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Is Computer Extension of Series a Part of CFD?

  • Conference paper
Proceedings of the Ninth GAMM-Conference on Numerical Methods in Fluid Mechanics

Part of the book series: Notes on Numerical Fluid Mechanics (NNFM) ((NNFM,volume 35))

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Summary

A path midway between pure analysis and sheer number-crunching is provided by the technique of extending a regular perturbation series to high order by computer, and then analyzing and improving the results. This three-step process has, during the past two decades, been applied to perhaps a hundred problems in many branches of fluid mechanics. However, there has been no great rush to follow this route. Some researchers assert that it is not a part of computational fluid mechanics. Here we survey the technique using the flat-plate boundary layer as a simple example, consider the reasons for its relative neglect, and discuss prospects for the future.

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References

  1. Van Dyke, M.: Extension of Goldstein’s series for the Oseen drag of a sphere.1 Fluid Mech 44 (1970) 365–372

    Article  ADS  MATH  Google Scholar 

  2. Van Dyke, M: Computer-extended series, Ann. Rev Fluid Mech. 16 (1984) 237–309, Annual Reviews Inc., Palo Alto

    Article  ADS  Google Scholar 

  3. Gaunt, D. S. & Guttmann, A J.: Asymptotic analysis of coefficients, Phase Transitions and Cntical Phenomena 3 (1974) 287–309, Academic Press

    Google Scholar 

  4. Guttmann, A J.: Asymptotic analysis of power series, Phase Transitions and Critical Phenomena 13 (1989) 1–234, Academic Press

    Google Scholar 

  5. Adler, J, Meir, Y, Amnon, A., Harris, A B. & Klein, L: Low-concentration series in general dimensions, J.Sfatisiica/Phya 58 (1990) 511–538

    ADS  MATH  Google Scholar 

  6. Munk, M. & Rawling, G.: Calculation of compressible subsonic flow past a circular cylinder, US Nay Orifinance Lail NA TtORDRep. 2477 (1952)

    Google Scholar 

  7. Van Dyke, M. & Guttmann, A J.: Subsonic potential flow past a circle and the transonic controversy, f. Austral Math Soc, Ser. B 24 (1983) 243–261

    MATH  Google Scholar 

  8. Guttmann, A J. & Thompson, C J.: Subsonic potential flow and the transonic controversy.Thbepubl/shed

    Google Scholar 

  9. Domb, C and Sykes, M. F.: On the susceptibility of a ferromagnetic above the Curie point, 1 vcz Roy Sac LondonA 240 (1957) 214–228

    MATH  Google Scholar 

  10. Schlichting H: andxmdary~/ayrrThe ty,7th ed. (1979), McGraw-Hill

    Google Scholar 

  11. Blasius, H.: Grenzschichten in Flüssigkeiten mit kleiner Reibung Z Math a Phys 56 (1908) 1–37; English transL NACA Tech Memo 1256

    Google Scholar 

  12. Richardson, S.: On Blasius’s equation governing flow in the boundary layer on a flat plate, Phvc Camlx Ph O. Soc 74 (1978)179–184

    Google Scholar 

  13. Schwartz, L W: Computer extension and analytic continuation of Stokes’ expansion for gravity waves, J. Fluid Mech. 62 (1974) 553–578

    Google Scholar 

  14. Schwartz, L W. & Fenton, J. D.: Strongly nonlinear waves, Ann. Rev Fhu/d Mech 44 (1982) 39–60, Annual Reviews Inc, Palo Alto

    Google Scholar 

  15. Guderley, G: Starke kugelige und zylindrische Verdichtungsstösse in der Nähe des Kugelmittelpunktes bzw. der Zylinderachse, Lutï/ähicrschímg 19 (1942) 302–312

    MathSciNet  Google Scholar 

  16. Van Dyke, M. & Guttmann, A J.: The converging shock wave from a spherical or cylindrical piston, J. Tad Mech 120 (1982) 451–462

    ADS  MATH  Google Scholar 

  17. Van Dyke, M: Extended Stokes series: laminar flow through a loosely coiled pipe, J. Fluid Mech 86 (1978) 129–145

    Article  ADS  MATH  Google Scholar 

  18. Ramshankar, R and Sreenivasaan, K. R.: A paradox concerning the extended Stokes series solution for the pressure drop in coiled pipes, Phys Fhddc 31 (1988) 1339–1347

    ADS  Google Scholar 

  19. Herbert, T. & Feng H. Y.: Flows in a loosely coiled pipe and their stability, and Bull Amer Phys Soc 34 (1989) 2319

    Google Scholar 

  20. Dingle, R B.: Asymptotic Etpansio s: Their Derivation and Intetpmtation (1973) AcademícPress

    Google Scholar 

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Author information

Authors and Affiliations

  1. Division of Applied Mechanics, Stanford University, Stanford, CA, 94305, USA

    Milton Van Dyke

Authors
  1. Milton Van Dyke
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Editor information

Editors and Affiliations

  1. FFA Stockholm, Box 11021, S-16111, Bromma 11, Sweden

    Arthur Rizzi

  2. Lausanne, Switzerland

    Inge L. Ryhming

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© 1992 Springer Fachmedien Wiesbaden

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Van Dyke, M. (1992). Is Computer Extension of Series a Part of CFD?. In: Vos, J.B., Rizzi, A., Ryhming, I.L. (eds) Proceedings of the Ninth GAMM-Conference on Numerical Methods in Fluid Mechanics. Notes on Numerical Fluid Mechanics (NNFM), vol 35. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-13974-4_3

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  • DOI: https://doi.org/10.1007/978-3-663-13974-4_3

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-528-07635-1

  • Online ISBN: 978-3-663-13974-4

  • eBook Packages: Springer Book Archive

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