Efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane

Chandler-Wilde, Simon N.; Hothersall, David

doi:10.1006/jsvi.1995.0110

Cited by 89 publications

(83 citation statements)

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“…These integrals are similar in difficulty to integral representations for the Green's function G β * , for which very efficient numerical schemes are proposed in [18]. The integrands are not oscillatory and the coefficients do not become more difficult to evaluate as k → ∞.…”

Section: Implementation and Numerical Resultsmentioning

confidence: 96%

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A Wavenumber Independent Boundary Element Method for an Acoustic Scattering Problem

Langdon¹,

Chandler-Wilde²

2006

SIAM J. Numer. Anal.

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Abstract. In this paper we consider the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data, a problem which models, for example, outdoor sound propagation over inhomogeneous flat terrain. To achieve good approximation at high frequencies with a relatively low number of degrees of freedom, we propose a novel Galerkin boundary element method, using a graded mesh with smaller elements adjacent to discontinuities in impedance and a special set of basis functions so that, on each element, the approximation space contains polynomials (of degree ν) multiplied by traces of plane waves on the boundary. We prove stability and convergence and show that the error in computing the total acoustic field is O(N −(ν+1) log 1/2 N ), where the number of degrees of freedom is proportional to N log N . This error estimate is independent of the wavenumber, and thus the number of degrees of freedom required to achieve a prescribed level of accuracy does not increase as the wavenumber tends to infinity.

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Section: Implementation and Numerical Resultsmentioning

confidence: 96%

“…Explicit representations and efficient calculation methods for G β * are discussed in [18]. We shall require later the following bounds on G β * [20, (2.9), (2.10)], which hold provided Reβ * ≥ and |β…”

Section: Integral Equation Formulation and Regularity Of The Solutionmentioning

confidence: 99%

A Wavenumber Independent Boundary Element Method for an Acoustic Scattering Problem

Langdon¹,

Chandler-Wilde²

2006

SIAM J. Numer. Anal.

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“…For the three impedance values, results are shown in Fig. 4 for 20 for configuration (B1) and with the boundary element method utilizing the openBEM toolbox 21 for configuration (B2). In the boundary element method, at least 10 elements per wavelength have been used for all calculations.…”

Section: Impedance Planementioning

confidence: 99%

Application of the Fourier pseudospectral time-domain method in orthogonal curvilinear coordinates for near-rigid moderately curved surfaces

Hornikx

Dragna

2015

The Journal of the Acoustical Society of America

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Link to publication Citation for published version (APA):Hornikx, M. C. J., & Dragna, D. (2015). Application of the Fourier pseudo spectral time-domain method in orthogonal curvilinear coordinates for near-rigid moderately curved surfaces. Journal of the Acoustical Society of America, 138(1), 425-435. DOI: 10.1121/1.4922954 General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. The Fourier pseudospectral time-domain method is an efficient wave-based method to model sound propagation in inhomogeneous media. One of the limitations of the method for atmospheric sound propagation purposes is its restriction to a Cartesian grid, confining it to staircase-like geometries. A transform from the physical coordinate system to the curvilinear coordinate system has been applied to solve more arbitrary geometries. For applicability of this method near the boundaries, the acoustic velocity variables are solved for their curvilinear components. The performance of the curvilinear Fourier pseudospectral method is investigated in free field and for outdoor sound propagation over an impedance strip for various types of shapes. Accuracy is shown to be related to the maximum grid stretching ratio and deformation of the boundary shape and computational efficiency is reduced relative to the smallest grid cell in the physical domain. The applicability of the curvilinear Fourier pseudospectral time-domain method is demonstrated by investigating the effect of sound propagation over a hill in a nocturnal boundary layer. With the proposed method, accurate and efficient results for sound propagation over smoothly varying ground surfaces with high impedances can be obtained.

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“…However, as mentioned in §2.1 and described schematically in Fig. 1,p refl can also be viewed as the result of a line of line sources along y = −y s with strengths given by a generalized reflection coefficient R(x) (11,12). Here, we investigate the generalized reflection coefficient R(x) further, and show how this can be interpreted as a generalization of the classical method of images which is similar to, although different from, the complex line source generalization of the method of images for a point source in 3D described by, for example, Taraldsen [10].…”

Section: The Generalized Reflection Coefficient At An Impedance Wallmentioning

confidence: 99%

“…There have been many studies of the behaviour of an infinite flat impedance surface subjected to a point source in 3D [5][6][7][8][9][10] and subjected to a line source in 2D [11][12][13][14]. None of these studies consider a mean flow.…”

Section: Introductionmentioning

confidence: 99%

Reflection of an acoustic line source by an impedance surface with uniform flow

Gabard

2014

Journal of Sound and Vibration

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An exact analytic solution is derived for the 2D acoustic pressure field generated by a time-harmonic line mass source located above an impedance surface with uniform grazing flow. Closed-form asymptotic solutions in the far-field are also provided. The analysis is valid for both locally-reacting and nonlocally-reacting impedances, as is demonstrated by analysing a nonlocally reacting effective impedance representing the presence of a thin boundary layer over the surface. The analytic solution may be written in a form suggesting a generalization of the method of images to account for the impedance surface. The line source is found to excite surface waves on the impedance surface, some of which may be leaky waves which contradict the assumption of decay away from the surface predicted in previous analyses of surface waves with flow. The surface waves may be treated either (correctly) as unstable waves or (artificially) as stable waves, enabling comparison with previous numerical or mathematical studies which make either of these assumptions.The computer code for evaluating the analytic solution and far-field asymptotics is provided in the supplementary material. It is hoped this work will provide a useful benchmark solution for validating 2D numerical acoustic codes.

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Efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane

Cited by 89 publications

References 0 publications

A Wavenumber Independent Boundary Element Method for an Acoustic Scattering Problem

A Wavenumber Independent Boundary Element Method for an Acoustic Scattering Problem

Application of the Fourier pseudospectral time-domain method in orthogonal curvilinear coordinates for near-rigid moderately curved surfaces

Reflection of an acoustic line source by an impedance surface with uniform flow

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