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A Computational Method to Calculate the Exact Solution for Acoustic Scattering by Fluid Spheroids

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The problem of scattering of harmonic plane acoustic waves by fluid spheroids (prolate and oblate) is addressed from an analytical approach. Mathematically, it consists in solving the Helmholtz equation in an unbounded domain with Sommerfeld radiation condition at infinity. The domain where propagation takes place is characterised by density and sound speed values ρ 0 and c 0, respectively, while ρ 1 and c 1 are the corresponding density and sound speed values of an immersed object that is responsible of the scattered field. Since Helmholtz equation is separable in prolate/oblate spheroidal coordinates, its exact solution for the scattered field can be expressed as an expansion on prolate/oblate spheroidal functions multiplied by coefficients whose values depend upon the boundary conditions verified at the medium-immersed fluid obstacle interface. The general case (c 0c 1 ) is cumbersome because it requires to solve successive matrix systems that are ill-conditioned when c 1 /c 0 is far from unity. In this paper, a numerical implementation of the general exact solution that is valid for any range of eccentricity values and for c 0c 1, is provided. The high level solver code has been written in the Julia programming language while a software package recently released in the literature has been used to compute the spheroidal functions. Several limit cases (Dirichlet and Neumann boundary conditions, spheroid tending to sphere) have been satisfactorily verified using the implemented code. The corresponding example scripts can be downloaded from the authors' web (GitHub) site. The numerical implementation of the exact solution leads to results that are in agreement with reported results obtained through approximate solutions for far-field and near-field regimes. Additionally, the new code has been used to extend results reported in the literature.
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Document Type: Research Article

Publication date: November 1, 2016

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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