An improved axisymmetric Convected Boundary Element Method formulation with uniform flow

Bassem Barhoumi (1)

1 LR-MAI-ENIT - Laboratoire de Mécanique Appliquée et Ingénierie [Tunis]

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.

Mots clés: Axisymmetric Convected Boundary Element Method; Convected Helmholtz equation; Axisymmetric convected Green's function; Singular integrals; Finite Element Method; Axisymmetric infinite rigid duct

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Acoustique [physics.class-ph]

Bassem Barhoumi. An improved axisymmetric Convected Boundary Element Method formulation with uniform flow. Mechanics & Industry, 2015, ⟨10.1051/meca/2016064⟩. ⟨hal-01232124v3⟩