Relaxation Method for the Full-Potential Equation

  • Jean-Jacques Chattot
  • Colette Coulombeix
Part of the Notes on Numerical Fluid Mechanics book series (NONUFM, volume 3)


In this paper a brief and fragmentary account is made of our contribution to the GAMM workshop on Numerical Methods for the Computation of Inviscid Transonic Flow with Shock Waves, since the main objective is the comparison, during the actual workshop, of the results obtained by various methods. Emphasis however is put in the first paragraph on the basic assumptions underlying the mathematical modelling of transonic flow, using the full-potential equation. In particular the semi-conservative form of the equation, used in the method, is derived. In the second part, the discretization schemes and the solution algorithm are sketched and reference is given to a more detailed paper. A sample of results is presented in the last paragraph, and the sensitivity of the numerical solution to the space discretization is shown due to an insufficient mesh concentration of the proposed mesh in the nose region.


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  1. [1]
    CHATTOT, J.J., “Condition d’unicité pour les écoulements irrotationnels stationnaires de fluide parfait compressible”, C.R.Ac. Sc., Paris, t. 268-A (1978), p. 111–113.Google Scholar
  2. [2]
    JAMESON, A., “Transonic flow calculations”, VKI Lecture Series 87, March 15–19, 1976.Google Scholar
  3. [3]
    MURMAN,E.M., COLE, J.D., “Calculation of plane steady transonic flows”, AIAA Journal, vol. 9, 1971, p. 114–121.ADSGoogle Scholar
  4. [4]
    HOLST, T.L., BALLHAUS, W.F., “Conservative implicit schemes for the full potential equation applied to transonic flows”, NASA TM-78469, March 1978.Google Scholar
  5. [5]
    HAFEZ, M.M., SOUTH, J.C., MURMAN, E.M., “Artificial compressibility methods for numerical solution of transonic full potential equation”, AIAA paper 78–1148, July 1978.Google Scholar
  6. [6]
    VIVIAND, H., “Conservative forms of gas dynamics equations”, La Rech. Aérosp., No 1, (1974), p. 65–68.Google Scholar
  7. [7]
    CHATTOT, J.J., COULOMBEIX, C., da SILVA TOME, C., “Calculs d’écoulements transsoniques autour d’ailes”, La Rech. Aérosp., 1978–4, p. 143–159.Google Scholar
  8. [8]
    BALLHAUS, W.F., STEGER, J.L., “Implicit approximate factorization schemes for the low frequency transonic equation”, NASA, TM X - 73, 082, 1975.Google Scholar
  9. [9]
    LOCK, R.C., “Test cases for numerical methods in two-dimensional transonic flows”, AGARD Report No 575, Nov. 1970.Google Scholar
  10. [10]
    GARABEDIAN, P.R., KORN, D.G., “Numerical design of transonic airfoils”, Numerical solution of partial differential equations. II–Academic Press, New York, 1971, pp. 253–271.Google Scholar

Copyright information

© Springer Fachmedien Wiesbaden 1981

Authors and Affiliations

  • Jean-Jacques Chattot
    • 1
  • Colette Coulombeix
    • 1
  1. 1.Office National d’Etudes et de Recherches Aérospatiales (ONERA)ChâtillonFrance

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