Proper orthogonal decomposition investigation in fluid structure interaction

Liberge, Erwan; Benaouicha, Mustapha; Hamdouni, Aziz

doi:10.3166/remn.16.401-418

Cited by 15 publications

(16 citation statements)

References 15 publications

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“…The low-order dynamical system was obtained by projecting the initial discrete problem to the POD basis. The solution proposed by Liberge et al (2007) gave better results. We propose in this article an extension of the method presented by Liberge et al (2007) for the interaction between turbulent fluid flow and structures.…”

Section: Mathematical Formulationmentioning

confidence: 86%

“…Then, a characteristic function is introduced to follow the different domains. This method has been used by Liberge et al (2007) for the POD application for fluid-structure interaction problems. The global velocity field denoted by v, is decomposed as…”

Section: Proposed Solutionmentioning

confidence: 99%

“…A standard snapshot POD method, computing the POD modes by the discrete scalar product, has been tested by Liberge (2008), and by Liberge et al (2007) on a one-dimensional case of the Burgers equation coupled with a spring. The low-order dynamical system was obtained by projecting the initial discrete problem to the POD basis.…”

Section: Mathematical Formulationmentioning

confidence: 99%

See 2 more Smart Citations

Reduced order modelling method via proper orthogonal decomposition (POD) for flow around an oscillating cylinder

Liberge

Hamdouni

2010

Journal of Fluids and Structures

127

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Section: Mathematical Formulationmentioning

confidence: 86%

Section: Proposed Solutionmentioning

confidence: 99%

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Reduced order modelling method via proper orthogonal decomposition (POD) for flow around an oscillating cylinder

Liberge

Hamdouni

2010

Journal of Fluids and Structures

127

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“…The grid velocity is given by solving the diffusion equation (11) with a space dependent diffusivity coefficient l l = ( ) x . Thus, the large displacements of the solid can be carried out without critical mesh deformations.…”

Section: Discussionmentioning

confidence: 99%

Fluid-structure interaction with an application to a body immersed and anchored in a fluid flow

Benaouicha¹,

Hamdouni

2011

Int Appl Mech

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In this paper, an implicit coupling algorithm for fluid-structure interaction problems with under-time steps for the solid is presented. Its implementation on two configurations is achieved by using the CASTEM finite-elements code. First, the free oscillations of a cylinder in an annular fluid domain where its movement is determined by the coupled fluid-solid action is considered in the case of viscous fluid. It should be noted that the implicit coupling algorithm gives the best prediction of the structure oscillations. The under-time steps for the solid are introduced in order to obtain better results. Then, an application whose final objective is to model a floating barrage is studied. The main goal of this application is to predict the displacements of a ring completely immersed and anchored by a cable to the lower boundary of the fluid domain. The finite-element discretization of the Navier-Stokes equations in the ALE formulation is used Keywords: fluid-structure interaction, arbitrary Lagrangian-Eulerian method (ALE), moving boundaries 1. Introduction. The applications where fluid-structure interaction phenomena occur are numerous: aerodynamics [9], hydrodynamics, biomechanics [17, 10], nuclear safety, environmental protection [2], etc. Many examples can be cited: flow around an antipollution floating barrage, flow around a boat, blood flow in the arteries, flow around an airfoil, wind influence on the apron of a bridge (as occurred in the rupture of the Tacoma bridge in 1940). There are many and various industrial and environmental applications where this phenomenon occurs. This justifies the important number of works on this class of problems during last years. This growth also comes from the development of the means of calculation which allowed the implementation of algorithms in fluid-structure interaction [8].The application of these methods for modeling the antipollution floating barrage makes possible a better prediction of its behavior in real situation. The study of this typical problem of fluid-structure interaction, which imposes many difficulties, consists to treat the problem by taking into account the contribution of all parameters of the system. Thus, it will be necessary to model the structure, the flow, the fluid-structure interaction, the anchorage (cable), the free surface.The general context of this study is to develop a numerical tool by using the CASTEM finite-element code, through which such a problem can be apprehended in its global nature. In the paper, only a preliminary result is presented. The use of CASTEM to develop a numerical tool for study of the fluid-structure interaction problems is very interesting. Indeed, CASTEM has a proper language (GIBIANE) which makes it possible to establish the link between the fluid code and the structure code in the same environment. Thus, it is not necessary to develop a particular interface between two distinct codes as it is usually done.The proposed fluid-structure coupling algorithm is an alternative of the implicit scheme suggested in [1]....

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“…These are applied for Fluid-Structure Interaction problems [1][2][3][4][5][6][7], stability study [8], shape optimization problems [9,10], optimal control problems [11,12] etc....…”

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confidence: 99%

On the sensitivity of the POD technique for a parameterized quasi-nonlinear parabolic equation

Akkari

Hamdouni

Liberge

et al. 2014

Adv. Model. and Simul. in Eng. Sci.

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Background:In what follows, we consider the Proper Orthogonal Decomposition (POD) technique of model order reduction, for a parameterized quasi-nonlinear parabolic equation. Methods: A POD basis associated with a set of reference values of the characteristic parameters is considered. From this basis, a parametric reduced order model (ROM) projecting the initial equation is constructed. Results: A mathematical a priori estimate of the parametric squared L 2 -error induced by this projection is developed. This later estimate is based on both, the parametric behavior of the squared L 2 -ROM-error thanks to the resolution of a Ricatti differential inequality in the parametric ROM-error, and the convergence rate of the parametric ROM to the full problem, via the augmentation of the basis dimension. Indeed, under restrictive conditions on the solutions regularity of such equations, we are able to precise the slope of the logarithm of the squared L 2 -norm of the ROM error, as a function of the logarithm of the basis modes number. Numerical experiments of our theoretical estimate, are presented for the 2D Navier-Stokes equations in the case of an unsteady and incompressible fluid flow in a channel around a circular cylinder. Conclusion: A mathematical a priori estimate of the parametric squared L 2 -error induced by the model reduction by POD is developped for a parameterized quasi-nonlinear parabolic equation. This estimate is obtained thanks to the resolution of a Ricatti differential inequality.

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Proper orthogonal decomposition investigation in fluid structure interaction

Cited by 15 publications

References 15 publications

Reduced order modelling method via proper orthogonal decomposition (POD) for flow around an oscillating cylinder

Reduced order modelling method via proper orthogonal decomposition (POD) for flow around an oscillating cylinder

Fluid-structure interaction with an application to a body immersed and anchored in a fluid flow

On the sensitivity of the POD technique for a parameterized quasi-nonlinear parabolic equation

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