Comptes Rendus
no. 9
A simple and effective axisymmetric convected Helmholtz integral equation
Mohamed Beldi1  ; Bassem Barhoumi1
1 MAI Laboratory, University Tunis El Manar II, BP 37, Campus universitaire El-Manar, 2092 El Manar, Tunisia
Comptes Rendus. Mécanique, Volume 343 (2015) no. 9, pp. 457-470.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2015.07.001
Mots clés : Axisymmetric, Axisymmetric convected Green's function, Convected boundary integral formulation, Weakly singular integrals, Monopole source in a uniform flow
Mohamed Beldi 1 ; Bassem Barhoumi 1

1 MAI Laboratory, University Tunis El Manar II, BP 37, Campus universitaire El-Manar, 2092 El Manar, Tunisia 
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Mohamed Beldi; Bassem Barhoumi. A simple and effective axisymmetric convected Helmholtz integral equation. Comptes Rendus. Mécanique, Volume 343 (2015) no. 9, pp. 457-470. doi : 10.1016/j.crme.2015.07.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.07.001/

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