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Stability and accuracy of finite element methods for flow acoustics. II: two-dimensional effects

Stability and accuracy of finite element methods for flow acoustics. II: two-dimensional effects
Stability and accuracy of finite element methods for flow acoustics. II: two-dimensional effects
This is the second of two articles that focus on the dispersion properties of finite element models for acoustic propagation on mean flows. We consider finite element methods based on linear potential theory in which the acoustic disturbance is modelled by the convected Helmholtz equation, and also those based on a mixed Galbrun formulation in which acoustic pressure and Lagrangian displacement are used as discrete variables.

The current paper focuses on the effects of numerical anisotropy which are associated with the orientation of the propagating wave to the mean flow and to the grid axes. Conditions which produce aliasing error in the Helmholtz formulation are of particular interest. The 9-noded Lagrangian element is shown to be superior to the more commonly used 8-noded serendipity element. In the case of the Galbrun elements, the current analysis indicates that isotropic meshes generally reduce numerical error of triangular elements and that higher order mixed quadrilaterals are generally less effective than an equivalent mesh of lower order triangles.
finite element methods, aeroacoustics, dispersion error, helmholtz, galbrun
0029-5981
974-987
Gabard, G.
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
Astley, R.J.
cb7fed9f-a96a-4b58-8939-6db1010f9893
Ben Tahar, M.
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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. II: two-dimensional effects. International Journal for Numerical Methods in Engineering, 63 (7), 974-987. (doi:10.1002/nme.1319).

Record type: Article

Abstract

This is the second of two articles that focus on the dispersion properties of finite element models for acoustic propagation on mean flows. We consider finite element methods based on linear potential theory in which the acoustic disturbance is modelled by the convected Helmholtz equation, and also those based on a mixed Galbrun formulation in which acoustic pressure and Lagrangian displacement are used as discrete variables.

The current paper focuses on the effects of numerical anisotropy which are associated with the orientation of the propagating wave to the mean flow and to the grid axes. Conditions which produce aliasing error in the Helmholtz formulation are of particular interest. The 9-noded Lagrangian element is shown to be superior to the more commonly used 8-noded serendipity element. In the case of the Galbrun elements, the current analysis indicates that isotropic meshes generally reduce numerical error of triangular elements and that higher order mixed quadrilaterals are generally less effective than an equivalent mesh of lower order triangles.

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

Identifiers

Local EPrints ID: 28387
URI: https://eprints.soton.ac.uk/id/eprint/28387
ISSN: 0029-5981
PURE UUID: 6eb1f960-abbd-4d39-af85-0637b8b11676

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Date deposited: 02 May 2006
Last modified: 09 Sep 2019 17:53

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Contributors

Author: G. Gabard
Author: R.J. Astley
Author: M. Ben Tahar

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