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Stability and accuracy of finite element methods for flow acoustics: I: general theory and application to one-dimensional propagation

Stability and accuracy of finite element methods for flow acoustics: I: general theory and application to one-dimensional propagation
Stability and accuracy of finite element methods for flow acoustics: I: general theory and application to one-dimensional propagation
The dispersion properties of finite element models for aeroacoustic propagation based on the convected scalar Helmholtz equation and on the Galbrun equation are examined. The current study focusses on the effect of the mean flow on the dispersion and amplitude errors present in the discrete numerical solutions. A general two-dimensional dispersion analysis is presented for the discrete problem on a regular unbounded mesh, and results are presented for the particular case of one-dimensional acoustic propagation in which the wave direction is aligned with the mean flow. The magnitude and sign of the mean flow is shown to have a significant effect on the accuracy of the numerical schemes. Quadratic Helmholtz elements in particular are shown to be much less effective for downstream - as opposed to upstream - propagation, even when the effect of wave shortening or elongation due to the mean flow is taken into account. These trends are also observed in solutions obtained for simple test problems on finite meshes. A similar analysis of two-dimensional propagation is presented in an accompanying article.
finite element methods, aeroacoustics, dispersion error, helmholtz, galbrun
0029-5981
947-973
Gabard, G.
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
Astley, R.J.
cb7fed9f-a96a-4b58-8939-6db1010f9893
Ben Tahar, M.
a4a3c0d5-301e-4dbe-9907-641542b6ae75
Gabard, G.
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
Astley, R.J.
cb7fed9f-a96a-4b58-8939-6db1010f9893
Ben Tahar, M.
a4a3c0d5-301e-4dbe-9907-641542b6ae75

Gabard, G., Astley, R.J. and Ben Tahar, M. (2005) Stability and accuracy of finite element methods for flow acoustics: I: general theory and application to one-dimensional propagation. International Journal for Numerical Methods in Engineering, 63 (7), 947-973. (doi:10.1002/nme.1308).

Record type: Article

Abstract

The dispersion properties of finite element models for aeroacoustic propagation based on the convected scalar Helmholtz equation and on the Galbrun equation are examined. The current study focusses on the effect of the mean flow on the dispersion and amplitude errors present in the discrete numerical solutions. A general two-dimensional dispersion analysis is presented for the discrete problem on a regular unbounded mesh, and results are presented for the particular case of one-dimensional acoustic propagation in which the wave direction is aligned with the mean flow. The magnitude and sign of the mean flow is shown to have a significant effect on the accuracy of the numerical schemes. Quadratic Helmholtz elements in particular are shown to be much less effective for downstream - as opposed to upstream - propagation, even when the effect of wave shortening or elongation due to the mean flow is taken into account. These trends are also observed in solutions obtained for simple test problems on finite meshes. A similar analysis of two-dimensional propagation is presented in an accompanying article.

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Published date: 2005
Keywords: finite element methods, aeroacoustics, dispersion error, helmholtz, galbrun
Organisations: Acoustics Group

Identifiers

Local EPrints ID: 10401
URI: https://eprints.soton.ac.uk/id/eprint/10401
ISSN: 0029-5981
PURE UUID: d5988b68-975c-4874-8d53-b8419f3b2fd4

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Date deposited: 26 May 2005
Last modified: 09 Sep 2019 17:57

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