A Two-Dimensional Acoustic Tangential Derivative Boundary Element Method Including Viscous and Thermal Losses

Andersen, Poul; Henrı́quez, Vicente Cutanda; Aage, Niels; Marburg, Steffen

doi:10.1142/s2591728518500366

Cited by 6 publications

(3 citation statements)

References 16 publications

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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

101

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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

101

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“…[11][12][13][14] Compared with the traditional finite element method (FEM) commonly used in topology optimization, the boundary element method (BEM) seems to be more favorable when optimizing the distribution of sound-absorbing materials in the exterior sound field, [15][16][17][18] since only the boundaries need to be discretized and the Sommerfeld boundary condition is automatically satisfied. [19][20][21] Similarly, the BEM is used in many situations. [22][23][24][25][26] The traditional topology optimization finds the optimal solution at a specific frequency, and thus the results may not work for another frequency.…”

Section: Introductionmentioning

confidence: 99%

“…Topology optimization technology is one of the powerful tools to find the optimal distribution of sound‐absorbing materials 11‐14 . Compared with the traditional finite element method (FEM) commonly used in topology optimization, the boundary element method (BEM) seems to be more favorable when optimizing the distribution of sound‐absorbing materials in the exterior sound field, 15‐18 since only the boundaries need to be discretized and the Sommerfeld boundary condition is automatically satisfied 19‐21 . Similarly, the BEM is used in many situations 22‐26 .…”

Section: Introductionmentioning

confidence: 99%

A BEM broadband topology optimization strategy based on Taylor expansion and SOAR method—Application to 2D acoustic scattering problems

Chen,

Zhao,

Lian

et al. 2023

Numerical Meth Engineering

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In this article, an innovative method is proposed for broadband topology optimization of sound‐absorbing materials adhering to the surface of a sound barrier structure. Helmholtz equation for the acoustic problems is solved using the boundary element method, while sensitivities of the objective function with respect to a large number of design variables are calculated via a sensitivity analysis method originated from the adjoint variable method (AVM), and the optimal solution is obtained by the method of moving asymptotes (MMA). Since the traditional single‐frequency topology optimization is frequency dependent, that is, the optimal solution at a certain frequency may not be optimal at other frequencies, broadband topology optimization of sound‐absorbing materials is conducted in this work. To address the problem of tremendous computational cost due to repetitive calculations at each discrete frequency point during broadband optimization, Taylor expansion of the Hankel function is performed to decouple the frequency dependent and independent terms in the BEM equations. For large‐scale problems, a reduced‐order model that retains the essential structures and key properties of the original model is built using the second‐order Arnoldi (SOAR) method. The accuracy and feasibility of the proposed algorithms are finally validated via some two‐dimensional numerical examples.

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Subdivision Surfaces — Boundary Element Accelerated by Fast Multipole for the Structural Acoustic Problem

Chen

Zhao

et al. 2020

J. Theor. Comp. Acout.

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A novel boundary element method based on subdivision surfaces is applied to simulate wave scattering problems governed by the Helmholtz equation. The Loop subdivision scheme widely used in the CAD (computer aided design) field is applied to represent the geometric model and approximate physical field variables. The novelty of this work is that it is the first time to apply the fast multipole method for subdivision surface boundary element method to accelerate the solution of the system of equations. It is demonstrated that the subdivision surfaces boundary element method based on the Loop subdivision scheme performs well in terms of accuracy, and automatically provides multiresolution subdivision hierarchy models to meet the requirements of different precision. This approach is then applied to several real-world applications to illustrate the potential for integrated engineering analysis.

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A Two-Dimensional Acoustic Tangential Derivative Boundary Element Method Including Viscous and Thermal Losses

Cited by 6 publications

References 16 publications

The Boundary Element Method in Acoustics: A Survey

The Boundary Element Method in Acoustics: A Survey

A BEM broadband topology optimization strategy based on Taylor expansion and SOAR method—Application to 2D acoustic scattering problems

Subdivision Surfaces — Boundary Element Accelerated by Fast Multipole for the Structural Acoustic Problem

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