Answers are grounded in this paper and cite their sources.
Krupp, J.A., The Numerical of Plane Steady Transonic Flows Past Thin Lifting Airfoils, Boeing Scientific Research Lab. Rept. D180-12958-1, June 1971. Sirovich, L. and Huo, C., Simple Waves and the Transonic Similarity Parameter, AIAA Journal, Vol. 14, Aug. 1976, pp. 11251127. Germain, P., Ecoulements Transsoniques Homogenes, Progress in Aeronautical Sciences, Vol. 5, Pergamon Press, New York, 1964, pp. 143-273. Nonweiler, T.R.F., The Sonic Flow About Some Symmetric Half-Bodies, Journal of Fluid Mechanics, Vol. 4, 1958, pp. 140-148. Murman, E.M. and Cole, J.D., Calculation of Plane Steady Transonic Flovts, AIAA Journal, Vol. 9, Jan. 1971, pp. 114-121. Klunker, E.B. and Newman, P.A., Computation of Transonic Flow About Lifting Wing-Cylinder Combinations, Journal of Aircraft, Vol. 11, April 1974, pp. 254-256. Jameson, A., Iterative Solutions of Transonic Flows Over Airfoils and Wings, Including Flows at Mach 1, CPAM, Vol. XXVII, 1974, pp. 283-309.
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Ghia et al. (1979) studied this question.
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