A Discrete Kinetic Model Resembling Retrograde Gases

  • K. Piechór
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


A discrete kinetic system modelling some properties of retrograde fluids is proposed. Plane shock waves corresponding to the model Euler, Navier-Stokes and kinetic approximations are studied. It turns out that in some cases the number density must decrease in order to obtain a stable shock wave. The shock structure and its thickness in the kinetic approximation are determined and are consistent those of Cramer and Kluwick [14].


Shock Wave Euler Equation Shock Structure Plane Shock Wave Euler Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Meier G.E.A., Thompson P.A. in Lecture Notes in Physics, vol. 235 (1985), 103–114. Springer-VerlagGoogle Scholar
  2. 2.
    Gatignol R., Théorie Cinétique des Gaz â Répartition Discrete de Vitesses, Lecture Notes in Physics, vol.36, (1975), Springer-VerlagGoogle Scholar
  3. 3.
    Platkowski T., Illner R., SIAM Review, vol. 30 (1988), 213–255CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Broadwell J.E., Phys. Fluids, vol.7 (1964), 1243–1247CrossRefMATHADSGoogle Scholar
  5. 5.
    Caflish R.E., Comm. Pure Appl. Math. vol. 32 (1979), 521–554Google Scholar
  6. 6.
    Monaco R., Acta Mech. vol. 55 (1985), 239–251CrossRefMATHADSMathSciNetGoogle Scholar
  7. 7.
    Monaco R., Proc. 15th RGP Symp., Grado; ed. V.Boffi, C.Cercignani, Teubner, 1986, 245–254Google Scholar
  8. 8.
    Platkowski T., Mech. Res. Comm. vol. 14 (1987), 347–354CrossRefMATHGoogle Scholar
  9. 9.
    Platkowski T., in Discrete Kinetic Theory, Lattice Gas Dynamics and Foundations of Hydrodynamics, ed. R.Monaco, World Scientific, 1989, 248–255Google Scholar
  10. 10.
    Piechór K., To be published in Archive of MechanicsGoogle Scholar
  11. 11.
    Thompson P.A., Lambrakis K.C., Journal Fluid Mech. vol. 60 (1973), 187–208CrossRefMATHADSGoogle Scholar
  12. 12.
    Lax P.D., Comm. Pure Appl. Math. vol. 10 (1957), 537–566MATHMathSciNetGoogle Scholar
  13. 13.
    Liu T.-P., Memoirs of AMS, No 240, 1981Google Scholar
  14. 14.
    Cramer M.S., Kluwick A., Journal Fluid Mech. vol. 142 (1984), 9–37CrossRefMATHADSMathSciNetGoogle Scholar
  15. 15.
    Chaves H., Hermann E., Meier G.E.A., Kowalczyk P., Walenta Z.A., To be published.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • K. Piechór
    • 1
  1. 1.Institute of Applied Mathematics and MechanicsUniversity of WarsawWarszawa, Pkin, p.IXPoland

Personalised recommendations