Problems and Results of the Integral Equation Method for Transonic Flows

  • A. Frohn
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


The basic idea of transonic integral equation which was first derived by Oswatitsch [1], [2] is the following: The nonlinear differential operator governing the transonic flow problem is split into a linear elliptic operator and a nonlinear rest operator, which can be done in many different ways. Then the elliptic operator is transformed to Laplace operator by a linear coordinate transformation. Thus one obtains formally a Poisson equation, the right hand side being the unknown nonlinear rest term. By applying Green’ s formula one obtains the nonlinear Integral Equation.


Shock Wave Integral Term Nonlinear Integral Equation Transonic Flow Line Integral 
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  1. 1.
    Oswatitsch, K.: Die Geschwindigkeitsverteilung bei lokalen Überschallgebieten an flachen Profilen. ZAMM, Band 30, Heft 1/2 (1950), 17–24.MathSciNetMATHGoogle Scholar
  2. 2.
    Oswatitsch, K.: Die Geschwindigkeitsverteilung an symmetrischen Profilen beim Auftreten lokaler Überschallgebiete. Acta Physica Austriaca, Band IV, Heft 2/3 (1950), 228–271.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag, Berlin/Heidelberg 1976

Authors and Affiliations

  • A. Frohn
    • 1
  1. 1.Institut für Strömungsmechanik Abt. TheoretischeGasdynamik der Deutschen Forschungs- und Versuchsanstalt für Luft- und RaumfahrtGöttingenGermany

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