An Implementation of a Wave-Based Finite Difference Scheme for a 3-D Acoustic Problem

Ruiz, Gabriel; Rice, Henry J.

doi:10.1006/jsvi.2001.4218

Cited by 13 publications

(11 citation statements)

References 3 publications

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“…The wave expansion method (WEM) was first proposed by Caruthers et al [8], and was more recently used by Ruiz and Rice [10] and Barrera Rolla and Rice [15] to investigate sound propagation in quiescent media. The discretisation scheme may be used for solving linearised time-harmonic propagation equations.…”

Section: Wave Expansion Discretisation Schemementioning

confidence: 99%

“…Therefore, this boundary condition may be imposed by augmenting Eqn. 2 at each boundary point with an additional constraint row [10]. As the potential at each point is the superposition of plane wave functions, its derivatives in Eqn.…”

Section: Implementation Of a Flow Impedance Boundary Condition In Thementioning

confidence: 99%

“…At the inlet of the tube (the left-hand boundary) a Dirichlet condition is used to introduce plane waves. Dirichlet type boundary conditions may be implemented in the WEM by simply constraining the appropriate entries in the overall stiffness matrix K [10], i.e. setting the appropriate row to zeros with a one on the diagonal and entering the desired solution values into f.…”

Section: No Flow Casementioning

confidence: 99%

“…The implementation of a flow impedance boundary condition in the WEM has not been examined in the past, but is of interest due to the inherent efficiency of the scheme. The WEM uses fundamental solutions of the wave operator and so accurate solutions to linearised propagation equations may be obtained with only two-to-three points-per-wavelength [10], which is significantly less than the six-to-ten points-per-wavelength of comparable traditional finite difference and finite element methods. The method is robust to meshing and could be implemented in a meshless manner (only points, no elements).…”

Section: Introductionmentioning

confidence: 99%

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A wave expansion method for acoustic propagation in lined flow ducts

O’Reilly

2015

Applied Acoustics

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Acoustic liners are used extensively in engineering applications, particularly in aero-engines and automotive exhaust systems. In this paper, a flow impedance boundary conditions is introduced into the wave expansion method with the aim of providing an efficient methodology for computing the acoustic propagation through a lined duct with flow. For a potential flow, the boundary layer and the lined wall are included in the discretisation scheme by the Myers flow impedance boundary condition. The acoustic propagation through a flow-impedance tube is computed in order to validate the implementation of the impedance boundary condition in this scheme. The results show that this computationally light methodology provides generally good agreement with the experimental data.

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Section: Wave Expansion Discretisation Schemementioning

confidence: 99%

Section: Implementation Of a Flow Impedance Boundary Condition In Thementioning

confidence: 99%

Section: No Flow Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A wave expansion method for acoustic propagation in lined flow ducts

O’Reilly

2015

Applied Acoustics

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“…A sim ple m ethod to im plem ent a n atu ral radiation boundary condition [87] is to restrict th e propagation directions of th e fundam ental basis solutions to a selection of those propagating outw ards from th e com putational dom ain as shown in figure 3.4. A special "radiating" tem plate equation m ay then be constructed,…”

Section: N a Tu R A L R A D Ia Tio N B O U N D A R Y C O N D Itio Nmentioning

confidence: 99%

A forward-advancing wave expansion method for numerical solution of large-scale sound propagation problems

Rolla

Rice

2006

Journal of Sound and Vibration

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Dynamic solution of unbounded domains using finite element method: discrete Green's functions in frequency domain

Boroomand

Mossaiby

2006

Numerical Meth Engineering

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SUMMARYIn this paper we present a new approach for finite element solution of time-harmonic wave problems on unbounded domains. As representatives of the wave problems, discrete Green's functions are evaluated in finite element sense. The finite element mesh is considered to be of repeatable pattern (cell) constructed in rectangular co-ordinates. The system of FE equations is therefore reduced to a set of well-known dispersion equations by using a spectral solution approach. The spectral wave bases are constructed directly from the FE dispersion equations. Radiation condition is satisfied by selecting the wave bases so that the wave information is transmitted in appropriate directions at the cell level. Dirichlet/Neumann boundary conditions are defined at the edges of a quadrant of the main domain while using the axes of symmetry of the problem. A new discrete transformation method, recently proposed by the authors, is used to satisfy the boundary conditions. Comprehensive studies are made for showing the validity, accuracy and convergence of the solutions. The results of the benchmark problems indicate that the proposed method can be used to evaluate discrete Green's functions whose analytical forms are not available.

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An Implementation of a Wave-Based Finite Difference Scheme for a 3-D Acoustic Problem

Cited by 13 publications

References 3 publications

A wave expansion method for acoustic propagation in lined flow ducts

A wave expansion method for acoustic propagation in lined flow ducts

A forward-advancing wave expansion method for numerical solution of large-scale sound propagation problems

Dynamic solution of unbounded domains using finite element method: discrete Green's functions in frequency domain

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