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Application of two-point difference schemes to the conservative Euler equations for one-dimensional flows

  • Stephen F. Wornom
Contributed Papers
Part of the Lecture Notes in Physics book series (LNP, volume 170)

Abstract

An implicit finite-difference method is presented for obtaining steady-state solutions to the time-dependent, conservative Euler equations for flows containing shocks. The method uses a two-point central difference scheme with dissipation added at supersonic points via the retarded density concept. Application of the method to the one-dimensional nozzle flow equations for various combinations of subsonic and supersonic boundary conditions show the method to be very efficient. Residuals are typically reduced to machine zero in approximately 35 time steps for 50 mesh points. It is shown that the scheme offers certain advantages over the more widely-used three-point schemes, especially in regard to application of boundary conditions.

Keywords

Transonic Flow Sonic Point Physical Boundary Condition Geometry Case Machine Zero 
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References

  1. 1.
    Yee, H.C.; Beam, R.M.; and Warming R.F.: Proceedings of AIAA 5th Computational Fluid Dynamics Conference, June 1981, pp. 125–135.Google Scholar
  2. 2.
    Keller, Herbert B.; and Cebeci, Tuncer: Proceedings of the Second International Conference on Numerical Methods in Fluid Dynamics. Volume 8 of Lecture Notes in Physics, Maurice Holt, ed., Springer Verlag, 1971, pp. 92–100.Google Scholar
  3. 3.
    Wornom, Stephen F.: NASA TM 83262, May 1982.Google Scholar
  4. 4.
    Hafez, M.; South, J.; and Murman, E.: AIAA J., vol. 17, No 8, Aug. 1979, pp. 838–844.Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Stephen F. Wornom
    • 1
  1. 1.NASA Langley Research CenterHamptonUSA

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