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Gwenael Gabard

Bio: Gwenael Gabard is an academic researcher from Centre national de la recherche scientifique. The author has contributed to research in topics: Finite element method & Euler equations. The author has an hindex of 19, co-authored 113 publications receiving 1307 citations. Previous affiliations of Gwenael Gabard include University of Technology of Compiègne & University of Southampton.


Papers
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Journal ArticleDOI
TL;DR: In this article, an analytical model for sound radiation from a semi-infinite unflanged annular duct is presented, where noise propagates along the annular bypass duct, refracts through the external bypass stream and radiates to the far field.
Abstract: An analytical model is presented for sound radiation from a semi-infinite unflanged annular duct. The duct carries a jet which issues into a uniform mean flow while an inner cylindrical centre body extends downstream from the duct exit. This geometrical arrangement forms an idealized representation of a turbofan exhaust where noise propagates along the annular bypass duct, refracts through the external bypass stream and radiates to the far field. The instability wave of the vortex sheet and its interaction with the acoustic field are accounted for in an exact way in the current solution. Efficient numerical procedures are presented for evaluating near-field and far-field solutions, and these are used as the basis for a parametric study to illustrate the effect of varying the hub–tip ratio, and the ratio of jet velocity to external flow velocity. Since the ‘Kutta’ condition can be turned on and off in the current solution, this capability is used to assess the effect of vortex shedding on noise radiation. Far-field directivity patterns are presented for single modes and also for a multi-mode ‘broadband’ source model in which all cut-on modes are assumed to be present with equal modal power. Good agreement is found between analytical solutions and experimental data. Near-field pressure maps of the acoustic and instability portions of the solution are generated for selected tones.

173 citations

Journal ArticleDOI
TL;DR: The main feature of the method is the use of plane waves instead of polynomials to approximate the solution in each element, which requires only a small number of elements per wavelength to obtain accurate solutions and is more efficient than high-order DRP schemes.

106 citations

Journal ArticleDOI
TL;DR: In this paper, a comparison of the Myers condition and the boundary layer profile of turbofan engines is presented, and it is shown that boundary layer thickness has a significant impact on sound absorption, although its actual influence depends on the details of the incident sound field.

81 citations

Journal ArticleDOI
TL;DR: In this paper, a finite element (FE) mode-matching approach for duct acoustics with flow and circumferentially varying liners is presented for sound attenuation in turbofan inlets and bypass ducts.

81 citations

Journal ArticleDOI
TL;DR: An efficient implementation of the high‐order finite element method (FEM) for tackling large‐scale engineering problems arising in acoustics with the ability to select automatically the order of interpolation in each element so as to obtain a target accuracy while minimizing the cost.
Abstract: Computational modeling remains key to the acoustic design of various applications, but it is constrained by the cost of solving large Helmholtz problems at high frequencies. This paper presents an efficient implementation of the high-order Finite Element Method for tackling large-scale engineering problems arising in acoustics. A key feature of the proposed method is the ability to select automatically the order of interpolation in each element so as to obtain a target accuracy while minimising the cost. This is achieved using a simple local a priori error indicator. For simulations involving several frequencies, the use of hierarchic shape functions leads to an efficient strategy to accelerate the assembly of the finite element model. The intrinsic performance of the high-order FEM for 3D Helmholtz problem is assessed and an error indicator is devised to select the polynomial order in each element. A realistic 3D application is presented in detail to demonstrate the reduction in computational costs and the robustness of the a priori error indicator. For this test case the proposed method accelerates the simulation by an order of magnitude and requires less than a quarter of the memory needed by the standard FEM.

78 citations


Cited by
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Journal ArticleDOI
TL;DR: To the best of our knowledge, there is only one application of mathematical modelling to face recognition as mentioned in this paper, and it is a face recognition problem that scarcely clamoured for attention before the computer age but, having surfaced, has attracted the attention of some fine minds.
Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

3,015 citations

Book ChapterDOI
01 Jan 1998
TL;DR: A discrete technique of the Schwarz alternating method is presented, to combine the Ritz-Galerkin and finite element methods, well suited for solving singularity problems in parallel.
Abstract: A discrete technique of the Schwarz alternating method is presented in this last chapter, to combine the Ritz-Galerkin and finite element methods. This technique is well suited for solving singularity problems in parallel, and requires a little more computation for large overlap of subdomains. The convergence rate of the iterative procedure, which depends upon overlap of subdomains, will be studied. Also a balance strategy will be proposed to couple the iteration number with the element size used in the FEM. For the crack-infinity problem of singularity the total CPU time by the technique in this chapter is much less than that by the nonconforming combination in Chapter 12.

389 citations

Dissertation
01 Mar 2009
TL;DR: In this paper, the relationship between these transforms and their properties was discussed and some important applications in physics and engineering were given, as well as their properties and applications in various domains.
Abstract: Integral transforms (Laplace, Fourier and Mellin) are introduced with their properties, the relationship between these transforms was discussed and some important applications in physics and engineering were given. ااااااا دقل مت ضارعتسإ ةساردو ل ةيلماكتلا تليوحتلا لك ، سلبل تلوحت نم روف ي ر نيليمو عم ةشقانم كلذكو ،اهنم لك صاوخ و صئاصخ ةقلعلا ةشقانم مت هذه نيب طبرلاو و ،تليوحتلا مت ميدقت تاقيبطتلا ضعب تليوحتلا هذهل ةمهملا يف تلاجم ءايزيفلا ةسدنهلاو.

383 citations

Journal ArticleDOI
TL;DR: A priori convergence analysis of PWDG in the case of $p$-refinement is concerned, that is, the study of the asymptotic behavior of relevant error norms as the number of plane wave directions in the local trial spaces is increased.
Abstract: Plane wave discontinuous Galerkin (PWDG) methods are a class of Trefftz-type methods for the spatial discretization of boundary value problems for the Helmholtz operator $-\Delta-\omega^2$, $\omega>0$. They include the so-called ultra weak variational formulation from [O. Cessenat and B. Despres, SIAM J. Numer. Anal., 35 (1998), pp. 255-299]. This paper is concerned with the a priori convergence analysis of PWDG in the case of $p$-refinement, that is, the study of the asymptotic behavior of relevant error norms as the number of plane wave directions in the local trial spaces is increased. For convex domains in two space dimensions, we derive convergence rates, employing mesh skeleton-based norms, duality techniques from [P. Monk and D. Wang, Comput. Methods Appl. Mech. Engrg., 175 (1999), pp. 121-136], and plane wave approximation theory.

192 citations