On the symmetric conservative form of a binary reacting mixture

  • Mariano Torrisi
  • Rita Tracinà
Original Papers
  • 21 Downloads

Summary

We consider the system governing a non equilibrium gas flow with a chemical reaction, neglecting, as usual for detonation phenomena, transport effects. It is shown that it is possible to put the system in symmetric and conservative form. Moreover we write the generating shock function and discuss it in the case of a polytropic mixture.

Keywords

Mathematical Method Conservative Form Transport Effect Detonation Phenomenon Shock Function 

Sommario

Si considéra il sistema di equazioni che governano un gas in cui avviene una reazione chimica trascurando, com'é usuale per i fenomeni di detonazione, gli effetti di trasporto. Si fa vedere che é possibile mettere il sistema in forma simmetrica e conservativa. Inoltre viene scritta la funzione génératrice degli urti che viene discussa nel caso di una miscela di gas politropici.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    F. A. Williams,Combustion Theory. The Benjamin/Cummings Publ. Co., Menlo Park, California 1985.Google Scholar
  2. [2]
    W. Fickett and W. C. Davis,Detonation. University of California Press, Berkeley 1979.Google Scholar
  3. [3]
    K. O. Friedrichs and P. D. Lax,Systems of conservation equations with a convex extension. Proc. Nat. Acad. Sci. U.S.A.,68, 1686–1688 (1971).Google Scholar
  4. [4]
    S. K. Godunov,An interesting class of quasi-linear systems, Soviet Math.2, 4, 947–949 (1961).Google Scholar
  5. [5]
    G. Boillat,Sur l'existence et la recherche d'équations de conservation supplémentaires pour les systèmes hyperboliques. C.R. Acad. Sci. Paris,278, Série A, 909–912 (1974).Google Scholar
  6. [6]
    T. Ruggeri and A. Strumia,Main field and convex covariant density for quasi-linear hyperbolic systems. Ann. Inst. Henri Poincaré34, 65–84 (1981).Google Scholar
  7. [7]
    A. E. Fischer and J. E. Marsden,The Einstein evolution equations as a first order quasi-linear symmetric hyperbolic system. Commun. Math. Phys.,28, 1–38 (1972).Google Scholar
  8. [8]
    P. D. Lax,Shock waves and entropy, in:Contributions to Nonlinear Functional Analysis. Ed. by E. H. Zarantonello, Academic Press, New York 1971.Google Scholar
  9. [9]
    G. Boillat.Sur une function croissante comme l'entropie et génératrice des chocs dans les systèmes hyperboliques. C.R. Acad. Sci. Paris,283, Série A, 409–412 (1976).Google Scholar
  10. [10]
    G. Boillat and T. Ruggeri,Limite de la vitesse des chocs dans les champs à densité d'énergie convexe. C.R. Acad. Sci. Paris,289, Série A, 257–258 (1979).Google Scholar
  11. [11]
    W. G. Vincenti and C. H. Kruger,Introduction to Physical Gasdynamics. R. E. Krieger Publ., New York 1977.Google Scholar
  12. [12]
    J. D. Buckmaster and G. S. S. Ludford,Theory of Laminar Flames. Cambridge University Press, 1982.Google Scholar
  13. [13]
    M. Torrisi,Conservation laws and growth of discontinuities in a reactive polytropic gas. ZAMP,38, 117–128 (1987).Google Scholar
  14. [14]
    I. Prigogine and G. Nicolis,Le strulture dissipative. Sansoni, Firenze 1982.Google Scholar
  15. [15]
    G. B. Whitham,Linear and Non Linear Waves. John Wiley and Sons, New York 1974.Google Scholar
  16. [16]
    G. Boillat,Chocs caractéristiques. C.R. Acad. Sci. Paris,274, Série A, 1018–1021 (1972).Google Scholar
  17. [17]
    D. Fusco,Alcune considerazioni sulle onde d'urto in fluidodinamica. Atti Sem. Mat. Fis. Univ. Modena,28, 223–236 (1979).Google Scholar
  18. [18]
    T. Ruggeri,In Lectures at VI Scuola Estiva di Fisica Matematica del C.N.R. (G.N.F.M.). Ravello (1981).Google Scholar

Copyright information

© Birkhäuser Verlag 1991

Authors and Affiliations

  • Mariano Torrisi
    • 1
  • Rita Tracinà
    • 1
  1. 1.Dipartimento di MatematicaUniversité di CataniaCataniaItaly

Personalised recommendations