Boundary element and finite element coupling for aeroacoustics simulations

Balin, Nolwenn; Casenave, Fabien; Dubois, François; Duceau, Eric; Duprey, Stefan; Terrasse, I.

doi:10.1016/j.jcp.2015.03.044

Cited by 23 publications

(24 citation statements)

References 40 publications

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“…The boundary conditions of the rigid and lined ducts are represented by transparent boundary conditions suitable for use in a finite element scheme which based on the Dirichlet-to-Neumann (DtN) boundary condition [5]. For particular acoustic domains, [6] has determined the acoustic propagation in a transformed domain by the Prandtl-Glauert transformation.…”

Section: Introductionmentioning

confidence: 99%

“…It is known that the finite element method has its limitations in modeling infinite domains. The unbounded medium contains the non-reflection condition which is represented by the Sommerfeld radiation condition in a medium at rest [7] or in a subsonic uniform flow [6]. Using the boundary element method (BEM), which requires a discretization of only the generator of the acoustic domain and that this Sommerfeld condition is automatically fulfilled by the fundamental solution.…”

Section: Introductionmentioning

confidence: 99%

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An improved axisymmetric convected boundary element method formulation with uniform flow

Barhoumi¹

2017

Mechanics & Industry

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This paper presents an improved form of the convected Boundary Element Method (BEM) for axisymmetric problems in a subsonic uniform flow. The proposed formulation based on the axisymmetric Convected Helmholtz Equation (CHE) and its fundamental solution that describes the sound radiation from a monopole source. The variables in the new axisymmetric boundary integral formulation can be expressed explicitly in terms of the acoustic pressure and its particular normal derivative. Also, the constant coefficients are expressed only in terms of the axisymmetric convected Green's function and its convected normal derivative. The particular and convected derivatives reduce the flow effects of the normal and the flow direction derivatives incorporated in the conventional convected boundary integral formulas. The advanced form of the axisymmetric boundary integral representation with flow is a similar form of the axisymmetric boundary element method without flow. Precisely, the two new operators significantly reduce the computational burden of the classical BEM and then becomes the CPU time of BEM without flow. The formula is verified comparing to both analytical and Finite Element Methods (FEM) of an axisymmetric infinite rigid duct in a subsonic uniform flow.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An improved axisymmetric convected boundary element method formulation with uniform flow

Barhoumi¹

2017

Mechanics & Industry

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“…However, due to the variable transformation, the physical space is deformed in the direction of the mean flow. The deformation of the domain complicates the formulation of the boundary conditions and the implementation of the transmission conditions for coupled formulations [13,14]. Alternatively, this drawback can be overcome by using an integral formulation in the physical space as proposed by Wu and Lee [15] in the frequency domain and by Hu [16] in the time domain.…”

Section: Introductionmentioning

confidence: 99%

An integral formulation for wave propagation on weakly non-uniform potential flows

Mancini

Astley

Sinayoko

et al. 2016

Journal of Sound and Vibration

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An integral formulation for acoustic radiation in moving flows is presented. It is based on a potential formulation for acoustic radiation on weakly non-uniform subsonic mean flows. This work is motivated by the absence of suitable kernels for wave propagation on non-uniform flow. The integral solution is formulated using a Green's function obtained by combining the Taylor and Lorentz transformations. Although most conventional approaches based on either transform solve the Helmholtz problem in a transformed domain, the current Green's function and associated integral equation are derived in the physical space. A dimensional error analysis is developed to identify the limitations of the current formulation. Numerical applications are performed to assess the accuracy of the integral solution. It is tested as a means of extrapolating a numerical solution available on the outer boundary of a domain to the far field, and as a means of solving scattering problems by rigid surfaces in non-uniform flows. The results show that the error associated with the physical model deteriorates with increasing frequency and mean flow Mach number. However, the error is generated only in the domain where mean flow non-uniformities are significant and is constant in regions where the flow is uniform.

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“…The integral representations can be formulated in the transformed acoustic medium [1,2] or in the original acoustic medium [3,4]. However, the advantages of using boundary integral formulations in an untransformed acoustic medium are that the convection effects are explicit and that complex boundary conditions can be handled easily.…”

Section: Introductionmentioning

confidence: 99%

“…JID:CRAS2B AID:3361 /FLA [m3G; v1.159; Prn:29/07/2015; 16:49] P.4(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) …”

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confidence: 99%

A simple and effective axisymmetric convected Helmholtz integral equation

Beldi¹,

Barhoumi²

2015

Comptes Rendus. Mécanique

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In this paper, we develop an axisymmetric boundary integral equation that derives from a reformulation of the 3D Helmholtz integral formula for the acoustic radiation problems in a subsonic uniform flow. Through the use of a new non-standard derivative operator, the axisymmetric convected Helmholtz integral equation substantially reduces the effects of flow incorporated in the classical convected boundary integral formulations, and involved in the normal derivative and the derivative in the flow direction of the axisymmetric convected Green's function. As for the free term derived from the singular integrals, it is given by a new expression independent of complete elliptic integrals and evaluated analytically as a convected angle in the meridian plane. The numerical treatment of singular integrals requires only the use of standard Gauss quadrature rules. Different test cases are presented.

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Boundary element and finite element coupling for aeroacoustics simulations

Cited by 23 publications

References 40 publications

An improved axisymmetric convected boundary element method formulation with uniform flow

An improved axisymmetric convected boundary element method formulation with uniform flow

An integral formulation for wave propagation on weakly non-uniform potential flows

A simple and effective axisymmetric convected Helmholtz integral equation

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