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On the equations of multi-component perfect of real gas inviscid flow

Numerical Analysis

Part of the Lecture Notes in Mathematics book series (LNM,volume 1402)

Keywords

  • Riemann Problem
  • Contact Discontinuity
  • Riemann Solver
  • Riemann Invariant
  • Specific Heat Ratio

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References

  1. R. ABGRALL, “Généralisation du schéma de Roe pour le calcul d'écoulements de mélanges de gaz à concentrations variables”, to appear in La Recherche Aérospatiale.

    Google Scholar 

  2. R. ABGRALL, “Preliminary results on the extension of Roe's scheme to a class of real gas mixtures”, to appear.

    Google Scholar 

  3. R. ABGRALL, private communication.

    Google Scholar 

  4. R. ABGRALL & J. L. MONTAGNE, “Généralisation du schéma d'Osher pour le calcul d'écoulements de mélanges de gaz à concentrations variables et de gaz réels”, submitted to La Recherche Aérospatiale.

    Google Scholar 

  5. J. A. BEATTIE & I. OPPENHEIM, “Principles of thermodynamics”, Studies in modern thermodynamics, 2, Elsevier, Amsterdam, (1979).

    Google Scholar 

  6. F. BENKHALDOUN, A. DERVIEUX, G. FERNANDEZ, H. GUILLARD & B. LARROUTUROU, “Some finite-element investigations of stiff combustion problems: mesh adaption and implicit time-stepping”, Mathematical modelling in combustion and related topics, Brauner & Schmidt-Lainé eds., pp. 393–409, NATO ASI Series E, Nijhoff, Doordrecht, (1988).

    Google Scholar 

  7. A. BOURGEADE, “Quelques méthodes numériques pour le traitement des écoulements réactifs”, CEA Report CEA-N-2570, (1988).

    Google Scholar 

  8. J. D. BUCKMASTER & G. S. S. LUDFORD, “Theory of laminar flames”, Cambridge Univ. Press, Cambridge, (1982).

    CrossRef  MATH  Google Scholar 

  9. G. V. CANDLER & R. W. McCORMACK, “The computation of hypersonic flows in chemical and thermal nonequilibrium”, Paper N o 107, Third National Aero-Space Plane Technology Symposium, (1987).

    Google Scholar 

  10. D. CHARGY, A. DERVIEUX & B. LARROUTUROU, “Upwind adaptive finite-element investigations of two-dimensional transonic reactive flows”, to appear.

    Google Scholar 

  11. P. COLELLA & H. M. GLAZ, “Efficient solution algorithms for the Riemann problem for real gases”, J. Comp. Phys., 59, pp. 264–289, (1985).

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. R. COURANT & K. O. FRIEDRICHS, “Supersonic flow and shock waves”, Appl. Math. Sciences, 21, Springer Verlag, New-York, (1948).

    Google Scholar 

  13. A. DERVIEUX, “Steady Euler simulations using unstructured meshes”, Partial differential equations of hyperbolic type and applications, Geymonat ed., pp. 33–111, World Scientific, Singapore, (1987).

    CrossRef  Google Scholar 

  14. J. A. DESIDERI, N. GLINSKY & E. HETTENA, “Hypersonic reactive flow computations”, to appear in Computers and Fluids.

    Google Scholar 

  15. G. FERNANDEZ, “Implicit conservative upwind schemes for strongly transient flows”, INRIA Report 873, (1988).

    Google Scholar 

  16. G. FERNANDEZ & B. LARROUTUROU, “On the use of hyperbolic schemes for multi-component Euler flows”, proceedings of the Second Int. Conf. on hyperbolic problems, to appear.

    Google Scholar 

  17. L. FEZOUI, “Résolution des équations d'Euler par un schéma de Van Leer en éléments finis”, INRIA Report 358, (1985).

    Google Scholar 

  18. L. FEZOUI & B. LARROUTUROU, “Upwind conservative schemes for multi-component perfect or real gas flows”, INRIA Report, to appear.

    Google Scholar 

  19. L. FEZOUI & B. STOUFFLET, ‘A class of implicit upwind schemes for Euler simulation with unstructured meshes”, to appear in J. Comp. Phys..

    Google Scholar 

  20. H. GILQUIN, “Analyse numérique d'un problème hyperbolique multidimensionnel en dynamique des gaz avec frontières mobiles”, Thesis, Université de Saint-Etienne, (1984).

    Google Scholar 

  21. P. GLAISTER, “An approximate linearised Riemann solver for the Euler equations for real gases”, J. Comp. Phys., 74, pp. 382–408, (1988).

    CrossRef  MATH  Google Scholar 

  22. J. GLIMM, “Solutions in the large for non linear hyperbolic systems of equations”, Comm. Pure Appl. Math., 18, pp. 697–715, (1965).

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. S. K. GODUNOV, “A difference scheme for numerical computation of discontinuous solutions of equations of fluid dynamics”, Math. Sbornik, 47, pp. 271–306, (1959) (in russian).

    MathSciNet  MATH  Google Scholar 

  24. N. A. GOKCEN, “Thermodynamics”, Techscience Inc., Hawthorne, (1975).

    Google Scholar 

  25. A. HABBAL, A. DERVIEUX, H. GUILLARD & B. LARROUTUROU, “Explicit calculations of reactive flows with an upwind finite-element hydrodynamical code”, INRIA Report 690, (1987).

    Google Scholar 

  26. A. HARTEN, P. D. LAX & B. VAN LEER, “On upstream differencing and Godunov type schemes for hyperbolic conservation laws”, SIAM Review, 25, pp. 35–61, (1983).

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. B. LARROUTUROU, “Introduction to mathematical and numerical modelling in gaseous combustion”, Applied Mathematics, Gordon and Breach, to appear.

    Google Scholar 

  28. P. D. LAX, “Hyperbolic systems of conservation laws and the mathematical theory of shock waves”, CBMS regional conference series in applied mathematics, 11, SIAM, Philadelphia, (1972).

    Google Scholar 

  29. A. LERAT, “Propriété d'homogénéité et décomposition des flux en dynamique des gaz”, J. Méca. Théor. Appl., 2, (2), pp. 185–213, (1983).

    MathSciNet  MATH  Google Scholar 

  30. M. S. LIOU, B. VAN LEER & J. S. SHUEN, “Splitting of inviscid fluxes for real gases”, NASA Technical memorandum 100856, (1988).

    Google Scholar 

  31. T. P. LIU, “The Riemann problem for general systems of conservation laws”, J. Diff. Equ., 18, pp. 218–234, (1975).

    CrossRef  MathSciNet  MATH  Google Scholar 

  32. A. MAJDA, “High Mach number combustion”, Combustion and chemical reactors, Ludford ed., pp. 109–184, Lecture in Appl. Math., 24, (1), AMS, Providence, (1986).

    Google Scholar 

  33. J. L. MONTAGNE, H. C. YEE & M. VINOKUR, “Comparative study of high-resolution shock capturing schemes for a real gas”, NASA Technical memorandum 100004, (1987).

    Google Scholar 

  34. S. OSHER & F. SOLOMON, “Upwind schemes for hyperbolic systems of conservation laws”, Math. Comp., 38, (158), pp. 339–374, (1982).

    CrossRef  MathSciNet  MATH  Google Scholar 

  35. P. L. ROE, “Approximate Riemann solvers, parameters vectors and difference schemes”, J. Comp. Phys., 43, pp. 357–372, (1981).

    CrossRef  MathSciNet  MATH  Google Scholar 

  36. J. SMOLLER, “Shock waves and reaction-diffusion equations”, Springer Verlag, New-York, (1983).

    CrossRef  MATH  Google Scholar 

  37. G. A. SOD, “A survey of several finite-difference methods for systems of nonlinear hyperbolic conservation laws”, J. Comp. Phys., 27, pp. 1–31, (1977).

    CrossRef  MathSciNet  MATH  Google Scholar 

  38. J. L. STEGER & R. F. WARMING, “Flux vector splitting for the inviscid gas dynamic equations with applications to finite-difference methods”, J. Comp. Phys., 40, (2), pp. 263–293, (1981).

    CrossRef  MathSciNet  MATH  Google Scholar 

  39. B. VAN LEER, “Towards the ultimate conservative difference scheme III — Upstream centered finite-difference schemes for ideal compressible flow”, J. Comp. Phys., 23, pp. 263–275, (1977).

    CrossRef  MATH  Google Scholar 

  40. B. VAN LEER, “Flux-vector splitting for the Euler equations”, Eighth international conference on numerical methods in fluid dynamics, Krause ed., pp. 507–512, Lecture notes in physics, 170, Springer-Verlag, (1982).

    Google Scholar 

  41. B. VAN LEER, J. L. THOMAS, P. L. ROE & R. W. NEWSOME, “A comparison of numerical flux formulas for the Euler and Navier-Stokes equations”, AIAA paper 87-1104, (1987).

    Google Scholar 

  42. G. VIJAYASUNDARAM, “Transonic flow simulations using an upstream-centered scheme of Godunov in finite elements”, J. Comp. Phys., 63, (1986).

    Google Scholar 

  43. F. A. WILLIAMS, “Combustion theory”, second edition, Benjamin Cummings, Menlo Park, (1985).

    Google Scholar 

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Larrouturou, B., Fezoui, L. (1989). On the equations of multi-component perfect of real gas inviscid flow. In: Carasso, C., Charrier, P., Hanouzet, B., Joly, JL. (eds) Nonlinear Hyperbolic Problems. Lecture Notes in Mathematics, vol 1402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083869

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  • DOI: https://doi.org/10.1007/BFb0083869

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