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Computation of a class of subsonic flow patterns

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Summary

For flows bounded by segments of straight lines and segments of free boundaries, the flow in the pseudo-logarithmic plane was considered in [B.2]. The method described was based on the determination of a fundamental solution possessing a singularity at a point corresponding to a source or a sink. The computation of the fundamental solution requires the evaluation of many terms which are iterated double integrals involving a functionP(λ) which appears in the differential equation. The computational aspects of the evaluation of these integrals are discussed in this paper. First a numerical procedure for approximating the functionP(λ) by a polynomial is described. Then the approximate evaluation of the iterated double integrals is discussed. This may be accomplished by replacing the integrals by summations over a sufficiently dense set of points or by using special systems such as FORMAC.

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Bibliography

  • B.1, Bergman, S.: Integral operators in the theory of linear partial differential equations. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 23. Berlin-Heidelberg-New York: Springer 1969.

    Google Scholar 

  • B.2.,—: Application of the kernel function for the computation of flows of compressible fluids. Quart. Appl. Math.25, 301–310 (1968).

    Google Scholar 

  • B.3.,Bergman, S.: The kernel function and conformal mapping. Math. Survey, vol. 5, Amer. Math. Soc., 2nd edition, 1970.

  • B.H.1— Herriot, J. G.: Numerical solution of boundary value problems by the method of integral operators. Numer. Math.7, 42–65 (1965).

    Google Scholar 

  • D.1., Davis, P. J.: Interpolation and approximation. New York: Blaisdell Publishing Co. 1963.

    Google Scholar 

  • D.R.1., Davis, P., Rabinowitz, P.: Appendix in M.Z. v. Krzywoblocki, Bergman's linear integral operator method in the theory of compressible fluid flow. Wien: Springer 1960.

    Google Scholar 

  • P.S.1., Picard, E., Simart, G.: Théorie, des fonctions algébriques de deux variables indépendants, vol. I. Paris: Gauthier-Villars 1897.

    Google Scholar 

  • T.1., Tashjian, H.: Evaluation of certain iterated double integrals arising in the theory of compressible fluid. AEC Computer Information Meeting, Idaho Falls, Idaho, Oct. 6–8, 1969.

  • T.2., Tashjian, H.: Computation of the potential function of a compressible fluid near Mach number one. Nat. Aero. Space Admin. (NASA) TN D-5713, 1970.

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Authors and Affiliations

  1. Stanford University, 94305, Stanford, Cal.

    S. Bergman & J. G. Herriot

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  1. S. Bergman
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  2. J. G. Herriot
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Additional information

This work, was supported in part by contract AEC 326-P 22 and National Science Foundation Grant GP 7657 at Stanford University.

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Bergman, S., Herriot, J.G. Computation of a class of subsonic flow patterns. Numer. Math. 17, 247–252 (1971). https://doi.org/10.1007/BF01436381

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