Journal of Statistical Physics

, Volume 99, Issue 1–2, pp 115–140 | Cite as

Shock Waves for a Discrete Velocity Gas Mixture

  • Carlo Cercignani
  • Henri Cornille


We introduce three new models for a binary mixture which have only 6+5, 8+5, and 12+5 velocities and study the properties of the first two. The models are plane and have five conservation laws as expected for a binary mixture in the plane case. We look for exact solutions corresponding to traveling waves, which turn out to have the properties of a structured shock wave, and study their properties. Particular attention is paid to the overshoots in the profiles of internal energy for the mixture and the two components.

shock wave structure discrete velocity models mixtures 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. V. Bobylev and C. Cercignani, Discrete velocity models for mixtures, J. Stat. Phys. 91:327–342 (1998); 21st International Symposium on Rarefied Gas Dynamics, RGD I:71–78 (1999).Google Scholar
  2. 2.
    H. Cornille, JMP 28:1567–79 (1987); JPA: Math. Gen. 31:671–86 (1998).Google Scholar
  3. 3.
    H. Cornille, Trans. Theo. Stat. Phys. 24:709–29 (1995) and 26:359–71 (1997); WASCOM95, S. Rionero and T. Ruggeri, eds. (World Scientific, 82–91, 1995); J. Stat. Phys. 81:335–46 (1995); H. Cornille and A. d'Almeida, J. Math. Phys. 37:5476–95 (1998).Google Scholar
  4. 4.
    G. L. Caraffini and G. Spiga, Trans. Theo. Stat. Phys. 23:9–25, (1994); R. Monaco and L. Preziosi, Fluid Dynamic Applications of the Discrete Boltzmann Equation (World Scientific, Singapore, 1991).Google Scholar
  5. 5.
    H. Cabannes, The discrete Boltzmann equation, Lecture notes (University of California, Berkeley, 1980).Google Scholar
  6. 6.
    G. A. Bird, Shock wave structure in gas mixture, in RGD, H. Ogushi, ed., pp. 175–182 (University of Tokyo Press, 1984); The search for solutions in RGD, in RGD, J. Harvey and G. Lord, eds, Vol. 2, 753–762 (Oxford University Press, Oxford, 1995).Google Scholar
  7. 7.
    Ching Shen, Shock wave in gas mixtures with internal energy relaxation (1986).Google Scholar
  8. 8.
    C. Cercignani, On the thermodynamics of a discrete velocity gas, Transp. Th. Stat. Phys. 23:1–8 (1994); Temperature, entropy and kinetic theory, J. Stat. Phys. 87:1097–1109 (1997).Google Scholar

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Carlo Cercignani
    • 1
  • Henri Cornille
    • 2
  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
  2. 2.Service de Physique Théorique, CE SaclayGif-sur-YvetteFrance

Personalised recommendations