Improvement and Application of a Two Stream-Function Formulation Navier-Stokes Procedure

  • Leiping Xue
  • Thomas Rung
  • Frank Thiele
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NONUFM, volume 48)


An improved structured-grid multiblock Navier-Stokes procedure, based on the two stream-function Euler-Potential formulation, is presented for the simulation of threedimensional incompressible flows in complex geometries. The algorithm is based on general non-orthogonal coordinates and employs a fully co-located storrage arrangement for all transport properties. In this, diffusion terms are approximated using second-order central differences, whereas advective fluxes are approximated using upwind biased schemes. The solution is iterated to convergence employing an ILU type (SIP) procedure. The numerical procedure has been parallelized by means of a domain decomposition strategy. Results are reported in comparison to measurements for a laminar curved duct flow and the simulation of three-dimensional wing flow at low angle of attack. The principal aim of the paper is to convey the capabilities of the pure stream-function formulation for the simulation of internal and external aerodynamic flows.


Grid Block Processor Array Communication Step Secondary Motion Domain Decomposition Strategy 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Xue, L., Rung, T., Thiele, F.: “Simulation of Unsteady Viscous Three-Dimensional Flow Fields Using a Two Stream Function Formulation”, Notes on Numerical Fluid Mechanics, 38 (1993), pp. 393–406.Google Scholar
  2. [2]
    Schütz, H., Thiele, F.: “Zur Stromfunktionsformulierung der Navier-Stokes Gleichungen für dreidimensionale Strömungen”, ZAMM, 69 (1989), pp. 573–575.Google Scholar
  3. [3]
    Lilek, Z., Períc, M., Seidl, V.: “Development and Application of a Finite Volume Method for the Prediction of Complex Flows”, in this publication.Google Scholar
  4. [4]
    Durst, F., Peric, M., Schäfer, M., Schreck, E.: “Parallelization of Efficient Numerical Methods for Flows in Complex Geometries”, Notes on Numerical Fluid Mechanics, 38 (1993), pp. 79–92.Google Scholar
  5. [5]
    Hofhaus, J., Meinke, M., Krause, E.: “Parallelization of Solution Schemes for the Navier-Stokes Equations”, in this publication.Google Scholar
  6. [6]
    Durst, F., Schäfer, M., Wechsler, K.: “Efficient Simulation of Incompressible Viscous Flows on Parallel Computers”, in this publication.Google Scholar
  7. [7]
    Xue, L., Rung, T., Thiele, F.: “Entwicklung eines imiten Volumenverfahrens zur Lösung der 3-D, inkompressiblen Navier-Stokes-Gleichung in der Euler-Potentialformulierung”, ZAMM 73 (1993), pp. T589–T592.CrossRefGoogle Scholar
  8. [8]
    Bärwolff, G., Ketelsen, K., Thiele, F.: “Parallelization of a Finite-Volume Navier-Stokes Solver on a T3D Massively Parallel System”, Proc. 6th International Symposium on Computational Fluid Dynamics (1995), pp. 63–68, Lake Tahoe, Nevada, USA.Google Scholar
  9. [9]
    Morzynski, M., Thiele, F.: “Numerical Investigation of Wake Instabilities”, Bluff-Body Wakes, Dynamics and Instabilities. Springer-Verlag, Berlin 1993, pp. 135–142.Google Scholar
  10. [10]
    Lugt, H. J., Haussling, H. J.: “Laminar Flow Past an Abruptly Accelerated Elliptic Cylinder at 45° Incidence”, J. Fluid Mech., 65 (1974), pp. 711–734.zbMATHCrossRefGoogle Scholar
  11. [11]
    Stone, H. L.: “Iterative Solution of Implicit Approximations of Multidimensional Partial Differential Equations”, SIAM J. Numer. Anal., 5 (1968), pp. 530–558.MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    Taylor, A. M. K. P., Whitelaw, J. H., Yianneskis, M.: “Curved Ducts With Strong Secondary Motion: Velocity Measurements of Developing Laminar and Turbulent Flow”, ASME J. Fluids Engineering, 104 (1982), pp. 350–359.CrossRefGoogle Scholar
  13. [13]
    Humphrey, J. A. C., Taylor, A. M. K. P., Whitelaw, J. H.: “Laminar Flow in a Squared Duct of Strong Curvature”, J. Fluid Mech., 83 (1977), pp. 509–527.zbMATHCrossRefGoogle Scholar
  14. [14]
    Schwamborn, D.:“Simulation of the DLR-F5 Wing Experiment Using a Block Structured Explicit Navier-Stokes Method”, Notes on Numerical Fluid Mechanics, 22 (1988), pp. 244–268.Google Scholar

Copyright information

© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1996

Authors and Affiliations

  • Leiping Xue
    • 1
  • Thomas Rung
    • 1
  • Frank Thiele
    • 1
  1. 1.Hermann-Föttinger-Institut für StrömungsmechanikTechnische Universität, BerlinBerlinGermany

Personalised recommendations