Liberge Erwan | Université De La Rochelle (original) (raw)

Papers by Liberge Erwan

Motivés par la construction de modèles réduits en interaction fluide structure, nous avons étudié... more Motivés par la construction de modèles réduits en interaction fluide structure, nous avons étudié l'application de la POD dans ce domaine. Cette méthode a été choisie suite à son utilisation en mécanique des fluides, domaine dans lequel elle a largement fait ses preuves. Nous avons donc dans un premier temps présenté et rappelé les principaux résultats de la POD. Ces résultats ont été illustrés sur l'équation de Burgers monodimensionnelle et un écoulement à faible Reynolds autour d'un cylindre. La décomposition Bi-orthogonale (BOD) a également été testée pour ces deux cas, celle-ci n'améliorant pas les résultats obtenus par la POD. La POD pour l'étude de structures en vibration a également été testée. Ensuite, nous avons étudié son application pour des problèmes d'interaction fluide structure. La complexité tient dans le caractère mobile des domaines alors que la base POD est spatiale et indépendante du temps. Pour remédier à cet inconvénient, on propose d&#3...

La réduction de modèle par système dynamique d'ordre bas permet d'obtenir des modèles numériques ... more La réduction de modèle par système dynamique d'ordre bas permet d'obtenir des modèles numériques dont le temps de résolution est très faible par rapport à une résolution classique. L'application de la décomposition orthogonale aux valeurs propres (POD) comme outil de réduction est maintenant répandue en mécanique des fluides et en interaction fluide structure (IFS). Trois méthodes de réductions de modèles en interaction fluide structure utilisant la POD sont ici détaillées.

This paper describes Reduced Order Modeling (ROM) in Fluid Structure Interaction (FSI) and discus... more This paper describes Reduced Order Modeling (ROM) in Fluid Structure Interaction (FSI) and discusses Proper Orthogonal Decomposition (POD) utilization. In fact to use POD in a moving domain, a reference fixed domain, with a fixed uniform grid, is introduced. Next the solution is interpolated from the time-variant grid to the fixed uniform grid to obtain the global velocity field (fluid and structure). Thus PODs modes are obtained for the global velocity field and not only for the fluid velocity. Then a method to reduce dynamical system in rigid body fluid interaction is developed. This method uses the fictitious domain method approach, which consists in treating the entire fluid-solid domain as a fluid by adding a distributed Lagrange multiplier in the weak formulation on solid domain. The results are compared with computational solution and discussed.

Communications in Nonlinear Science and Numerical Simulation, 2015

ABSTRACT The pressure term which appears in the ROM (reduced order model) associated to the incom... more ABSTRACT The pressure term which appears in the ROM (reduced order model) associated to the incompressible Navier-Stokes equations, in particular for the shear flows, plays an important role on the velocity. The aim of this paper is to propose a Proper Orthogonal Decomposition based reduced order model (POD-ROM) to obtain both the velocity and pressure fields for incompressible flows. Two PODs are performed, one for the velocity and the other for the pressure. Contrary to existing projection methods available in the literature, the temporal velocity and pressure coefficients are sought by minimizing the residual of the momentum equation only, without the need of a Poisson equation. For the numerical test cases considered in this paper, the proposed minimum residual projection enables to obtain accurately the pressure field, and in turn to slightly improve the velocity one. The method is tested on two fluid flows: a transient mixed-convection flow and a periodic flow around a circular cylinder. In this last case, the drag, lift and pressure coefficients, as well as the Strouhal number are properly recovered compared to those of the full model.

Volume 4: Fluid-Structure Interaction, 2013

Orthogonal Decomposition Reduced-Order Method has been proven to be efficient for the low-cost st... more Orthogonal Decomposition Reduced-Order Method has been proven to be efficient for the low-cost study of fluid-structure interaction mechanisms. Applications to a single tube under cross-flow, then to a tube bundle system revealed good behaviours of this method, which was shown to be able to accurately reproduce the velocity flow field as well as the solid displacement, even in the case of large magnitudes. The goal here is to go further by studying an instability mechanism with the Multiphase-POD technique, involving a tube array configuration because of its high interest in the nuclear domain. We first want to know if this method can reproduce critical to unstable cases and finally, we are interested in the possibility of leading a parametric study coupled with the Multiphase-POD Method in order to evaluate the instability threshold. Indeed, parametric studies coupled with a reduced-order method could lead to a CPU time additional gain, since only one basis calculation could cover several configurations with low computational cost.

Advanced Modeling and Simulation in Engineering Sciences, 2014

In what follows, we consider the Proper Orthogonal Decomposition (POD) technique of model order r... more 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.

univ-ubs.fr

Cet article s'intéresse à la réduction de modèle en Interaction Fluide Structure. Trois méthodes ... more Cet article s'intéresse à la réduction de modèle en Interaction Fluide Structure. Trois méthodes utilisant de manière différentes la POD sont comparées. La première, utilisée en aéroélasticité, applique la POD de la même manière qu'en mécanique des fluide. Une seconde méthode utilise une formulation multiphasique du problème d'interaction fluide structure pour l'écriture du modèle réduit. La dernière combine POD et décomposition de domaine.

Physics of Fluids, 2012

Boiling" in the water evaporating meniscus induced by Marangoni flow Appl. Phys. Lett. 101, 21160... more Boiling" in the water evaporating meniscus induced by Marangoni flow Appl. Phys. Lett. 101, 211602 (2012) Multiscale turbulence models based on convected fluid microstructure J. Math. Phys. 53, 115614 (2012) Optimized working conditions for a thermoelectric generator as a topping cycle for gas turbines J. Appl. Phys. 112, 073515 (2012) Application of dynamic global-coefficient subgrid-scale models to turbulent natural convection in an enclosed tall cavity Phys. Fluids 24, 094105 (2012)

Journal of Fluids and Structures, 2010

This paper presents reduced order modelling (ROM) in fluid-structure interaction (FSI). The ROM v... more This paper presents reduced order modelling (ROM) in fluid-structure interaction (FSI). The ROM via the proper orthogonal decomposition (POD) method has been chosen, due to its efficiency in the domain of fluid mechanics. POD-ROM is based on a low-order dynamical system obtained by projecting the nonlinear Navier-Stokes equations on a smaller number of POD modes. These POD modes are spatial and temporally independent. In FSI, the fluid and structure domains are moving, owing to which the POD method cannot be applied directly to reduce the equations of each domain. This article proposes to compute the POD modes for a global velocity field (fluid and solid), and then to construct a low-order dynamical system. The structure domain can be decomposed as a rigid domain, with a finite number of degrees of freedom. This low-order dynamical system is obtained by using a multiphase method similar to the fictitious domain method. This multiphase method extends the Navier-Stokes equations to the solid domain by using a penalisation method and a Lagrangian multiplier. By projecting these equations on the POD modes obtained for the global velocity field, a nonlinear low-order dynamical system is obtained and tested on a case of high Reynolds number.

Journal of Computational and Applied Mathematics, 2013

ABSTRACT In this work, we present contributions concerning a mathematical study of the sensitivit... more ABSTRACT In this work, we present contributions concerning a mathematical study of the sensitivity of a reduced order model (ROM) by the proper orthogonal decomposition (POD) technique applied to a quasi-linear parabolic equation. In particular, we apply our theoretical study to the Navier-Stokes equations for a 2D incompressible fluid flow. We present a numerical test of our theoretical result, for an unsteady fluid flow in a channel around a circular cylinder.

Revue européenne de mécanique numérique, 2010

Ce papier décrit la réduction de modèle pour les problèmes d'interaction entre un fluide et un so... more Ce papier décrit la réduction de modèle pour les problèmes d'interaction entre un fluide et un solide rigide. La méthode de réduction de modèle utilisée ici est la décomposition orthogonale aux valeurs propres (POD). La principale difficulté d'application de la POD étant lié au caractère mobile des domaines, un domaine de référence est utilisé. La POD est alors appliquée au champ de vitesse dans le domaine fixe. Ensuite une méthode de réduction de modèle pour les problème d'interaction fluide solide rigide est introduite. Cette méthode considère l'ensemble du domaine fluide-solide comme un domaine fluide. Ainsi le solide rigide est considéré comme un fluide par l'intermédiaire d'une forte viscosité, qui joue le rôle de facteur de pénalisation de la contrainte de rigidité. La base POD est alors utilisée dans la formulation faible et permet d'obtenir un système dynamique réduit. ABSTRACT. This paper describes the Reduced Order Modeling (ROM) for fluid rigid body interaction problem and discusses Proper Orthogonal Decomposition (POD) utilisation. The principal difficulty for using POD being the moving domains, a referenced fixed domain is introduced. The POD is applied for the velocity field obtained on the fixed domain. Then a method to reduce dynamical system in rigid body fluid interaction is developed. This method uses the fictitious domain method approach, which consists in treating the entire fluid-solid domain as a fluid. The rigid body is considered as a fluid, by using a high viscosity which can play the role of a penalisation factor of the rigidity constraint, and by adding a distributed Lagrange multiplied associated to this constraint in the weak formulation. The fluid flow problem is then formulated on the reference domain and POD modes are used in the weak formulation. MOTS-CLÉS : réduction de modèle, interaction fluide structure, POD, formulation multiphasique KEYWORDS: reduced order modeling, fluid structure interaction, proper orthogonal decomposition (POD), multiphase formulation L'objet. Volume 8 -n˚2/2005, pages 1 à 15

In this work, the non-isothermal Navier-Stokes equations are studied from the group theory point ... more In this work, the non-isothermal Navier-Stokes equations are studied from the group theory point of view. The symmetry group of the equations is presented and discussed. Some standard turbulence models are analyzed with the symmetries of the equations. A class of turbulence models which preserve the physical properties contained in the symmetry group is built. The proposed turbulence models are applied to an illustrative example of natural convection in a differentially heated cavity, and the results are presented.

The International Journal of Multiphysics, 2008

This paper describes Reduced Order Modeling (ROM) in fluid rigid body interaction problem and dis... more This paper describes Reduced Order Modeling (ROM) in fluid rigid body interaction problem and discusses Proper Orthogonal Decomposition (POD) utilization. The principal difficulty for using POD being the moving domains, a referenced fixed domain is introduced. The POD is applied for the velocity field obtained on the fixed domain. Then a method to reduce dynamical system in rigid body fluid interaction is developed. This method uses the fictitious domain method approach, which consists in treating the entire fluid-solid domain as a fluid. The rigid body is considered like a fluid, by using a high viscosity which can play the role of a penalization factor of the rigidity constraint, and by adding a distributed Lagrange multiplied associated to this constraint in the weak formulation. The fluid flow problem is then formulated on the reference domain and POD modes are used in the weak formulation. The results are compared with computational solution and discussed.

ASME 2010 Pressure Vessels and Piping Conference: Volume 4, 2010

ABSTRACT Tube bundles in steam boilers of nuclear power plants and nuclear on-board stokehold are... more ABSTRACT Tube bundles in steam boilers of nuclear power plants and nuclear on-board stokehold are known to be exposed to high levels of vibrations. This coupled fluid-structure problem is very complex to numerically set up, because of its three-dimensional characteristics and because of the large number of degrees of freedom involved. A complete numerical resolution of such a problem is currently not viable, all the more so as a precise understanding of this system behaviour needs a large amount of data, obtained by very expensive calculations. We propose here to apply the now classical reduced order method called Proper Orthogonal Decomposition to this case. This choice could lead to reduced calculation times and allow parametrical investigations thanks to a low data quantity. But, it implies several challenges inherent to the fluid-structure characteristic of the problem. Previous works on the dynamic analysis of steam generator tube bundles already provided interesting results in the case of non flowing fluid — i.e. quiescent fluid [J.F. Sigrist, D. Broc; Dynamic Analysis of a Steam Generator Tube Bundle with Fluid-Structure Interaction; Pressure Vessel and Piping, July 27–31, 2008, Chicago]. A first step on the implementation of POD in academic cases (one-dimensional equations, 2D-single tube configuration) is presented. Future work will consist in working on the tube bundle configuration, first in the fixed case and then with structure motion allowed. Present study shows the efficiency of the reduced model to reproduce similar problems from a unique data set for various configurations as well as the efficiency of the reduction for simple cases.