A Numerical Model of an Acoustic Metamaterial Using the Boundary Element Method Including Viscous and Thermal Losses

Juhl, Peter Møller; Henrı́quez, Vicente Cutanda; Andersen, Poul; Jensen, Jakob Søndergaard; Sánchez‐Dehesa, José

doi:10.1142/s0218396x17500060

Cited by 30 publications

(17 citation statements)

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“…Similar to the approach in half-pace problems, discussed in Section 5.1.2, aero-acoustic problems are adapted for the BEM by revising the Green's function [308][309][310]. Recently the BEM in acoustics has been adapted to model viscous and thermal losses [311][312][313].…”

Section: Aero-acousticsmentioning

confidence: 99%

The Boundary Element Method in Acoustics: A Survey

Kirkup

2019

Applied Sciences

108

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The boundary element method (BEM) in the context of acoustics or Helmholtz problems is reviewed in this paper. The basis of the BEM is initially developed for Laplace’s equation. The boundary integral equation formulations for the standard interior and exterior acoustic problems are stated and the boundary element methods are derived through collocation. It is shown how interior modal analysis can be carried out via the boundary element method. Further extensions in the BEM in acoustics are also reviewed, including half-space problems and modelling the acoustic field surrounding thin screens. Current research in linking the boundary element method to other methods in order to solve coupled vibro-acoustic and aero-acoustic problems and methods for solving inverse problems via the BEM are surveyed. Applications of the BEM in each area of acoustics are referenced. The computational complexity of the problem is considered and methods for improving its general efficiency are reviewed. The significant maintenance issues of the standard exterior acoustic solution are considered, in particular the weighting parameter in combined formulations such as Burton and Miller’s equation. The commonality of the integral operators across formulations and hence the potential for development of a software library approach is emphasised.

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Section: Aero-acousticsmentioning

confidence: 99%

The Boundary Element Method in Acoustics: A Survey

Kirkup

2019

Applied Sciences

108

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“…In many cases, the SFD-BEM performance is similar to the original FDD-BEM formulation, for example a metamaterial model. 6 However, the SFD-BEM shows its benefits in cases where the calculation is affected by several sources of instability. In this section we use a three-dimensional BEM model of a condenser microphone as a test case.…”

Section: Microphone Test Casementioning

confidence: 99%

“…Devices of this kind are acoustic transducers, couplers, hearing aids and small-scale acoustic metamaterials. 4,5,6 For intricate and highly coupled devices, approximate solutions taking limiting hypothesis may not be sufficient for appropriate modeling. They must be tested or even replaced by full numerical models of the sound field with viscous and thermal losses.…”

Section: Introductionmentioning

confidence: 99%

A Three-Dimensional Acoustic Boundary Element Method Formulation with Viscous and Thermal Losses Based on Shape Function Derivatives

Henrı́quez

Andersen

2018

J. Theor. Comp. Acout.

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Sound waves in fluids are subject to viscous and thermal losses, which are particularly relevant in the so-called viscous and thermal boundary layers at the boundaries, with thicknesses in the micrometer range at audible frequencies. Small devices such as acoustic transducers or hearing aids must then be modeled with numerical methods that include losses. In recent years, versions of both the Finite Element Method (FEM) and the Boundary Element Method (BEM) including viscous and thermal losses have been developed. This paper deals with an improved formulation in three dimensions of the BEM with losses which avoids the calculation of tangential derivatives on the surface by finite differences used in a previous BEM implementation. Instead, the tangential derivatives are obtained from the element shape functions. The improved implementation is demonstrated using an oscillating sphere, where an analytical solution exists, and a condenser microphone as test cases.

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“…55 This induces a high computational burden of CPU time. For example, the computational code of OpenBEM 56 and AIBEM 57 used for numerically solving the Helmholtz problems with axisymmetric and non-axisymmetric boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

A modal boundary element method for axisymmetric acoustic problems in an arbitrary uniform mean flow

Barhoumi

Bessrour

2020

International Journal of Aeroacoustics

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This paper presents a new numerical analysis approach based on an improved Modal Boundary Element Method (MBEM) formulation for axisymmetric acoustic radiation and propagation problems in a uniform mean flow of arbitrary direction. It is based on the homogeneous Modal Convected Helmholtz Equation (MCHE) and its convected Green’s kernel using a Fourier transform method. In order to simplify the flow terms, a general modal boundary integral solution is formulated explicitly according to two new operators such as the particular and convected kernels. Through the use of modified operators, the improved MBEM approach with flow takes a convective form of the general MBEM approach and has a similar form of the nonflow MBEM formulation. The reference and reduced Helmholtz Integral Equations (HIEs) are implicitly taken into account a new nonreflecting Sommerfeld condition to solve far field axisymmetric regions in a uniform mean flow. For isolating the singular integrations, the modal convected Green’s kernel and its modified normal derivative are performed partly analytically in terms of Laplace coefficients and partly numerically in terms of Fourier coefficients. These coefficients are computed by recursion schemes and Gauss-Legendre quadrature standard formulae. Specifically, standard forms of the free term and its convected angle resulting from the singular integrals can be expressed only in terms of real angles in meridian plane. To demonstrate the application of the improved MBEM formulation, three exterior acoustic case studies are considered. These verification cases are based on new analytic formulations for axisymmetric acoustic sources, such as axisymmetric monopole, axial and radial dipole sources in the presence of an arbitrary uniform mean flow. Directivity plots obtained using the proposed technique are compared with the analytical results.

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A Numerical Model of an Acoustic Metamaterial Using the Boundary Element Method Including Viscous and Thermal Losses

Abstract: Published 26In recent years, boundary element method (BEM) and finite element method (FEM) implementa-

Cited by 30 publications

References 10 publications

The Boundary Element Method in Acoustics: A Survey

The Boundary Element Method in Acoustics: A Survey

A Three-Dimensional Acoustic Boundary Element Method Formulation with Viscous and Thermal Losses Based on Shape Function Derivatives

A modal boundary element method for axisymmetric acoustic problems in an arbitrary uniform mean flow

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