phys. Fluids A 1 (1989) 781; D.L. Morris, L. Hannon, A.L. Garcia, Phys. Rev. A 46 (1992) 5279.
30. D.C. Wadsworth, Phys. Fluids A 5 (1993) 1831.
31. M. Malek Mansour, F. Baras, Physica A 188 (1992) 253.
32. L.D. Landau, E.M. Lifshitz, Fluid Mechanics, Pergamon, Oxford, 1959.
33. C. Cercignani, The Boltzmann Equation and its Applications, Springer, New York, 1988; C. Cercignani, Mathematical Methods in Kinetic Theory, Plenum, New York, 1990.
34. C. Cercignani, The Boltzmann Equation and its Applications, Springer, New York, 1988; C. Cercignani, Mathematical Methods in Kinetic Theory, Plenum, New York, 1990.
35. G.N. Patterson, Molecular Flow of Gases, Wiley, New York, 1956; V.P. Shidlovskii, Introduction to Dynamics of Rarefied Gases, Elsevier, New York, 1967.
36. G.N. Patterson, Molecular Flow of Gases, Wiley, New York, 1956; V.P. Shidlovskii, Introduction to Dynamics of Rarefied Gases, Elsevier, New York, 1967.
37. E.H. Kennard, Kinetic Theory of Gases, McGraw-Hill, New York, 1938; D.K. Bhattacharya, G.C. Lie, Phys. Rev. Lett. 62 (1989) 897.
38. E.H. Kennard, Kinetic Theory of Gases, McGraw-Hill, New York, 1938; D.K. Bhattacharya, G.C. Lie, Phys. Rev. Lett. 62 (1989) 897.
39. G.A. Bird, Molecular Gas Dynamics, Clarendon, Oxford, 1976; G.A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon, Oxford, 1994.
40. G.A. Bird, Molecular Gas Dynamics, Clarendon, Oxford, 1976; G.A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon, Oxford, 1994.
41. L. Hannon, G. Lie, E. Clementi, Phys. Lett. A 119 (1986) 174.
42. S. Chapman, T.G. Cowling, The Mathematical Theory of Non-Uniform Gases, Cambridge University Press, Cambridge, 1960.
43. J.H. Ferziger, H.G. Kapper, Mathematical Theory of Transport Processes in Gases, North-Holland, Amsterdam, 1972.
44. E. Salomons, M. Mareschal, Phys. Rev. Lett. 69 (1992) 269.
45. M. Tij, A. Santos, J. Stat. Phys. 76 (1994) 1399.
46. A. Santos, J.J. Brey, C.S. Kim, J.W. Dufty, Phys. Rev. A 39 (1989) 320; C.S. Kim, J.W. Dufty, A. Santos, J.J. Brey, Phys. Rev. A 40 (1989) 7165.
47. A. Santos, J.J. Brey, C.S. Kim, J.W. Dufty, Phys. Rev. A 39 (1989) 320; C.S. Kim, J.W. Dufty, A. Santos, J.J. Brey, Phys. Rev. A 40 (1989) 7165.