Legendre, Guillaume (2003) Acoustic radiation in a moving fluid: mathematical and numerical analysis of the Galbrun's equation. PhD thesis Sciences mécaniques, Université Paris VI - Pierre et Marie Curie / ENSTA / UMA - Laboratoire de Mathématiques Appliquées, ENSTA 2003PA066384.
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Abstract
The works presented in this document are concerned with the numerical simulation of acoustic propagation in a moving fluid, in the frequency domain. The model retained for these studies is the Galbrun's equation which describes the linear wave propagation in presence of a perfect fluid flow in adiabatic motion and uses the lagrangian displacement as a variable. Mathematical analysis shows that a nodal finite element method is not, in general, suited to approximate the solution of the equation, the computed results being strongly polluted by spurious numerical modes. In the first part of the thesis, we propose a regularization method for which we prove the convergence of a nodal finite element method for diffraction problems in a duct and in presence of uniform or sheared subsonic flows. The second part of the document is devoted to the construction and analysis of perfectly matched absorbing layers for the radiation of a compact source, placed in a duct in a uniform flow. We successively treat the case of an acoustic source, which leads to a scalar problem, and of a more general source of perturbations. A limiting absorption principle is established in the general case and we prove that the convergence of the PML method is exponential with respect to the size of the layers. Numerical results that illustrate these two approaches are presented.
| Item Type: | PhD Thesis (PhD) |
|---|---|
| Thesis Supervisor: | Bonnet-Ben Dhia, Anne-Sophie |
| Date: | September 2003 |
| Board of examiners: | Bendali, Abderrahmane and Després, Bruno and Dubois, François and Pagneux, Vincent and Peyret, Christophe and Poirée, Bernard |
| Ecole Doctorale: | ED 386 SCIENCES MATHEMATIQUES DE PARIS CENTRE |
| Discipline: | Sciences mécaniques |
| Collection (Fonds): | ENSTA |
| Institution: | ENSTA |
| Department: | Université Paris VI - Pierre et Marie Curie / ENSTA / UMA - Laboratoire de Mathématiques Appliquées |
| Subjects: | 1. Mathematics and Applications 4. Materials Science, Mechanics and Mechanical Engineering |
| Uncontrolled Keywords: | Aeroacoustics, Galbrun's equation, Waveguide, Time-harmonic dependance, Regularization, Finite element method, Perfectly matched layers, Acoustique en écoulement, équation de Galbrun, Guide d'ondes, Régime harmonique, Régularisation, Méthode des éléments finis, Couches absorbantes parfaitement adaptées |
| ID Code: | 2068 |
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| Deposited By: | Julien Karachehayas |
| Deposited On: | 23 April 2007 |
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