Advertisement

Finite-Volume Methods for the Solution of Euler Equations

  • A. Lerat
  • J. Sidès
Part of the Notes on Numerical Fluid Mechanics book series (NONUFM, volume 3)

Abstract

This contribution to the GAMM Workshop on Numerical Methods for the Computation of Inviscid Transonic Flow with Shock Waves is concerned with finite-volume methods to solve a pseudo-unsteady system deduced from the unsteady Euler equations by using the condition of constant total enthalpy This simplification is consistent with the steady-state solution in the present case of iso-energetic flows. The reason for the choice of finite-volume methods is their property of being exactly in conservation form so that in a balance of computed mass, momentum or energy in a domain made of mesh cells, the interior numerical fluxes cancel out two by two.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. /1/.
    Mac Cormack, R.W., and Paullay, A.J.: Computational Efficiency Achieved by Time-Splitting of Finite-Difference Operators. AIAA Paper 72–154 (1972).Google Scholar
  2. /2/.
    Rizzi, A.W. and Inouye, M.–A Time-Split Finite-Volume Technique for Three-Dimensional Blunt-Body Flow. AIAA Journal 11, p. 1478–1485 (1973).ADSzbMATHCrossRefGoogle Scholar
  3. /3/.
    Mac Cormack, R.W., Rizzi, A.W., and Inouye, M. - Steady Supersonic Flowfields with Embedded Subsonic Regions. In “Computational Methods and Problems in Aeronautical Fluid Dynamics” edited by Hewitt, B.L. et al., Academic Press (1976).Google Scholar
  4. /4/.
    Lax, P.D., and Wendroff, B.–Systems of Conservation Laws. Comm. Pure Appl. Math. 13, p. 217–237 (1960).MathSciNetzbMATHCrossRefGoogle Scholar
  5. /5/.
    Lerat, A., and Sidès, J.–Numerical Simulation of Unsteady Transonic Flows Using the Euler Equations in Integral Form. 21st Israel Annual Conference on Aviation and Astronautics. Feb. 1979. To appear. Provisional edition: TP ONERA n° 1979–10.Google Scholar
  6. /6/.
    Viviand, H., and Veuillot, J.P.–Méthodes pseudo-instationnaires pour le calcul d’écoulements transsoniques. Publication ONERA n° 1978–4 (1978).Google Scholar
  7. /7/.
    Chattot, J.C., Coulombeix, C., and da Silva Tomé, C: lements transsoniques autour d’ailes. La Recherche p. 143–159 (1978).Google Scholar
  8. /8/.
    Jameson, A. - Three Dimensional Flows Around Airfoi is with Shocks. Lecture Notes in Computer Science 11, p. 185–212 (1 974).Google Scholar
  9. /9/.
    Lerat, A., and Peyret, R.–The Problem of Spurious Oscillations in the -Numerical Solution of the Equations of Gas Dynamics. Lecture Notes in Physics 35, p. 251–256 (1975).MathSciNetADSCrossRefGoogle Scholar
  10. /10/.
    Lerat, A., and Peyret, R.–Propriétés dispersives et dissipatives d’une classe de schémas aux différences pour les systèmes hyperboliques non linéaires. La Recherche Aérospatiale n° 1975–2, p. 61–79 (1975).MathSciNetGoogle Scholar
  11. /11/.
    Livne, A.–Seven-Point Difference Schemes for Hyperbolic Equations. Math. Comput. 29, p. 425–433 (1975).CrossRefGoogle Scholar
  12. /12/.
    Lerat, A., and Sidès, J. - Calcul numérique d’écoulements transsoniques instationnaires. AGARD Conf. Proceed. 226, p.15.1–15.10 (1977). English translation available as TP ONERA 1977–19E.Google Scholar

Copyright information

© Springer Fachmedien Wiesbaden 1981

Authors and Affiliations

  • A. Lerat
    • 1
    • 2
    • 3
  • J. Sidès
    • 1
  1. 1.Office National d’Etudes et de Recherches Aérospatiales (ONERA)ChâtillonFrance
  2. 2.Ecole Nationale Supérieure d’Arts et MétiersParis Cédex 13France
  3. 3.Laboratoire de Mécanique théoriqueUniversité Paris VI - Consultant at ONERAFrance

Personalised recommendations