Numerical Simulation of Turbulent Flows Using Navier Stokes Equations

  • Wolfgang Schmidt
Conference paper


The numerical simulation of turbulent flow fields by solving the Navier Stokes equations is no longer limited to basic research applications. New high speed vector computers along with fast numerical algorithms and better physical models allow pioneering application even in industry. The emphasis in the following article will be on the discussion of the requirements and so far limitations in numerical simulation from an industrial point of view. It will be pointed out clearly that our physical understanding of flow topology and turbulence is still limited. Much more detailed experimental investigations are mandatory to validate numerical simulations.


Wind Tunnel Navier Stokes Equation Hypersonic Flow Transonic Flow Total Pressure Loss 
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  1. 1.
    Jameson, A.; Baker, T.J.; and Weatherhill, N.P. Calculation of Inviscid Transonic Flow Over a Complete Aircraft, AIAA-86–0103 (Jan. 1986)Google Scholar
  2. 2.
    Fritz, W. Two Dimensional Euler and Navier-Stokes Solutions of Flow Over the Mid Section of a Car, 2nd IAVD Congress on Vehicle Design and Components, Geneva, 1985Google Scholar
  3. 3.
    Leicher, S. Analysis of Transonic and Supersonic Flows Around Wing-Body Combinations, ICAS 84–1. 2. 2 (1984)Google Scholar
  4. 4.
    Seibert, W. An Approach to the Interactive Generation of Block Structured Volume Grids Using Computer Graphics Devices, First International Conference on Numerical Grid Generation in Computational Fluid Dynamics, Landshut, Germany (1986)Google Scholar
  5. 5.
    Fritz, W. Two Dimensional Navier-Stokes Solutions for Section Shapes, to be published, 1987Google Scholar
  6. 6.
    Shang, J.S. An Assessment of Numerical Solutions of the Compressible Navier-Stokes Equations, J. Aircraft, Vol. 22, No. 5, May 1985, pp. 353–370CrossRefADSGoogle Scholar
  7. 7.
    Schmidt, W.; Jameson, A.; Pulliam, T.; Thompson, J.F. Navier-Stokes Flow Simulations, AIAA Professional Study Seminar, June 1986, San DiegoGoogle Scholar
  8. 8.
    Jameson, A.; Schmidt, W.; Turkel, E. Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes, AIAA Paper NO. 81–1259 (June 1981)Google Scholar
  9. 9.
    Jameson, A.; Leicher, S.; Dawson, J. Remarks on the Development of a Multiblock Three-Dimensional Euler Code for Out of Core and Multiprocessor Calculations, in: Progress and Supercomputing in Computational Fluid Dynamics, Birkhäuser-Verlag (1985)Google Scholar
  10. 10.
    Jameson, A.; Schmidt, W. Some Recent Developments in Numerical Methods for Transonic Flows, Comp. Meth. in Applied Mech. and Eng. 51 (1985) 467–493CrossRefMATHADSMathSciNetGoogle Scholar
  11. 11.
    Bradshaw, P. et al Engineering Calculation Methods for Turbulent Flow, Academic Press, 1981, ISBN 0–12–12. 4550–0 496Google Scholar
  12. 12.
    Rodi, Wolfgang Turbulence Models and their Application in Hydraulics IAHR Publication, 1980, DelftGoogle Scholar
  13. 13.
    Murphy, J.D. Turbulence Modelling NASA-TN-85889, 1984Google Scholar
  14. 14.
    Marvin, Joseph Turbulence Modelling for Computational Aerodynamics AIAA Journal Vol. 21, No. 7, July 1983, p. 941Google Scholar
  15. 15.
    Gilbert, N.; Kleiser, L. Low Resolution Simulations of Transitional and Turbulent Channel Flow. To appear in Proc. of Int. Conf. on Fluid Mechanics, Beijing, July 1–4, 1987, ChinaGoogle Scholar
  16. 16.
    Stock, H.W.; Haase, W. An analytical eddy viscosity model for attached and slightly detached flows in Navier Stokes computations. AV BF30–46/86, 1986, Dornier GmbHGoogle Scholar
  17. 17.
    Yoshihara, H.; Sacher, P. (editors) Test Cases for Inviscid Flow Field Methods, AGARD-AR-2111 (1985)Google Scholar
  18. 18.
    Deiwert, G.S. Numerical Simulation of Three-Dimensional Boattail After-body Flowfields. AIAA J., Vol. 19, No. 2, 1981, p. 582CrossRefADSGoogle Scholar
  19. 19.
    Miyakawa, J.; Takanashi, S.; Fuji, K.,and Amano, K. Searching the Horizon of Navier-Stokes Simulation of Transonic Flows. AIAA-Paper 87–0524Google Scholar
  20. 20.
    Srinivasan, G.R.; McCroskey, W.J. et al Numerical Simulation of Tip Vortices of Wings in Subsonic and Transonic Flows. AIAA-Paper 86–1095Google Scholar
  21. 21.
    Wagner, B. Calculation of Turbulent Flow about Missile Afterbodies Containing an Exhaust Jet. Zeitschrift für Flugwissenschaften und Weltraumforschung, Vol. 9, pp. 333–338, 1985. (Results also in “Aerodynamics of Aircraft Afterbody”, AGARD Advisory Report, No. 226, 1986)ADSGoogle Scholar
  22. 22.
    Haase, W.; Echtle, H. Computational Results for Viscous Transonic Flows Around Airfoils. AIAA-Paper 87–0422Google Scholar
  23. 23.
    Davis, R.L. et al Cascade Viscous Flow Analysis Using the Navier Stokes Equations. AIAA-Paper 86–0033, 1986Google Scholar
  24. 24.
    Fritz, W. Porsche 956 2D-Section Navier-Stokes Calculations. To be published, 1987Google Scholar
  25. 25.
    Rieger, H. Solution of Some 3-D Viscous and Inviscid Supersonic Flow Problems by Finite-Volume Space Marching Schemes. AGARD Fluid Dynamics Panel Symposium on Aerodynamics of Hypersonic Lifting Vehicles, April 6–9, 1987, Bristol U.K.Google Scholar
  26. 26.
    Yang, R.-J.; Chang, J.L.C.,and Kwak, D. A Navier-Stokes Flow Simulation of the Space Shuttle Main Engine Hot Gas Manifold. AIAA-Paper 87–0368Google Scholar
  27. 27.
    Haase, W.; Misegades, K.; Wagner, B. Numerische Strömungssimulation für den Kompressionshub in einem Dieselmotor (Numerical Flow Simulation during the Compression Stroke in a Diesel Engine). Dornier Internal Report BF10/84 B, revised version 1986.Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1987

Authors and Affiliations

  • Wolfgang Schmidt
    • 1
  1. 1.AerodynamicsDornier GmbHFriedrichshafenGermany

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