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A mixed finite element method for acoustic wave propagation in moving fluids based on an Eulerian-Lagrangian description

A mixed finite element method for acoustic wave propagation in moving fluids based on an Eulerian-Lagrangian description
A mixed finite element method for acoustic wave propagation in moving fluids based on an Eulerian-Lagrangian description
A nonstandard wave equation, established by Galbrun in 1931, is used to study sound propagation in nonuniform flows. Galbrun's equation describes exactly the same physical phenomenon as the linearized Euler's equations (LEE) but is derived from an Eulerian–Lagrangian description and written only in term of the Lagrangian perturbation of the displacement. This equation has interesting properties and may be a good alternative to the LEE: only acoustic displacement is involved (even in nonhomentropic cases), it provides exact expressions of acoustic intensity and energy, and boundary conditions are easily expressed because acoustic displacement whose normal component is continuous appears explicitly. In this paper, Galbrun's equation is solved using a finite element method in the axisymmetric case. With standard finite elements, the direct displacement-based variational formulation gives some corrupted results. Instead, a mixed finite element satisfying the inf-sup condition is proposed to avoid this problem. A first set of results is compared with semianalytical solutions for a straight duct containing a sheared flow (obtained from Pridmore–Brown's equation). A second set of results concerns a more complex duct geometry with a potential flow and is compared to results obtained from a multiple-scale method (which is an adaptation for the incompressible case of Rienstra's recent work).
0001-4966
705-716
Treyssède, F.
679320c0-d1a3-4451-901f-d789c7a249ee
Gabard, G.
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
Ben Tahar, M.
a4a3c0d5-301e-4dbe-9907-641542b6ae75
Treyssède, F.
679320c0-d1a3-4451-901f-d789c7a249ee
Gabard, G.
bfd82aee-20f2-4e2c-ad92-087dc8ff6ce7
Ben Tahar, M.
a4a3c0d5-301e-4dbe-9907-641542b6ae75

Treyssède, F., Gabard, G. and Ben Tahar, M. (2003) A mixed finite element method for acoustic wave propagation in moving fluids based on an Eulerian-Lagrangian description. Journal of the Acoustical Society of America, 113 (2), 705-716. (doi:10.1121/1.1534837).

Record type: Article

Abstract

A nonstandard wave equation, established by Galbrun in 1931, is used to study sound propagation in nonuniform flows. Galbrun's equation describes exactly the same physical phenomenon as the linearized Euler's equations (LEE) but is derived from an Eulerian–Lagrangian description and written only in term of the Lagrangian perturbation of the displacement. This equation has interesting properties and may be a good alternative to the LEE: only acoustic displacement is involved (even in nonhomentropic cases), it provides exact expressions of acoustic intensity and energy, and boundary conditions are easily expressed because acoustic displacement whose normal component is continuous appears explicitly. In this paper, Galbrun's equation is solved using a finite element method in the axisymmetric case. With standard finite elements, the direct displacement-based variational formulation gives some corrupted results. Instead, a mixed finite element satisfying the inf-sup condition is proposed to avoid this problem. A first set of results is compared with semianalytical solutions for a straight duct containing a sheared flow (obtained from Pridmore–Brown's equation). A second set of results concerns a more complex duct geometry with a potential flow and is compared to results obtained from a multiple-scale method (which is an adaptation for the incompressible case of Rienstra's recent work).

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Published date: 2003
Organisations: Acoustics Group

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Local EPrints ID: 28448
URI: http://eprints.soton.ac.uk/id/eprint/28448
ISSN: 0001-4966
PURE UUID: 5c5dc6a0-47af-4226-a850-9f3c14f67b06

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Date deposited: 02 May 2006
Last modified: 15 Mar 2024 07:25

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Contributors

Author: F. Treyssède
Author: G. Gabard
Author: M. Ben Tahar

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