The theory of Green's functions for the wave and Helmholtz equations is examined with particular attention to their use in aeroacoustics for the extrapolation of acoustic wavefields from numerical flow simulations. In a new synthesis that permits straightforward generalization of previously published results, spatial and temporal windowing functions are employed to provide equivalent-source expressions to account for both initial and boundary conditions. Detailed results describe the transformation of both source terms and Green's functions to take account of uniform subsonic mean flow, and expressions are given for free-field Green's functions, both with and without flow, in time, frequency and wavenumber domains. A worked example illustrates the non-uniqueness of the Green's function for a simple one-dimensional bounded problem.
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References
1.
LighthillM. J.1952On sound generated aerodynamically. I. General theory. Proc. R. Soc. A211, 564–587.
2.
WilliamsFfowcs J. E. & HawkingsD. L.1969Sound generation by turbulence and surfaces in arbitrary motion. Phil. Trans. R. Soc. A264, 321–342.
3.
MorfeyC. L. & WrightM. C. M.2007Extensions of Lighthill's acoustic analogy with application to computational aeroacoustics. Proc. R. Soc. A463, 2101–2127.
4.
MorseP. M. & FeshbachH.1953Methods of Theoretical Physics. New York: McGraw-Hill.
5.
FarassatF.2001Acoustic radiation frm rotating blades—the Kirchhoff method in aeroacoustics. J. Sound Vib.239, 785–800.
6.
FarassatF. & BrentnerK. S.1998The acoustic analogy and the prediction of the noise of rotating blades. Theoret. & Comp. Fluid Dyn.10, 155–170.
7.
LilleyG. M.1974On the noise from jets. Ch. 13, Noise Mechanisms. AGARD-CP-131 pp. 13.1–13.12.
8.
TesterB. J. & MorfeyC. L.2010Solving the Lilley equation with quadrupole and dipole sources. Int. J. Aeroacoustics9, 419–460.
9.
DuffyD. G.2001Green's Functions with Applications. Boca Raton: Chapman and Hall/CRC.
10.
GoldsteinM. E.1976Aeroacoustics. New York: McGraw-Hill.
11.
SpalartP. R. & ShurM. L.2009Variants of the Ffowcs Williams–Hawkings equation and their coupling with simulations of hot jets. Int. J. Aeroacoustics8, 477–491.
12.
DoakP. E.1960Acoustic radiation from a turbulent fluid containing foreign bodies. Proc. R. Soc. A254, 129–145.
13.
PowellA.1960Aerodynamic noise and the plane boundary. J. Acoust. Soc. Am.32, 982–990.
14.
MattheijR. M. M.RienstraS. J. & BoonkkampThijeTenJ. H. M.2005Partial Differential Equations: Modeling, Analysis, Computation. Philadelphia: Society for Industrial and Applied Mathematics.
