Test Problems for Inviscid Transonic Flow

  • Leland A. Carlson
Part of the Notes on Numerical Fluid Mechanics book series (NONUFM, volume 3)


This paper will briefly discuss some of the results obtained in the process of solving the test problems for the GAMM Workshop on “Numerical Methods for the Computation of Inviscid Transonic Flow with Shock Waves” with the TRANDES program. Briefly, this method, 1–5 utilizes the full, inviscid, perturbation-potential flow equation in a Cartesian grid system that is stretched to infinity. This equation is represented by a non-conservative system of finite difference equations that includes at supersonic points a rotated difference scheme and is solved by column relaxation. The solution usually starts from a zero perturbation potential on a very coarse grid (typically 13 × 7) followed by several grid halvings until a final solution is obtained on a fine grid (97×49). Occasionally, for cases having high local Mach numbers, the solution must be started on the coarse grid (25 × 13). Since the airfoil does not coincide with the grid points, the surface boundary conditions are represented as two-term Taylor series about dummy points inside the airfoil. On the outer boundaries, the exact infinity conditions are used. This method can, if desired, include the effects of weak viscous interaction or be used in the design mode. 2–6


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  1. 1.
    Carlson, L.A., “Transonic Airfoil Analysis and Design Using Cartesian Coordinates,” J. of Arcft, Vol. 13, May 1976 pp. 349–356.Google Scholar
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    Carlson, L.A., “Transonic Airfoil Flowfield Analysis Using Cartesian Coordinates,” NASA CR-2577, Aug. 1975.Google Scholar
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    Carlson, L.A., “TRANDES: A Fortran Program for Transonic Airfoil Analysis and Design,” NASA CR-2821, June 1977.Google Scholar
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  5. 5.
    Carlson, L.A. and Rocholl, B.M., “Application of Direct Inverse Techniques to Airfoil Analysis and Design,” NASA CP-2045, Pt. 1, pp 55–72.Google Scholar
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    Carlson, L.A., “Test Problems for Inviscid Transonic Flow,” Texas Engr. Expt. Station Rept. TAMRF-3224–7904, 1979.Google Scholar
  7. 7.
    Lock, R.C., “Test Cases for Numerical Methods in Two Dimensional Transonic Flow,” AGARD Rept R-575–70, 1970.Google Scholar
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    Murman, E.M., “Computation of Wall Effects on Ventilated Transonic Wind Tunnels,” AIAA Paper No. 72–1007, Sept. 1972.Google Scholar

Copyright information

© Springer Fachmedien Wiesbaden 1981

Authors and Affiliations

  • Leland A. Carlson
    • 1
  1. 1.Texas A&M UniversityCollege StationUSA

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