Time harmonic acoustic scattering in presence of a shear flow and a Myers impedance condition

The problem of a time-harmonic acoustic wave scattering from a cylindrical object in shallow oceans is solved by an approximate boundary integral method. In the method we employ a Green's function of the Helmholtz equation with sound soft sea level and sound hard sea bottom conditions, and reformulate the problem into a boundary integral equation on the surface of the scattering object. The kernel of the integral equation is given by an infinite series, and is approximated by an appropriate truncation. The integral equation is then fully discretized by applying a quadrature rule. The method has an O(N−3) rate of convergence. Various numerical examples are presented.

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MATHEMATICAL ANALYSIS OF THE ACOUSTIC DIFFRACTION BY A MUFFLER CONTAINING PERFORATED DUCTS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202505000649 ◽

2005 ◽

Vol 15 (07) ◽

pp. 1059-1090 ◽

Cited By ~ 11

Author(s):

A. S. BONNET-BEN DHIA ◽

D. DRISSI ◽

N. GMATI

Keyword(s):

Three Dimensional ◽

Two Dimensions ◽

Scalar Problem ◽

Fredholm Type ◽

Numerical Examples ◽

Time Harmonic ◽

Impedance Condition ◽

Absorbing Material ◽

Acoustic Diffraction ◽

Theoretical Results

We consider the three-dimensional scalar problem of acoustic propagation in a muffler. We develop and analyze a Fredholm-type formulation for a stationary fluid in the time-harmonic setting. We prove a homogenization result for a muffler containing periodically perforated ducts. Essentially, the perforated boundaries become completely transparent when the period of perforations, which is assumed to be of the same order as the size of perforations, tends to zero. We also derive a homogenized impedance condition when the perforated duct is coated by an absorbing material. We present numerical examples in two dimensions, obtained from coupling finite elements in the muffler with modal decompositions in the inlet and outlet ducts, which demonstrate the limiting validity of the theoretical results.

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Time-Harmonic Acoustic Scattering in a Complex Flow: A Full Coupling Between Acoustics and Hydrodynamics

Communications in Computational Physics ◽

10.4208/cicp.221209.030111s ◽

2012 ◽

Vol 11 (2) ◽

pp. 555-572 ◽

Cited By ~ 4

Author(s):

A.S.Bonnet-Ben Dhia ◽

J.F. Mercier ◽

F. Millot ◽

S. Pernet ◽

E. Peynaud

Keyword(s):

Complex Geometry ◽

Acoustic Scattering ◽

Mathematical Framework ◽

Perfectly Matched Layers ◽

Mean Flow ◽

Complex Flow ◽

Numerical Result ◽

Convection Equation ◽

Time Harmonic ◽

Artificial Boundaries

AbstractFor the numerical simulation of time harmonic acoustic scattering in a complex geometry, in presence of an arbitrary mean flow, the main difficulty is the coexistence and the coupling of two very different phenomena: acoustic propagation and convection of vortices. We consider a linearized formulation coupling an augmented Galbrun equation (for the perturbation of displacement) with a time harmonic convection equation (for the vortices). We first establish the well-posedness of this time harmonic convection equation in the appropriate mathematical framework. Then the complete problem, with Perfectly Matched Layers at the artificial boundaries, is proved to be coercive + compact, and a hybrid numerical method for the solution is proposed, coupling finite elements for the Galbrun equation and a Discontinuous Galerkin scheme for the convection equation. Finally a 2D numerical result shows the efficiency of the method.

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