Scattering of sound from axisymetric sources by multiple circular cylinders

Sherer, Scott E.

doi:10.1121/1.1641790

Cited by 41 publications

(23 citation statements)

References 15 publications

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“…12, and compared to the analytical solution by Sherer. 25 Additional simulations were subsequently performed with eleven-point Lagrange polynomials, to ascertain the origin of the remaining errors. A simulation with interpolation based on eleven-point Lagrange polynomials was undertaken on an identical grid, and yielded identical results, indicating that the residual errors in the spline simulation were not due to the choice of spline interpolation.…”

Section: Diffraction By Two Cylindersmentioning

confidence: 99%

High-order Curvilinear Simulations of Flows Around Non-Cartesian Bodies

Marsden

Bogey

Bailly

2004

10th AIAA/CEAS Aeroacoustics Conference

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The current work describes the application of high-order numerical techniques to single or multiple overset curvilinear body-fitted grids, demonstrating the feasibility of direct computations of noise radiated by flows around complex non-Cartesian bodies. Flows of both physical and industrial interest can be investigated with this approach. We first rapidly describe the numerical techniques implemented in our curvilinear simulations. The explicit high-order differencing and filtering schemes are presented, as well as their application to the curvilinear Navier-Stokes equations. We then present brief results of various 2-D acoustic simulations. First the flow around a cylinder, and the associated acoustic field, are described. The diameter-based Reynolds number Re D = 150 is under the critical Reynolds number of the onset of 3-D phenomena in the vortex-shedding. Simulation results can thus be meaningfully compared to experimental measurements. A case of acoustic scattering is then examined. A non-compact monopolar source is placed half way between two differently sized cylinders. A complex diffraction pattern is created, and resulting RMS pressure data are compared to the analytical solution. Finally the noise generated by a low Reynolds number laminar flow around a NACA 0012 airfoil is presented.

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Section: Diffraction By Two Cylindersmentioning

confidence: 99%

High-order Curvilinear Simulations of Flows Around Non-Cartesian Bodies

Marsden

Bogey

Bailly

2004

10th AIAA/CEAS Aeroacoustics Conference

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“…The scattering of an harmonic source by two cylinders is a challenging Sherer [40]. The interference beams are very well reproduced in the region between the two cylinders.…”

Section: Scattering Of An Harmonic Source By Two Cylindersmentioning

confidence: 94%

Study of interpolation methods for high-accuracy computations on overlapping grids

Chicheportiche

Gloerfelt

2012

Computers & Fluids

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. AbstractOverset strategy can be an efficient way to keep high-accuracy discretization by decomposing a complex geometry in topologically simple subdomains.Apart from the grid assembly algorithm, the key point of overset technique lies in the interpolation processes which ensure the communications between the overlapping grids. The family of explicit Lagrange and optimized interpolation schemes is studied. The a priori interpolation error is analyzed in the Fourier space, and combined with the error of the chosen discretization to highlight the modification of the numerical error. When high-accuracy algorithms are used an optimization of the interpolation coefficients can enhance the resolvality, which can be useful when high-frequency waves or small turbulent scales need to be supported by a grid. For general curvilinear grids in more than one space dimension, a mapping in a computational space followed by a tensorization of 1-D interpolations is preferred to a direct evaluation of the coefficient in the physical domain. A high-order extension of the isoparametric mapping is accurate and robust since it avoids the inversion of a matrix which may be ill-conditioned. A posteriori error analyses indicate that the interpolation stencil size must be tailored to the accuracy of the discretization scheme. For well discretized wavelengthes, the resultsshow that the choice of a stencil smaller than the stencil of the corresponding finite-difference scheme can be acceptable. Besides the gain of optimization to capture high-frequency phenomena is also underlined. Adding order contraints to the optimization allows an interesting trade-off when a large range of scales is considered. Finally, the ability of the present overset strategy to preserve accuracy is illustrated by the diffraction of an acoustic source by two cylinders, and the generation of acoustic tones in a rotor-stator interaction.Some recommandations are formulated in the closing section.

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“…Multiple scattering problems occur in many applications related to various areas of applied science, e.g., acoustics [1,2], electromagnetism [3,4], elasticity [5], and water-wave [6] problems. Mathematically speaking, the scattering field appears as the superposition of free field and radiation field.…”

Section: Introductionmentioning

confidence: 99%

“…When the point source is far away the scatterer, the problem can be seen as a multiple scattering problem subject to the plane wave. Sherer [1] developed an analytical method for solving the scattering problem with multiple and rigid circular cylinders arranged in an arbitrary configuration. He used the Hankel transform method to calculate the incident field and determined the scattering fields from each cylinder in the collection through the separation of variables.…”

Section: Introductionmentioning

confidence: 99%

Scattering of sound from point sources by multiple circular cylinders using addition theorem and superposition technique

Chen

Lee

Lin

et al. 2011

Numer. Methods Partial Differential Eq.

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In this study, we use the addition theorem and superposition technique to solve the scattering problem with multiple circular cylinders arising from point sound sources. Using the superposition technique, the problem can be decomposed into two individual parts. One is the free-space fundamental solution. The other is a typical boundary value problem (BVP) with specified boundary conditions derived from the addition theorem by translating the fundamental solution. Following the success of null-field boundary integral formulation to solve the typical BVP of the Helmholtz equation with Fourier densities, the second-part solution is easily obtained after collocating the observation point exactly on the real boundary and matching the boundary condition. The total solution is obtained by superimposing the two parts which are the fundamental solution and the semianalytical solution of the Helmholtz problem. An example was demonstrated to validate the present approach. The parameter study of size and spacing between cylinders are addressed. The results are well compared with the available theoretical solutions and experimental data.

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Scattering of sound from axisymetric sources by multiple circular cylinders

Cited by 41 publications

References 15 publications

High-order Curvilinear Simulations of Flows Around Non-Cartesian Bodies

High-order Curvilinear Simulations of Flows Around Non-Cartesian Bodies

Study of interpolation methods for high-accuracy computations on overlapping grids

Scattering of sound from point sources by multiple circular cylinders using addition theorem and superposition technique

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