Skip to main content
SpringerLink
Log in

Analysis of thermal and shear waves according to BKG kinetic model

  • Original Papers
  • Published:
Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

Abstract

The dispersion relation for waves propagating in a gas according to kinetic theory is studied. Collisions are described by means of the model proposed by Bhatnagar, Gross and Krook (BGK). New numerical results for shear and thermal waves are given. The high frequency behaviour of the solutions obtained through analytic continuation of the dispersion relation is discussed.

Sommario

Si studia la relazione di dispersione per le onde che si propagano in un gas secondo la teoria cinetica. Gli urti sono descritti mediante il modello di Bhatnagar, Gross e Krook (BGK). Si danno risultati numerici nuovi sulle onde termiche e di taglio e si discute il comportamento alle alte frequenze delle soluzioni ottenute dal prolungamento analitico della relazione di dispersione.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C. Cattaneo, Atti Semin. Mat. Fis. Univ. Modena3, 3 (1948).

    Google Scholar 

  2. C. Cattaneo, C. R. Acad. Sci.247, 431 (1958).

    Google Scholar 

  3. P. Vernotte, C. R. Acad. Sci.246, 3154 (1958).

    Google Scholar 

  4. M. Kranys, Nuovo Cimento B50, 48 (1967).

    Google Scholar 

  5. M. Chester, Phys. Rev.131, 2013 (1963).

    Google Scholar 

  6. R. J. Swenson, Am. J. Phys.46, 76 (1978).

    Google Scholar 

  7. I. Müller, Z. Phys.198, 329 (1967).

    Google Scholar 

  8. C. Cercignani, Phys. Rev. Lett.50, 1122 (1983).

    Google Scholar 

  9. L. Sirovich and J. K. Thurber, inRarefied gas dynamics, J. A. Laurman, ed., Vol. I, p. 21. Academic Press, New York 1963.

    Google Scholar 

  10. L. Sirovich and J. K. Thurber, J. Acoust. Soc. Am.37, 329 (1965).

    Google Scholar 

  11. C. Cercignani,Elementary solutions of linearized kinetic models and boundary value problems in kinetic theory. Brown University Report 1965.

  12. P. F. Bhatnagar, E. P. Gross and M. Krook, Phys. Rev.94, 511 (1954).

    Google Scholar 

  13. C. Cercignani and F. Sernagiotto, Ann. Phys. (N. Y.).30, 154 (1964).

    Google Scholar 

  14. C. Cercignani, Ann. Phys. (N. Y.).40, 454 (1966).

    Google Scholar 

  15. K. Aoki and C. Cercignani, I, Z. angew. Math. Phys.35, 127 (1984) and II, Z. Angew. Math. Phys.35, 345 (1984).

    Google Scholar 

  16. C. Cercignani,Mathematical methods in kinetic theory. Plenum Press, New York, and McMillan, London 1969.

    Google Scholar 

  17. C. Cercignani,Theory and application of the Boltzmann equation. Scottish Academic Press, Edinburgh and Elsevier, New York 1975.

    Google Scholar 

  18. N. I. Muskhelishvili,Singular integral equations. Noordhoff, Groningen 1953.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipt. di Matematica, Politecnico di Milano, Milano

    Carlo Cercignani

  2. Dipt. di Matematica, Università di Catania, Catania, Italy

    Armando Majorana

Authors
  1. Carlo Cercignani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Armando Majorana
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cercignani, C., Majorana, A. Analysis of thermal and shear waves according to BKG kinetic model. Z. angew. Math. Phys. 36, 699–711 (1985). https://doi.org/10.1007/BF00960381

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00960381

Keywords

Search

Navigation