An improved time-dependent Boundary Element Method for two-dimensional acoustic problems in a subsonic uniform flow

Barhoumi, Bassem; Bessrour, Jamel

doi:10.1016/j.jocs.2017.04.019

Cited by 7 publications

(13 citation statements)

References 65 publications

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“…Precisely, the BEM formulations have important advantages over the FEM solutions for solving the propagation and radiation problems with mean flow, such as the mesh generation and the CPU time. 39 For 3 D and 2 D domains, the boundary element methods have an integration terms over surfaces and its generators and the finite element methods have integration terms over volumes and its surfaces, respectively. Thus, it can be deduced that the BEM approach reduces the mesh model by one-dimensional, comparing to FEM approach.…”

Section: Introductionmentioning

confidence: 99%

“…The main disadvantages of using classical modal Helmholtz integral formulations are the complexity of transformation methods, 36 the convection effects, 30 the singular integrations, 26 the convected free terms, 28 and the nonreflecting boundary conditions. 39…”

Section: Introductionmentioning

confidence: 99%

“…77,78 Compared to the BEM formulation without flow, the supplementary singular terms have an important impact on computational burden of BEM solution with flow. 39,47…”

Section: Introductionmentioning

confidence: 99%

“…81,82 For 3 D and 2 D exterior radiation domains in arbitrary uniform flows, a general Sommerfeld condition with flow for both the time domain and the frequency domain approaches has been developed to solve the nonreflecting acoustic waves at infinity. 39 For 3 D and 2 D transformed mediums by the Prandtl-Glauert method, the Sommerfeld radiation conditions have been proposed by 36,83,84 not satisfying the physical quantities in the presence of mean flow. For axisymmetric domains with mean flow, we have proposed improved nonreflecting conditions with arbitrary mean to describe the boundary conditions at infinity.…”

Section: Introductionmentioning

confidence: 99%

“…For axisymmetric domains with mean flow, we have proposed improved nonreflecting conditions with arbitrary mean to describe the boundary conditions at infinity. 47 For non-axisymmetric domains with mean flow, the conventional SRC formulations 39,78 do not explicitly taking into account the modal order of physical quantities.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…77,78 Compared to the BEM formulation without flow, the supplementary singular terms have an important impact on computational burden of BEM solution with flow. 39,47…”

Section: Introductionmentioning

confidence: 99%