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Strongly singular and hypersingular integrals for aeroacoustic incident fields
Author(s) -
Croaker P.,
Kessissoglou N.,
Marburg S.
Publication year - 2014
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3980
Subject(s) - mathematical analysis , polynomial , piecewise , mathematics , singularity , singular value , vector field , distribution (mathematics) , flow (mathematics) , geometry , physics , eigenvalues and eigenvectors , quantum mechanics
Summary Using the Burton and Miller formulation to predict the scattering of flow‐induced noise by a body immersed in the flow requires the near‐field pressure and pressure gradient incident on the body. In this paper, Lighthill's acoustic analogy is used to derive formulations for the near‐field pressure and pressure gradient at any point within the flow noise source region, including points on the body. These near‐field formulations involve strongly singular and hypersingular volume and surface integrals. To evaluate these singular integrals, an effective singularity regularization technique is derived. An analytical source distribution is used to demonstrate the accuracy of the method. A cell‐averaged representation of this analytical source distribution, similar to the data stored by computational fluid dynamics solvers, is also created. A piecewise linear, continuous source distribution is generated from these cell‐average values, producing a C 0 distribution. A k ‐exact reconstruction technique is then used to create high‐order polynomials of the solution variables for each volume cell. These high‐order polynomials are constructed from its cell average value and the average values of the nearby cells. The source distribution created using the k ‐exact reconstruction is discontinuous across cell boundaries but exhibits a smooth polynomial distribution within each cell. The near‐field pressure and pressure gradient predicted using these reconstructed source distributions are compared with the results obtained using the analytical distribution. Copyright © 2014 John Wiley & Sons, Ltd.