Image conditions for polar and cylindrical coordinate separation-of-variables acoustic multiple scattering models with perfectly reflecting flat boundaries

A - Papers appearing in refereed journals

Shin, H.-C. 2018. Image conditions for polar and cylindrical coordinate separation-of-variables acoustic multiple scattering models with perfectly reflecting flat boundaries. Quarterly Journal Of Mechanics And Applied Mathematics. 71 (3), pp. 273 - 296. https://doi.org/10.1093/qjmam/hby005

AuthorsShin, H.-C.
Abstract

This article addresses efficient implementation of the method of images for acoustic multiple scattering models (MSM) with perfectly reflecting flat boundaries. Time-harmonic problems are first solved in the polar coordinate system for circular scatterers; then the models are extended to the cylindrical coordinate system with (semi-)infinitely long circular cylinders. The MSM in this article is based on the method of separation of variables and Graf’s addition theorem. Derivations are provided for ‘image conditions’ which relate the unknown coefficients of outgoing waves from image scatterers with those of real counterparts. The method of images is applied to wedge-shaped domains with apex angles of π/n rad for a positive integer n. Image conditions make the MSM numerically more efficient: the system of linear equations for unknown coefficients is formulated 2n times faster; its memory requirements are reduced by 4n to the power of 2 times for direct solvers. The proposed model is applied to a benchmark wedge in ocean environment with n = 64. Good agreement is observed between the MSM with image conditions and the boundary element method. Furthermore, half- and quarter-space measurements in an anechoic chamber are in accordance with the correct use of image conditions. Incorrect image conditions reported elsewhere for polar coordinates are also discussed.

Year of Publication2018
JournalQuarterly Journal Of Mechanics And Applied Mathematics
Journal citation71 (3), pp. 273 - 296
Digital Object Identifier (DOI)https://doi.org/10.1093/qjmam/hby005
Open accessPublished as green open access
FunderEngineering and Physical Sciences Research Council
Funder project or codeEP/K03720X/1
Publisher's version
Output statusPublished
Publication dates
Online28 Mar 2018
Publication process dates
Accepted26 Feb 2018
PublisherOxford University Press (OUP)
Copyright licenseCC BY
ISSN0033-5614

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