Assier, RC and Peake, N (2012) *On the diffraction of acoustic waves by a quarter-plane.* Wave Motion, 49. pp. 64-82. ISSN 0165-2125

## Abstract

This paper follows the work of A.V. Shanin on diffraction by an ideal quarter-plane. Shanin's theory, based on embedding formulae, the acoustic uniqueness theorem and spherical edge Green's functions, leads to three modified Smyshlyaev formulae, which partially solve the far-field problem of scattering of an incident plane wave by a quarter-plane in the Dirichlet case. In this paper, we present similar formulae in the Neumann case, and describe a numerical method allowing a fast computation of the diffraction coefficient using Shanin's third modified Smyshlyaev formula. The method requires knowledge of the eigenvalues of the Laplace-Beltrami operator on the unit sphere with a cut, and we also describe a way of computing these eigenvalues. Numerical results are given for different directions of incident plane wave in the Dirichlet and the Neumann cases, emphasising the superiority of the third modified Smyshlyaev formula over the other two. © 2011 Elsevier B.V.

Item Type: | Article |
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Subjects: | UNSPECIFIED |

Divisions: | Div A > Energy |

Depositing User: | Cron Job |

Date Deposited: | 09 Dec 2016 17:23 |

Last Modified: | 28 Jan 2017 01:17 |

DOI: |