Development of a Three-Dimensional Upwind Parabolized Navier-Stokes Code

  • Scott L. Lawrence
  • Denny S. Chaussee
  • John C. Tannehill
Conference paper
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 29)


An algorithm for the integration of the parabolized Navier-Stokes (PNS) equations that is based on Roe’s flux-difference splitting approach in both crossflow directions has been developed. The algorithm was developed using finite-volumes to ensure accurate conservation of numerical fluxes and modifications have been applied to make the scheme implicit and second-order accurate in the crossflow directions. The resulting PNS code has been applied to hypersonic flow past two simple test geometries and results are presented here. The computed flow-fields for a 10 deg half-angle cone at a wide range of incidence angles are compared with experimental surface pressure and heat transfer as well as lee side pitot pressure profiles. Generally good agreement is observed though high grid density is needed to capture the lee side pitot pressure behavior at moderate to high angles of attack. Computed results are also presented for turbulent flow past a generic elliptic cone-based geometry.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Lawrence, S. L., Tannehill, J. C., and Chaussee, D. S., “An Upwind Algorithm for the Parabolized Navier-Stokes Equations,” AIAA Paper 86-1117, July 1986.Google Scholar
  2. [2]
    Vigneron, Y. C., Rakich, J. V., and Tannehill, J. C., “Calculation of Supersonic Viscous Flow over Delta Wings with Sharp Subsonic Leading Edges,” AIAA Paper 78-1137, July 1978.Google Scholar
  3. [3]
    Schiff, L. B. and Steger, J. L., “Numerical Simulation of Steady Supersonic Viscous Flow,” AIAA Paper 79-0130, Jan. 1979.Google Scholar
  4. [4]
    Roe, P. L., “Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes,” Journal of Computational Physics, Vol. 43, 1981, pp. 357–372.MathSciNetADSzbMATHCrossRefGoogle Scholar
  5. [5]
    Chakravarthy, S. R. and Szema, K. Y., “An Euler Solver for Three-Dimensional Supersonic Flows with Subsonic Pockets,” AIAA Paper 85-1703, July 1985.Google Scholar
  6. [6]
    Tracy, R. R., “Hypersonic Flow over a Yawed Circular Cone,” California Institute of Technology Graduate Aeronautical Laboratories, Pasadena, Calif., Memorandum No. 69, Aug. 1963.Google Scholar
  7. [7]
    Steger, J. L. and Chaussee, D. S., “Generation of Body Fitted Coordinates Using Hyperbolic Partial Differential Equations,” SIAM Journal Sci. Stat. Comput., Vol. 1, No. 4, Dec. 1980.Google Scholar
  8. [8]
    Baldwin, B. S. and Lomax, H., “Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows,” AIAA Paper 78-257, Jan. 1978.Google Scholar

Copyright information

© Springer Fachmedien Wiesbaden 1990

Authors and Affiliations

  • Scott L. Lawrence
    • 1
  • Denny S. Chaussee
    • 1
  • John C. Tannehill
    • 2
  1. 1.NASA Ames Research CenterMoffett FieldUSA
  2. 2.Iowa State UniversityAmesUSA

Personalised recommendations