RSS feeds
РусскийEnglish
Issue 11, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2000

 / 

June

←  →

Reviews of topical problems


Physical principles of the generalized Boltzmann kinetic theory of gases


M.V. Lomonosov Moscow State Academy of Fine Chemical Technology, prosp. Vernadskogo 86, Moscow, 117571, Russian Federation

This paper addresses the fundamental principles of generalized Boltzmann physical kinetics, which introduces terms accounting for the variation of the distribution function over times of the order of the collision time into the Boltzmann equation. The paper is primarily aimed at clarifying the qualitative aspects of the theory whose mathematical formalism was developed in the author’s earlier work. There is a detailed discussion of how the generalized Boltzmann equation obtained by the multiscale method relates to other alternative approaches used in the development of kinetic equations. The application of the generalized Boltzmann equation to certain classical transport processes is discussed.

Fulltext pdf (572 KB)
Fulltext is also available at DOI: 10.1070/PU2000v043n06ABEH000694
PACS: 05.20.Dd, 51.10.+y (all)
DOI: 10.1070/PU2000v043n06ABEH000694
URL: https://ufn.ru/en/articles/2000/6/d/
000165057200004
Citation: Alekseev B V "Physical principles of the generalized Boltzmann kinetic theory of gases" Phys. Usp. 43 601–629 (2000)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Алексеев Б В «Физические основы обобщенной больцмановской кинетической теории газов» УФН 170 649–679 (2000); DOI: 10.3367/UFNr.0170.200006d.0649

References (75) ↓ Cited by (26) Similar articles (20)

  1. Boltzmann L Sitzungsber. Kaiserl. Akad. Wiss. 66 (2) 275 (1872)
  2. Chapman S Philos. Trans. R. Soc. London Ser. A 216 279 (1916)
  3. Chapman S Philos. Trans. R. Soc. London Ser. A 217 115 (1917)
  4. Enskog D The Kinetic Theory of Phenomena in Fairly Rare Gases (Upsala, 1917)
  5. Enskog D Svensk. Vet. Akad. Arkiv f. Math. Ast. Fys. 16 1 (1921)
  6. Boltzmann L Vorlesungen über Gastheorie 2 Teil (Leipzig: J A Barth, 1912) [Translated into English: Lectures on Gas Theory (Berkeley: Univ. of California Press, 1964)]
  7. Ehrenfest P Collected Scientific Papers (Amsterdam: North-Holland, 1959) [Translated into Russian: Otnositel’nost’, Kvanty, Statistika (Moscow: Nauka, 1972)]
  8. Ehrenfest P Collected Scientific Papers (Ed. M J Klein, Amsterdam: North-Holland Publ. Co., 1959)
  9. Landau L D, Lifshitz E M Gidrodinamika (Kurs Teoreticheskoî Fiziki; T. 6, Hydrodynamics: Course of Theoretical Physics Vol. 6, Moscow: Nauka, 1988) [Translated into English (Oxford: Pergamon Press, 1990)]
  10. Woods L C An Introduction to the Kinetic Theory of Gases and Magnetoplasmas (Oxford: Oxford Univ. Press, 1993)
  11. Cattaneo C C.R. Acad. Sci. 247 431 (1958)
  12. Jarzebski A B, Thulli J W J. Comp. Phys. 63 236 (1986)
  13. Sobolev S L J. Phys. III (France) 3 2261 (1993)
  14. Rosenau Ph J. Am. Phys. Soc. 48 (7) 655 (1993)
  15. Bogolyubov N N Problemy Dinamicheskoî Teorii v Statisticheskoî Fizike (Dynamic Theory Problems in Statistical Physics, Moscow, Leningrad: Gostekhizdat, 1946) [Translated into English: The Dynamical Theory in Statistical Physics (Delhi: Hindustan Publ. Corp., 1965)]
  16. Born M, Green H S A Proc. R. Soc. London Ser. A 188 (1012) 10 (1946)
  17. Green H S The Molecular Theory of Fluids (Amsterdam: North-Holland Publ. Co., 1952)
  18. Kirkwood J G J. Chem. Phys. 15 (1) 72 (1947)
  19. Yvon J La Theorie Statistique des Fluides et l`Equation d`Etat (Paris: Hermann, 1935)
  20. Alekseev B V Matematicheskaya Kinetika Reagiruyushchikh Gazov (Mathematical Theory of Reacting Gases, Moscow: Nauka, 1982)
  21. Vlasov A A Nelokal’naya Statisticheskaya Mekhanika (Nonlocal Statistical Mechanics, Moscow: Nauka, 1978)
  22. Slezkin N A Dokl. Akad. Nauk SSSR 79 33 (1951)
  23. Slezkin N A Dokl. Akad. Nauk SSSR 77 205 (1951)
  24. Meshcherskiî I V Dinamika Tochki Peremennoî Massy (Dynamics of a Variable-Mass Point, St. Petersburg, 1897)
  25. Vallander S V Dokl. Akad. Nauk SSSR 78 25 (1951)
  26. Shaposhnikov I G Zh. Eksp. Teor. Fiz. 21 1310 (1951)
  27. Terletskiî Ya P Zh. Eksp. Teor. Fiz. 22 506 (1952)
  28. Terletskiî Ya P Statisticheskaya Fizika (Statistical Physics, Moscow: Vyssh. Shkola, 1994) [Translated into English (Amsterdam: North-Holland, 1971)]
  29. Gibbs J W The Collected Works of J. Willard Gibbs Vol. 2 (New York: Longmans, Green and Co., 1934) [Translated into Russian (Moscow: Gostekhizdat, 1946)]
  30. Alekseev B V, in 7-e Soveshchanie po Mekhanike Reagiruyushchikh Sred. Tez. Dokl. (7th Workshop on Mechanics of Reacting Media. Abstracts, Krasnoyarsk, 1988) p. 3
  31. Alexeev B V Philos. Trans. R. Soc. London Ser. A 349 417 (1994)
  32. Alexeev B V Physica A 216 459 (1995)
  33. Woods L C, in 17th Intern. Symp. RGD. Book of Abstracts Vol. 2 (Aachen, 1990) p. 442
  34. Alexeev B V, in 17th Intern. Symp. RGD. Book of Abstracts Vol. 2 (Aachen, Germany, 1990) p. 448
  35. Alekseev B V Zh. Vychisl. Mat. Mat. Fiz. 27 730 (1987)
  36. Alekseev B V, in Mekhanika i Elektrodinamika Sploshnykh Sred (Mechanics and Electrodynamics of Continua, Ed. B V Alekseev, Moscow: Izd. Mosk. Univ., 1990) p. 110
  37. Alexeev B V, in Proc. IUTAM Symp. Aerothermochemistry of Spacecraft and Associated Hypersonic Flows (Marseille, France, 1992) p. 85
  38. Alekseev B V Teplofiz. Vys. Temp. 31 626 (1993) [High Temp. (Russia) 31 573 (1993)]
  39. Nayfeh A H Perturbation Methods (New York: John Wiley & Sons, 1973) [Translated into Russian (Moscow: Mir, 1976)]
  40. Chapman S, Cowling T G The Mathematical Theory of Non-Uniform Gases 2nd ed. (Cambridge: Cambridge Univ. Press, 1952)
  41. Elizarova T G, Chetverushkin B N, in Matematicheskoe Modelirovanie (Mathematical Simulation, Eds A A Samarskiî et al., Moscow: Nauka, 1986) p. 261
  42. Elizarova T G, Chetverushkin B N, in Intern. Symp. on Comp. Fluid Dynamics (Nagoya, Japan, 1989)
  43. Elizarova T G, in Proc. IUTAM Symp. Aerothermochemistry of Spacecraft and Associated Hypersonic Flows (Marseille, France, 1992) p. 211
  44. Reitz R D J. Comp. Phys. 42 (1) 103 (1981)
  45. Klimontovich Yu L Statisticheskaya Teoriya Otkrytykh Sistem (Statistical Theory of Open Systems, Moscow: Yanus-K, 1995) [Translated into English (Fundamental Theories of Physics, Vol. 67, Dordrecht: Kluwer Acad. Publ., 1995)]
  46. Wieser W An Existence Theorem for Perturbed Boltzmann Equation (Mathematische Forschung Institute Oberwolfach, 1982)
  47. Klimontovich Yu L Teor. Mat. Fiz. 92 312 (1992)
  48. Silin V P Vvedenie v Kineticheskuyu Teoriyu Gazov (Introduction to the Kinetic Theory of Gases, Moscow: Nauka, 1971)
  49. Chapman S, Cowling T G The Mathematical Theory of Non-Uniform Gases (Cambridge: At the Univ. Press, 1952) [Translated into Russian (Moscow: IL, 1960)]
  50. Heisenberg W Ann. Phys. (Leipzig) 74 (5) 577 (1924)
  51. Heisenberg W, in Life of Physics: Evening Lectures at the International Centre of Theoretical Physics in Triest (Wiena: IAIA, 1969) [Translated into Russian Usp. Fiz. Nauk 102 298 (1970)]
  52. Reynolds O Philos. Trans. R. Soc. London 176 123 (1894)
  53. Favre A I A, in Studies in Turbulence (Eds T B Gatski, S Sarkar, C G Speziale, New York: Springer-Verlag, 1992) p. 324
  54. Alekseev B V, Mikhaîlov V V Teplofiz. Vys. Temp. 37 274 (1999)
  55. Fedoseyev A I, Alexeev B V, in Proc. Intern. Conf. Advances in Scientific Computing Modelling (Special Proceedings of IMACS’98, Eds S K Dey, G Ziebarth, Ferrandiz, Alicante, Spain, 1998) p. 158
  56. Fedoseyev A I, Alexeev B V, in Proc. Intern. Symp. on Continuum Models and Discrete Systems (Turkey, 1998, Eds E Inan, K Z Markov, River Edge, N.J.: World Scientific Publ. Co., 1998) p. 130
  57. Koseff J R, Street R L J. Fluids Eng. 106 21 (1984)
  58. Koseff J R, Street R L Trans. SAME 106 390 (1984)
  59. Koseff J R, Street R L J. Fluids Eng. 106 285 (1984)
  60. Arnal M, Laurel O, Liek Z, Peric M, in A GAMM Workshop (Notes on Numerical Fluid Mechanics, Vol. 36, Eds M Devill, T-H Le, Yu Morchois, Braunschweig: F. Vieweg, 1992) p. 13
  61. Verstappen R W C P, Veldman A E P, in Proc. Third ECCOMAS Computational Fluid Dynamics Conf. (Paris, France, 9-13 Sept. 1996, Eds J A Dosidori et al., New York: Wiley, 1996) p. 1073
  62. Cercignani C Theory and Application of the Boltzmann Equation (Edinburgh: Scottish Academic Press, 1975)
  63. Alekseev B V, Poddoskin A B, Mikhaîlov V V, in Mekhanika i Elektrodinamika Sploshnykh Sred (Mechanics and Electrodynamics of Continua, Ed. B V Alekseev, Moscow: Izd. Mosk. Univ., 1990) p. 25
  64. Alekseev B V Dokl. Akad. Nauk SSSR 313 1078 (1990) [Sov. Phys. Dokl. 35 748 (1990)]
  65. Sirovich L, Thurber J K J. Acoust. Soc. Am. 37 329 (1965)
  66. Greenspan M J. Acoust. Soc. Am. 28 644 (1956)
  67. Meyer E, Sessler G Z. Phys. 149 (15) 15 (1957)
  68. Pekeris C L, Alterman Z, Finkelstein L, in Symp. Numerical Treatment of Ordinary Differential Equations, Integral and Integro-differential Equations of PICC (Basel: Birkhauser Verlag, 1960) p. 338
  69. Pekeris C L, Alterman Z, Finkelstein L, Frankowski K Phys. Fluids 5 1608 (1962)
  70. Longo E, Preziosi L, Bellomo N, in Aerothermochemistry of Spacecraft and Associated Hypersonic Flows. Proc. IUTAM Symp. (Marseille, France, 1992) p. 41
  71. Bourgat J F, Le Tallec P, Malinger F, Tidriri D, Qiu Y, in Aerothermochemistry of Spacecraft and Associated Hypersonic Flows. Proc. IUTAM Symp. (Marseille, France, 1992) p. 60
  72. Alekseev B V, Polev V V Teplofiz. Vys. Temp. 28 614 (1990) [High Temp. (USSR) 28 896 (1990)]
  73. Schmidt B J. Fluid Mech. 39 (2) 361 (1969)
  74. Grad H Commun. Pure Appl. Math. 2 (4) 38 (1949)
  75. Holway L H Phys. Fluids 7 (6) 141 (1964)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions