Abstract
In this paper a method for obtaining uniformly valid asymptotic expansions of the solution of the boundary value problems in domains exterior to thin or slender regions is given. This approach combines the Tuck's method, based on the use of a suitable co-ordinates system with the method given by Handelsman and Keller yielding complete uniform asymptotic expansion of the solution for slender body problems.
Our method avoids the determination of the extremities of the segment containing singularities; it is pointed out that this last problem is a pure geometrical one and independent of solving concrete boundary value problems in the given domain.
Résumé
Nous présentons dans ce travail une méthode qui permet d'obtenir des séries asymptotiques uniformes pour la solution des problèmes de valeur limite dans des domaines extérieurs à des parties minces ou élancées.
Cette méthode d'approche combine la méthode de Tuck, basée sur un système de coordonées approprié et la méthode de Handelsman et Keller qui fournit la série asymptotique uniforme complète de la solution du problème pour les corps élancés.
Notre méthode évite de déterminer l'extrémité du segment qui contient des singularités. Nous soulignons que ce dernier problème est purement géométrique et indépendant de la solution des problèmes concrets de valeur limite dans le domaine donné.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. M. Munk,General theory of thin wing sections. Rep. Nat. Adv. Comm. Aero, Washington 1922, p. 142.
W. Birnbaum,Die tragende Wirbelfläche als Hilfsmittel zur Behandlung des ebenen Problems der Tragflügeltheorie. Z. angew. Math. Mech.3, 290 (1923).
H. Glauert,The elements of airfoil and airscrew theory. Cambridge University Press 1926.
M. M. Munk,The aerodynamic forces on airship hulls. Rep. Nat. Adv. Comm. Aero, Washington 1924, p.184.
R. T. Jones,Properties of low-aspect-ratio pointed wings at speeds below and above the speed of sound. Rep. Nat. Adv. Comm. Aero, Washington 1946, p. 835.
M. J. Lighthill,A new approach to thin aerofoil theory. Aeronaut. Quart.3, 193–210 (1951)
J. F. Moran,Line source distributions and slender-body theory. J. Fluid Mech.17, 205–304 (1963).
E. O. Tuck,Some methods for flows past blunt slender bodies. J. Fluid Mech.18, 619–635 (1964).
R. A. Handelsman and J. B. Keller,Axially symmetric potential flow around a slender body. J. Fluid Mech.28, 131–142 (1967).
R. A. Handelsman and J. B. Keller,The electrostatic field around a slender conducting body of revolution. SIAM J. Appl. Math.15, 824–841 (1967).
J. F. Geer,Uniform asymptotic solutions for potential flow about a slender body of revolution. J. Fluid Mech.67, 817–827 (1975).
J. P. K. Tillet,Axial and transverse Stokes flow past slender axisymmetric bodies. J. Fluid. Mech.44, 401–417 (1970).
J. F. Geer,Stokes flow past a slender body of revolution. J. Fluid. Mech.78, 577–600 (1976).
D. Homentcovschi,Axially symmetric Oseen flow past a slender body of revolution. SIAM J. Appl. Math.40, 99–112 (1981).
J. F. Geer,The scattering of a scalar wave by a slender body of revolution. SIAM J. Appl. Math.34, 348–370 (1978).
J. F. Geer,Electromagnetic scattering by a slender body of revolution. Axially incident plane wave. SIAM J. Appl. Math.38, 93–102 (1980).
J. F. Geer and J. B. Keller,Uniform asymptotic solutions for potential flow around a thin airfoil and the elctrostatic potential about a thin conductor. SIAM J. Appl. Math.16, 75–101 (1968).
J. F. Geer,Uniform asymptotic solutions for the two-dimensional potential field about a slender body. SIAM J. Appl. Math.26, 539–553 (1974).
D. Homentcovschi,Conformal mapping of the domain exterior to a thin symmetrical profile. Rev. Roum. Math. Pures et Appl.9, 1317–1326 (1979).
D. Homentcovschi,Conformal mapping of the domain exterior to a thin region. SIAM J. Appl. Math.10, 1246–1258 (1979).
D. Homentcovschi,Uniform asymptotic solutions for the potential field around a thin oblate body of revolution. SIAM J. Appl. Math., (1982).
R. N. Barshinger and J. F. Geer,The elctrostatic potential field about a thin oblate body of revolution. SIAM J. Appl. Math.41, 112–126 (1981).
D. Homentcovschi,Scattering of a scalar wave by a thin oblate body of revolution (to appear).
D. Homentcovschi,Uniform asymptotic solutions for two-dimensional potential field problem with joining relations on the surface of a slender body. Int. J. Engng. Sci.20, 753–767 (1982).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Homentcovschi, D. On boundary value problems for the domain exterior to a thin or slender region. Z. angew. Math. Phys. 34, 322–333 (1983). https://doi.org/10.1007/BF00944853
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00944853