On numerical calculation of transonic flow patterns

Authors:
S. Bergman, J. G. Herriot and T. G. Kurtz

Journal:
Math. Comp. **22** (1968), 13-27

MSC:
Primary 76.65

DOI:
https://doi.org/10.1090/S0025-5718-1968-0224335-0

MathSciNet review:
0224335

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References | Similar Articles | Additional Information

**[1]**S. Bergman, "The hodograph method in the theory of compressible fluids," Supplement to*Fluid Dynamics*by R. von Mises and K. O. Friedrichs, Brown University, Providence, R. I., 1942.**[2]**Stefan Bergman,*A formula for the stream function of certain flows*, Proc. Nat. Acad. Sci. U. S. A.**29**(1943), 276–281. MR**0010079****[3]**Stefan Bergman,*On representation of stream functions of subsonic and supersonic flows of compressible fluids*, J. Rational Mech. Anal.**4**(1955), 883–905. MR**0074206****[4]**S. Bergman, J. G. Herriot & T. G. Kurtz,*Numerical Calculation of Transonic Flow Patterns*, Tech. Rep. No. CS 51, Computer Science Department, Stanford University, 1966.**[5]**Lipman Bers,*Mathematical aspects of subsonic and transonic gas dynamics*, Surveys in Applied Mathematics, Vol. 3, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR**0096477****[6]**Lipman Bers and Abe Gelbart,*On a class of differential equations in mechanics of continua*, Quart. Appl. Math.**1**(1943), 168–188. MR**0008556**, https://doi.org/10.1090/S0033-569X-1943-08556-1**[7]**Lipman Bers and Abe Gelbart,*On a class of functions defined by partial differential equations*, Trans. Amer. Math. Soc.**56**(1944), 67–93. MR**0010910**, https://doi.org/10.1090/S0002-9947-1944-0010910-5**[8]**S. A. Chapltgin,*On Gas Jets*, Scientific Memoirs, Moscow University MathematicsPhysics Section, 21, 1904, pp. 1-121; English transl., published by NACA TM 1063, 1044. MR**7**, 495.**[9]**G. H. Golub & L. B. Smith,*Chebyshev Approximation of Continuous Functions by a Chebyshev's System of Functions*, Tech. Rep. No. CS 72, Computer Science Dept., Stanford University, 1967.**[10]**Richard von Mises,*Mathematical theory of compressible fluid flow*, Applied mathematics and mechanics. Vol. 3, Academic Press, Inc., New York, N.Y., 1958. MR**0094996****[11]**P. Molenbroek, "Über einige Bewegungen eines Gases mit Annahme eines Geschwindigkeitspotentials,"*Arch. Math. Phys.*(2), v. 9, 1890, pp. 157-195.**[12]**E. Ya. Remez,*General computation methods for Čebyšev approximation. Problems with real parameters entering linearly*, Izdat. Akad. Nauk Ukrainsk. SSR. Kiev, 1957 (Russian). MR**0088788****[13]**J. M. Stark,*Application of Bergman’s integral operators to transonic flows*, Internat. J. Non-Linear Mech.**1**(1966), 17–34 (English, with French, German and Russian summaries). MR**0230508****[14]**J. M. Stark,*Transonic Flow Patterns Generated by Bergman's Integral Operator*, Report, Department of Mathematics, Stanford University, 1964.

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DOI:
https://doi.org/10.1090/S0025-5718-1968-0224335-0

Article copyright:
© Copyright 1968
American Mathematical Society