Computation of fictitious gas flow with Euler equations

  • P. Li
  • H. Sobieczky
Part of the Acta Mechanica book series (ACTA MECH.SUPP., volume 4)


The Fictitious Gas Concept supports some computational design methods to construct shock-free transonic flows. It was originally developed for potential flows, here it is introduced to the Euler equations for more general applications. A new equation of state needs to be defined in order to simulate results of the simpler potential approach. An operational numerical Euler code was chosen for the modifications and tested on a basic boundary value problem: The inviscid flow past a circular cylinder with a local supersonic flow region. The numerical computation is based on a finite volume method to solve the time dependent Euler equations in integral form. Conclusions are drawn for a physical explanation of the hitherto abstract “fictitious” gas: an internal momentum and energy supply/removal is modelled and the results for locally non-isentropic flow may be interpreted as an internal cooling/heating process controlled by the flow velocity.


Euler Equation Transonic Flow Inviscid Flow Original Circle Euler Code 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Sobieczky, H.: Verfahren für die Entwurfsaerodynamik moderner Transportflugzeuge. DFVLR-FB 85–43 (1985).Google Scholar
  2. [2]
    Sobieczky, H., Seebass, A. R.: Supercritical airfoil and wing design. Ann. Rev. Fluid Mech. 16, 337–363 (1984).CrossRefADSGoogle Scholar
  3. [3]
    Sobieczky, H.: Progress in inverse design and optimization in aerodynamics. Conference on Computational Methods for Aerodynamic Design (Inverse) and Optimization, AGARD CP 463, pp. 1.1.-1. 10 (1989).Google Scholar
  4. [4]
    Zhu, Z., Sobieczky, H.: An engineering approach for nearly shock-free wing design. Chin. J. Aeronautics, 2, 81–86 (1989).Google Scholar
  5. [5]
    Kroll, N., Jain, R. K.: Solution of two-dimensional Euler equations — experience with a finite volume code. DFVLR-FB 87–41 (1987).Google Scholar
  6. [6]
    Rossow, C.: Berechnung von Strömungsfeldern durch Lösung der Euler-Gleichungen mit einer erweiterten Finite-Volumen Diskretisierungsmethode. DLR-FB 89–38 (1989).Google Scholar
  7. [7]
    Kroll, N., Rossow, C.: Foundations of numerical methods for the solution of Euler equations. Carl-Crantz-Gesellschaft Lecture Series F6. 03, Braunschweig, Germany 1989.Google Scholar
  8. [8]
    Jameson, A., Schmidt, W., Turkel, E.: Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time stepping schemes. AIAA Paper 81–1259 (1981).Google Scholar
  9. [9]
    Hall, M. G.: Cell-vertex multigrid scheme for solution of the Euler equations. Proceedings of the Conference on Numerical Methods for Fluid Dynamics, Reading, 1985.Google Scholar
  10. [10]
    Van Dyke, M., Guttmann, A. J.: Subsonic potential flow past a circle and the transonic controversy. J. Aust. Math. Soc. Ser. B24 (1983).Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • P. Li
    • 1
  • H. Sobieczky
    • 2
  1. 1.Institut für Strömungslehre und StrömungsmaschinenUniversität Karlsruhe (TH)KarlsruheGermany
  2. 2.DLR-Institut für Theoretische StrömungsmechanikGöttingenFederal Republic of Germany

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