Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A note on a solution of Possio's integral equation for an oscillating airfoil in subsonic flow

Author: John W. Miles
Journal: Quart. Appl. Math. 7 (1949), 213-216
MSC: Primary 76.1X
DOI: https://doi.org/10.1090/qam/30396
MathSciNet review: 30396
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Abstract: Following a procedure analogous to that used by Schwarz for solving the integral equation for an oscillating airfoil in incompressible flow, a method of attack on the same problem for subsonic, compressible flow is outlined. The circulation and kernel to the circulation integral equations are expanded in series with the coefficients $ {M^{2n}}$ and $ {M^{2n}}$ ln $ M$, and a corresponding expansion for the Green's function is thereby implicitly determined. The solution up to (but not including) terms of $ O\left( {{M^4},{M^4}\ln M} \right)$ is stated. A method of iteration for improving a given solution is also indicated.

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DOI: https://doi.org/10.1090/qam/30396
Article copyright: © Copyright 1949 American Mathematical Society

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