Infinite elements for transient flow acoustics

Astley, R.J.; Hamilton, J. A.

doi:10.2514/6.2001-2273

Cited by 7 publications

(5 citation statements)

References 22 publications

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“…As frequency increases it's normal to increase the number of degrees of freedom in the finite element mesh: as a general guideline, between 7 and 10 finite element nodes should be adopted per wavelength [21]. Thus, for HVAC silencers a very large number of degrees of freedom are often necessary, even for relatively small silencers.…”

Section: B Multi-mode Excitationmentioning

confidence: 99%

The influence of baffle fairings on the acoustic performance of rectangular splitter silencers

Kirby

2005

The Journal of the Acoustical Society of America

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A numerical model based on the finite element method is developed for a finite length, HVAC splitter silencer. The model includes an arbitrary number of bulk-reacting splitters separated from the airway by a thin perforated metal sheet and accommodates higher order modes in the incident sound field. Each perforated sheet is joined to rigid, impervious, metallic fairing situated at either end of a splitter. The transmission loss for the silencer is quantified by application of the point collocation technique, and predictions are compared to experimental measurements reported in the literature. The splitter fairing is shown to significantly affect silencer performance, especially when higher order incident modes are present. It is concluded that laboratory measurements, and theoretical predictions, that are based on a predominantly plane wave sound source are unlikely to reflect accurately the true performance of an HVAC silencer in a real ducting system. 3

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Section: B Multi-mode Excitationmentioning

confidence: 99%

The influence of baffle fairings on the acoustic performance of rectangular splitter silencers

Kirby

2005

The Journal of the Acoustical Society of America

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“…More recent formulations use orthogonal polynomials to improve conditioning [33]. With the infinite elements, the equations in the time domain may become instable [25], which makes time domain computations rather tricky. For spheroidal domains, the finite element-infinite element formulation leads to an index one stable system of differential algebraic equations [26].…”

Section: Finite Element Discretization Of Acoustic Problemsmentioning

confidence: 99%

“…Therefore, the linear systems that arise in implicit time integration methods are relatively easy to solve. When infinite elements are used, the matrices in (2) are non-symmetric, M can be singular, and there are cases where the equations are unstable [1,[23][24][25][26]. We have observed that infinite elements do not reduce the computational efficiency of the iterative linear systems solvers in the time domain.…”

Section: Introductionmentioning

confidence: 99%

Connection and comparison between frequency shift time integration and a spectral transformation preconditioner

Meerbergen

Coyette²

2008

Numerical Linear Algebra App

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The numerical study of exterior acoustics problems is usually carried out in the frequency domain. Finite element analyses often require the solution of large-scale algebraic linear systems. For very large problems, sometimes the time domain is used. Implicit time integration requires linear system solves, but these are often far easier than those from the frequency domain. This paper shows a connection between a spectral transformation preconditioner and a frequency shift time integration. This preconditioner is close to the shifted Laplace preconditioner. The preconditioned iterative method appears to be faster than time integration.

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“…However, infinite elements often introduce instabilities in the mathematical model. In the case of spherical infinite elements, there is a coupling between a second-and a first-order equation [7]. The first-order equation arises from the infinite elements.…”

Section: Introductionmentioning

confidence: 99%

“…These elements are based on a truncated multipole expansion in a suitable coordinate system (spherical, spheroidal or ellipsoidal coordinates can be selected for that purpose) and the selection of test functions built from complex conjugates of trial functions [5]. The resulting discrete matrices exhibit a simple polynomial frequency dependence [4][5][6][7] that allows for the direct set-up of the related transient model by application of a formal inverse Fourier transform. The time integration of related differential equations has been performed by several investigators [4,5] who already pointed some instability issues and proposed improved formulations [8,9].…”

Section: Introductionmentioning

confidence: 99%

Time integration for spherical acoustic finite–infinite element models

Coyette¹,

Meerbergen²,

Robbé³

2005

Numerical Meth Engineering

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SUMMARYIn this paper, we analyse the numerical time integration of models of exterior acoustics. The major challenge lies in the instabilities that may arise from the infinite elements. In this paper we consider the special case of spherical infinite elements formulations, which have shown their relevance for industrial applications. We propose a method that combines Crank-Nicholson's method with a filtering step by the backward Euler method. The paper is illustrated with an example relevant to industry.

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Infinite elements for transient flow acoustics

Cited by 7 publications

References 22 publications

The influence of baffle fairings on the acoustic performance of rectangular splitter silencers

The influence of baffle fairings on the acoustic performance of rectangular splitter silencers

Connection and comparison between frequency shift time integration and a spectral transformation preconditioner

Time integration for spherical acoustic finite–infinite element models

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