Analysis of high-order finite elements for convected wave propagation
Analysis of high-order finite elements for convected wave propagation
In this paper, we examine the performance of high-order finite element methods (FEM) for aeroacoustic propagation, based on the convected Helmholtz equation. A methodology is presented to measure the dispersion and amplitude errors of the p-FEM, including non-interpolating shape functions, such as ‘bubble’ shape functions. A series of simple test cases are also presented to support the results of the dispersion analysis. The main conclusion is that the properties of p-FEM that make its strength for standard acoustics (e.g., exponential p-convergence, low dispersion error) remain present for flow acoustics as well. However, the flow has a noticeable effect on the accuracy of the numerical solution, even when the change in wavelength due to the mean flow is accounted for, and an approximation of the dispersion error is proposed to describe the influence of the mean flow. Also discussed is the so-called aliasing effect, which can reduce the accuracy of the solution in the case of downstream propagation. This can be avoided by an appropriate choice of mesh resolution.
finite element method, dispersion analysis, high-order elements, p-FEM, convected propagation
665-688
Gabard, Gwenael
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
Beriot, Hadrien
af5a12ac-8347-48b9-9e15-9319a59163a9
Perrey-Debain, Emmanuel
0b3b8b55-4c98-4050-980f-a2f05ab21358
14 December 2013
Gabard, Gwenael
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
Beriot, Hadrien
af5a12ac-8347-48b9-9e15-9319a59163a9
Perrey-Debain, Emmanuel
0b3b8b55-4c98-4050-980f-a2f05ab21358
Gabard, Gwenael, Beriot, Hadrien and Perrey-Debain, Emmanuel
(2013)
Analysis of high-order finite elements for convected wave propagation.
International Journal for Numerical Methods in Engineering, 96 (11), .
(doi:10.1002/nme.4559).
Abstract
In this paper, we examine the performance of high-order finite element methods (FEM) for aeroacoustic propagation, based on the convected Helmholtz equation. A methodology is presented to measure the dispersion and amplitude errors of the p-FEM, including non-interpolating shape functions, such as ‘bubble’ shape functions. A series of simple test cases are also presented to support the results of the dispersion analysis. The main conclusion is that the properties of p-FEM that make its strength for standard acoustics (e.g., exponential p-convergence, low dispersion error) remain present for flow acoustics as well. However, the flow has a noticeable effect on the accuracy of the numerical solution, even when the change in wavelength due to the mean flow is accounted for, and an approximation of the dispersion error is proposed to describe the influence of the mean flow. Also discussed is the so-called aliasing effect, which can reduce the accuracy of the solution in the case of downstream propagation. This can be avoided by an appropriate choice of mesh resolution.
Text
IJNME_2012.pdf
- Accepted Manuscript
More information
e-pub ahead of print date: 29 August 2013
Published date: 14 December 2013
Keywords:
finite element method, dispersion analysis, high-order elements, p-FEM, convected propagation
Organisations:
Acoustics Group
Identifiers
Local EPrints ID: 364850
URI: http://eprints.soton.ac.uk/id/eprint/364850
ISSN: 0029-5981
PURE UUID: 4e4554a9-d0f2-4f2c-973c-e871b1378c81
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Date deposited: 13 May 2014 16:44
Last modified: 14 Mar 2024 16:42
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Contributors
Author:
Gwenael Gabard
Author:
Hadrien Beriot
Author:
Emmanuel Perrey-Debain
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