L'imagerie par Résonance Magnétique permet de mesurer l'écoulement sanguin. Au niveau cardiovasculaire, elle permet d'acquérir non seulement des images anatomiques du cœur et des gros vaisseaux mais aussi des images fonctionnelles de vitesse par contraste de phase. Cette technique offre des perspectives dans l'étude de la dynamique des fluides et dans la caractérisation des artères, en particulier pour les grosses artères systémiques comme l'aorte dont le rôle est primordial dans la circulation sanguine. Par ailleurs, l'un des paramètres qui entrent en jeu dans la détermination de la fonction cardiaque et du comportement vasculaire est la pression artérielle. La méthode de référence de la mesure de pression dans l'aorte étant le cathétérisme, plusieurs méthodes combinant la modélisation à l'imagerie ont été proposées afin d'estimer un gradient de pression de façon non invasive. Ce travail de thèse propose de mesurer la pression dans un segment d'aorte grâce à un modèle 1D simplifié et en utilisant les données mesurées par IRM et un modèle 0D représentant le réseau vasculaire périphérique comme conditions aux limites. Aussi, afin d'adapter le modèle à l'aorte du patient, une loi de pression exprimant une relation entre la section aortique à la pression et basée sur la compliance a été utilisée. Cette dernière, liée à la vitesse d'onde de pouls (VOP), a été mesurée en IRM sur les ondes de vitesse.Par ailleurs, les séquences de codage de vitesse et d'accélération sont longues et ponctuées d'artéfacts dus au mouvement du patient. Une apnée est requise afin de limiter le mouvement respiratoire. Cependant, la durée de l'apnée atteint 25 à 30 secondes pour de telles séquences, ce qui est souvent impossible à tenir pour les malades. Une technique d'optimisation de séquences dynamiques par réduction du champ de vue est proposée et étudiée. La technique décrit un dépliement des régions repliées par différence complexe de deux images, l'une codée et l'autre non codée en vitesse. Cette méthode réalise une réduction de plus de 25% de la durée d'apnée. / Magnetic Resonance Imaging (MRI) is used to measure blood flow. It allows assessing not only dynamic images of the heart and the large arteries, but also functional velocity images by means of Phase Contrast. This promising technique is important for studying fluid dynamics and characterizing the arteries, especially the large systemic arteries that play a prominent role in the blood circulation. One of the parameters used for determining the cardiac function and the vascular behavior is the arterial pressure. The reference technique for measuring the aortic pressure is catheterism, but several methods combining imaging and mathematical modeling have been proposed in order to non-invasively estimate a pressure gradient. This work proposes to measure pressure in an aortic segment through a simplified 1D model using MRI measured flow and 0D model representing the peripheral vascular system as boundary conditions. To adapt the model to the aorta of a patient, a pressure law was used forming a relation between the aortic section area and pressure, based on compliance, which is linked to pulse wave velocity (PWV) estimated on MRI measured flow waves.Scan duration was optimized, as it is often a limitation during image acquisition. Velocity and acceleration sequences require a long time and may cause artifacts. Hence, they are acquired during apnea to avoid respiratory motion. However, for such acquisitions, a subject would have to hold their breath for more than 25 seconds which can pose difficulties for some patients. A technique that allows dynamic acquisition time optimization through field of view reduction was proposed and studied. The technique unfolds fold-over regions by complex difference of two images, one of which is motion encoded and the other acquired without an encoding gradient. By implementing this method, we decrease the acquisition time by more than 25%

Le sujet de la thèse porte sur l'étude (existence, unicité, régularité) et le contrôle de problèmes fluide-structure possédant des conditions limites sur la pression. Le système étudié couple une partie fluide, décrite par les équations de Navier-Stokes incompressibles dans un domaine 2D et une partie structure, décrite par une équation 1D de poutre amortie située sur une partie du bord du domaine fluide. Dans le Chapitre 2, on étudie l'existence de solutions fortes pour ce modèle. Nous démontrons des résultats de régularité optimale pour le système de Stokes avec conditions de bord mixtes sur un domaine non régulier. Ces résultats sont ensuite utilisés pour prouver l'existence et l'unicité de solutions fortes, locales en temps, pour le système fluide-structure sans hypothèse de petitesse sur les données initiales. Le Chapitre 3 réutilise l'analyse précédente dans le cadre de solutions périodiques en temps. Nous développons un critère d'existence de solutions périodiques pour un problème parabolique abstrait. Ce critère est ensuite appliqué au système fluide-structure et nous obtenons l'existence de solutions strictes, périodiques et régulières en temps, pour des termes sources périodiques suffisamment petits. Le quatrième volet de la thèse porte sur la stabilisation du système fluide-structure au voisinage d'une solution périodique. Le système linéarisé sous-jacent est décrit à l'aide d'un opérateur A(t) dont le domaine dépend du temps. Nous démontrons l'existence d'un opérateur parabolique d'évolution pour ce système linéaire. Cet opérateur est ensuite utilisé, dans le cadre de la théorie de Floquet, pour étudier le comportement asymptotique du système. Nous adaptons la théorie existante pour des opérateurs à domaine constant au cas de domaine non constant. Nous obtenons la stabilisation exponentielle du système linéaire à l'aide d'un contrôle sur la frontière du domaine fluide. / In this thesis we study the well-posedness (existence, uniqueness, regularity) and the control of fluid-structure system with boundary conditions involving the pressure. The fluid part of the system is described by the incompressible Navier- Stokes equations in a 2D rectangular type domain coupled with a 1D damped beam equation localised on a boundary part of the fluid domain. In Chapter 2 we investigate the existence of strong solutions for this model. We prove optimal regularity results for the Stokes system with mixed boundary conditions in non-regular domains. These results are then used to obtain the local-in-time existence and uniqueness of strong solutions for the fluid-structure system without smallness assumption on the initial data. Chapter 3 uses the previous analysis in the framework of periodic (in time) solutions. We develop a criteria for the existence of periodic solutions for an abstract parabolic system. This criteria is then used on the fluid- structure system to prove the existence of a periodic and regular in time strict solution, provided that the periodic source terms are small enough. In Chapter 4 we study the stabilisation of the fluid-structure system in a neighbourhood of a periodic solution. The underlying linear system involves an operator A(t) with a domain which depends on time. We prove the existence of a parabolic evolution operator for this linear system. This operator is then used to apply the Floquet theory and to describe the asymptotic behaviour of the system. We adapt the known results for an operator with constant domain to the case of operators with non constant domain. We obtain the exponential stabilisation of the linear system with control acting on a part of the boundary of the fluid domain.

Le contrôle d'écoulements turbulents est un enjeu majeur en aérodynamique. Cependant, la présence d'un grand nombre de degrés de libertés et d'une dynamique complexe rend délicat la modélisation dynamique de ces écoulements qui est pourtant nécessaire à la conception d'un contrôle efficace. Au cours de cette thèse, différentes directions ont été suivies afin de développer des modèles réduits dans des configurations réalistes d'écoulements et d'utiliser ces modèles pour le contrôle.Premièrement, la décomposition en modes dynamiques (DMD), et certaines de ses variantes, ont été exploitées en tant que base réduite afin d'extraire au mieux le comportement dynamique de l'écoulement. Par la suite, nous nous sommes intéressés à l'assimilation de données 4D-Var qui permet de combiner des informations inhomogènes provenant d'un modèle dynamique, d'observations et de connaissances a priori du système. Nous avons ainsi élaboré des modèles réduits POD et DMD d'un écoulement turbulent autour d'un cylindre à partir de données expérimentales PIV. Finalement, nous avons considéré le contrôle d'écoulement dans un contexte d'interaction fluide/structure. Après avoir montré que les mouvements de solides immergés dans le fluide pouvaient être représentés comme une contrainte supplémentaire dans le modèle réduit, nous avons stabilisé un écoulement de sillage de cylindre par oscillation verticale. / Control of turbulent flows is still today a challenge in aerodynamics. Indeed, the presence of a high number of active degrees of freedom and of a complex dynamics leads to the need of strong modelling efforts for an efficient control design. During this PhD, various directions have been followed in order to develop reduced-order models of flows in realistic situations and to use it for control. First, dynamic mode decomposition (DMD), and some of its variants, have been exploited as reduced basis for extracting at best the dynamical behaviour of the flow. Thereafter, we were interested in 4D-variational data assimilation which combines inhomogeneous informations coming from a dynamical model, observations and an a priori knowledge of the system. POD and DMD reduced-order models of a turbulent cylinder wake flow have been successfully derived using data assimilation of PIV measurements. Finally, we considered flow control in a fluid-structure interaction context. After showing that the immersed body motion can be represented as an additional constraint in the reduced-order model, we stabilized a cylinder wake flow by vertical oscillations.

A interação entre fluidos e estruturas caracteriza um problema multi-físico não linear e está presente numa grande variedade de áreas da engenharia. Este trabalho apresenta o desenvolvi mento de ferramentas computacionais com base no Método dos Elementos Finitos (MEF) para a análise de interação fluido-estrutura (IFE) considerando escoamentos com baixas velocidades. Dada a interdisciplinaridade do tema, se faz necessário o estudo em três diferentes assuntos: a dinâmica das estruturas computacional, a dinâmica dos fluidos computacional, e o problema de acoplamento. No caso da dinâmica das estruturas empregar-se um elemento finito que seja adequado para a simulação de problemas de IFE, que claramente demandam uma análise não linear geométrica, optando-se pelo emprego de uma formulação descrita em posições, a qual evita problemas relativos à aproximação de rotações finitas. Quanto à dinâmica dos fluidos computacional, é empregado um método estável e ao mesmo tempo sensível à movimentação da estrutura, utilizando a descrição Lagrangeana-Euleriana Arbitrária (ALE). Os casos considerados neste trabalho, assim como muitos dos problemas de engenharia, ocorrem com escoamentos em baixas velocidades, implicando na incompressibilidade do fluido, o que demanda, para um método estável, a utilização de elementos que atendam à condição de Ladyzhenskaya-Babuska-Brezzi (LBB). Além disso, é necessário também o emprego de métodos que consigam neutralizar as variações espúrias decorrentes da não-linearidade de possíveis escoamentos com convecção dominante e que surgem com a aplicação do processo clássico de Galerkin. Para superar esse problema, é aplicado o método Streamline-Upwind/Petrov-Galerkin (SUPG), que adiciona difusividade artificial na direção do escoamento, controlando a amplitude dos termos convectivos. No que se refere ao acoplamento fluido-casca, buscam-se modularidade e versatilidade adotando-se o modelo particionado. O modelo de acoplamento implementado garante ainda a utilização de malhas do fluido e da estrutura sem a necessidade de coincidência de nós. / Interaction between fluids and structures characterizes a nonlinear multi-physics problem presente in a wide range of engineering fields. This works presets the development of computational tools based on finite element method (FEM) for fluid-structure interaction (FSI) analysis considering low speed flows (incompressible), as a great part of the engineering problems. Given the topic multidisciplinary nature, it is necessary to study three different subjects: the computational structural dynamics, the computational fluid mechanics and the coupling problem. Regarding structural mechanics, we seek to employ a finite element adequate to FSI simulation, what clearly demands a geometric nonlinear analysis. We chose to employ shell elements with formulation in terms of positions, which avoids problems related to finite rotations approximations. Concerning computational fluid dynamics, we employ a stable method, at same time sensible o structural movements, which is written in the arbitrary Lagrangian-Eulerian (ALE) description. The flow incompressibility demands, for a stable method, the use of elements according to the Ladyzhenskaya-Bbuska-Brezzi (LBB) condition. It is also necessary to employ methods able to neutralize the spurious variations that appears from convection dominated flows when applying the standard Galerking method. In order to overcome this problem, we apply the Streamline-Upwind/Petrov-Galerkin (SUPG) method, which adds artificial diffusivity to the streamline direction, controlling spurious variations. Considering the fluid-shell coupling, we seek modularity and versatility, adopting the partitioned model. The developed coupling model ensure the use of fluid and structure meshes with no need for matching nodes.

Neste trabalho, a resposta dinâmica de um riser marítimo devido à geração e desprendimento alternado de vórtices é investigada numericamente. O riser é dividido em seções bidimensionais ao longo de seu comprimento. O Método dos Vórtices Discretos é empregado para a determinação das forças hidrodinâmicas que agem nestas seções bidimensionais. As seções hidrodinâmicas são resolvidas independentemente, e o acoplamento entre as mesmas é feito através da solução da estrutura no domínio do tempo pelo Método dos Elementos Finitos. Os resultados numéricos são comparados com resultados obtidos experimentalmente. Processamento paralelo é empregado para melhorar a performance do método. As simulações são realizadas através de uma metodologia mestre-escravo, utilizando MPI Message Passing Interface para explorar o paralelismo. A escalabilidade do algoritmo é mostrada e discutida. Este trabalho representa o desenvolvimento de um simulador que permite, efetivamente, a análise dinâmica de um riser com características e dimensões representativas das condições reais encontradas em campo, a um custo computacional factível para seu uso como uma ferramenta de engenharia. Isto é obtido por meio da técnica de processamento paralelo, aliada à solução do escoamento através de um método eficiente de CFD Método dos Vórtices Discretos e à solução da estrutura através do Método dos Elementos Finitos. / In this work the dy6namic response of a marine riser due to vortex shedding is numerically investigated. The riser is divided in two-dimensional sections along the riser length. The Discrete Vortex Method is employed for the assessment of the hydrodynamic forces acting on these two-dimensional sections. The hydrodynamic sections are solved independently, and the coupling among the sections is taken into account by the solution of the structure in the time domain by the Finite Element Method. The numerical results are compared with results obtained experimentally. Parallel processing is employed to improve the performance of the method. The simulations are carried out through a master-slave approach using MPI Message Passing Interface to exploit the parallelism. Scalability of the algorithm is shown and discussed. This work represents the development of a simulator that effectively allows the dynamic analysis of a riser with representative characteristics and dimensions of real field conditions, with a feasible computational cost for its use as an engineering tool. This is obtained by means of the parallel processing technique, together with an efficient CFD solution of the flow with de Discrete Vortex Method and the solution of the structure with the Finite Element Method.

Cette thèse est consacrée à la modélisation mathématique du flux sanguin dans les artères en présence de la sténose à cause de l'athérosclérose. L'athérosclérose est une maladie vasculaire complexe caractérisée par la formation d'une plaque menant au rétrécissement de l'artère. Elle est responsable des crises cardiaques et des accidents vasculaires cérébraux. Quels que soient les nombreux facteurs de risque identifiés - cholestérol et lipides, pression, régime alimentaire malsain et obésité - seuls des facteurs mécaniques et hémodynamiques peuvent donner une cause précise de cette maladie. Dans la première partie de la thèse, nous introduisons le modèle mathématique tridimensionnel décrivant l'introduction entre le sang et la paroi artérielle. Le modèle consiste à coupler la dynamique du flux sanguin donnée par les équations de Navier-Stokes formulées dans le cadre Arbitrary Lagrangian Eulerian (ALE) avec les équations élastodynamiques décrivant l'élasticité de la paroi artérielle considérée comme un matériau hyperélastique modélisé par la loi de comportement non-linéaire de Saint Venant-Kirchhoff en tant que système d'interaction fluide-structure. Théoriquement, nous prouvons l'existence et l'unicité locale dans le temps de la solution pour ce système lorsque le fluide est supposé être un fluide homogène Newtonien incompressible et que la structure est décrite par la loi de comportement non-linéaire quasi-incompressible de Saint Venant-Kirchhoff. Les résultats sont établis en utilisant l'outil clé; le théorème du point fixe. La deuxième partie est consacrée à l'analyse numérique de ce modèle. Le sang est considéré comme un fluide non-Newtonien dont le comportement et les propriétés rhéologiques sont décrits par le modèle de Carreau, tandis que la paroi artérielle est un matériau homogène incompressible décrit par les équations élastodynamiques quasi-statiques. Les simulations sont effectuées dans l'espace à deux dimensions R^2 à l'aide du logiciel FreeFem ++ en utilisant la méthode des éléments finis. Nous nous concentrons sur l'étude de la viscosité, de la vitesse et des contraintes de cisaillement maximale. En outre, nous visons à localiser les zones de recirculation qui sont formées à la suite de l'existence de la sténose. En se basant sur de ces résultats, nous procédons à la détection de la zone de solidification où le sang passe de l'état liquide à un matériau de type gelée. Ensuite, nous spécifions que le sang solidifié est un matériau élastique linéaire qui obéit à la loi de Hooke et qui subit à une force de surface externe représentant la contrainte exercée par le sang sur la zone de solidification. Les résultats numériques concernant le sang solidifié sont obtenus en résolvant les équations d'élasticité linéaires à l'aide de FreeFem ++. Nous analysons principalement la déformation de cette zone ainsi que les contraintes de cisaillement la paroi. Les résultats obtenus vont nous permettre de proposer une hypothèse pour la formulation d'un modèle de rupture. / This thesis is devoted to the mathematical modeling of the blood flow in stenosed arteries due to atherosclerosis. Atherosclerosis is a complex vascular disease characterized by the build up of a plaque leading to the narrowing of the artery. It is responsible for heart attacks and strokes. Regardless of the many risk factors that have been identified- cholesterol and lipids, pressure, unhealthy diet and obesity- only mechanical and hemodynamic factors can give a precise cause of this disease. In the first part of the thesis, we introduce the three dimensional mathematical model describing the blood-wall setting. The model consists of coupling the dynamics of the blood flow given by the Navier-Stokes equations formulated in the Arbitrary Lagrangian Eulerian (ALE) framework with the elastodynamic equations describing the elasticity of the arterial wall considered as a hyperelastic material modeled by the non-linear Saint Venant-Kirchhoff model as a fluid-structure interaction (FSI) system. Theoretically, we prove local in time existence and uniqueness of solution for this system when the fluid is assumed to be an incompressible Newtonian homogeneous fluid and the structure is described by the quasi-incompressible non-linear Saint Venant-Kirchhoff model. Results are established relying on the key tool; the fixed point theorem. The second part is devoted for the numerical analysis of the FSI model. The blood is considered to be a non-Newtonian fluid whose behavior and rheological properties are described by Carreau model, while the arterial wall is a homogeneous incompressible material described by the quasi-static elastodynamic equations. Simulations are performed in the two dimensional space R^2 using the finite element method (FEM) software FreeFem++. We focus on investigating the pattern of the viscosity, the speed and the maximum shear stress. Further, we aim to locate the recirculation zones which are formed as a consequence of the existence of the stenosis. Based on these results we proceed to detect the solidification zone where the blood transits from liquid state to a jelly-like material. Next, we specify the solidified blood to be a linear elastic material that obeys Hooke's law and which is subjected to an external surface force representing the stress exerted by the blood on the solidification zone. Numerical results concerning the solidified blood are obtained by solving the linear elasticity equations using FreeFem++. Mainly, we analyze the deformation of this zone as well as the wall shear stress. These analyzed results will allow us to give our hypothesis to derive a rupture model.

Este trabalho consiste no desenvolvimento de ferramentas computacionais para análise não linear geométrica de interação fluido-casca utilizando o Método dos Elementos Finitos (MEF). O algoritmo para dinâmica dos fluidos é explícito e a integração temporal é baseada em linhas características. O código computacional é capaz de simular as equações de Navier-Stokes para escoamentos compressíveis tanto na descrição Euleriana como na descrição Lagrangeana-Euleriana arbitrária (ALE), na qual é possível prescrever movimentos para a malha do fluido. A estrutura é modelada em descrição Lagrangeana total através de uma formulação de MEF para análise dinâmica não linear geométrica de cascas baseada no teorema da mínima energia potencial total escrito em função das posições nodais e vetores generalizados e não em deslocamentos e rotações. Essa característica evita o uso de aproximações de grandes rotações. Dois modelos de acoplamentos são desenvolvidos. O primeiro modelo, ideal para problemas onde a escala de deslocamentos não é muito grande comparada com as dimensões do domínio do fluido, é baseado na descrição ALE e o acoplamento entre as duas diferentes malhas é feito através do mapeamento das posições locais dos nós do contorno do fluido sobre os elementos de casca e vice-versa, evitando a necessidade de coincidência entre os nós da casca e do fluido. A malha do fluido é adaptada dinamicamente usando um procedimento simples baseado nas posições e velocidades nodais da casca. O segundo modelo de acoplamento, ideal para problemas com grande escala de deslocamentos tais como estruturas infláveis, considera a casca imersa na malha do fluido e consiste em um procedimento robusto baseado em curvas de nível da função distância assinalada do contorno, o qual integra o algoritmo Lagrangeano de casca com o Fluido em descrição Euleriana, sem necessidade de movimentação da malha do fluido, onde a representação computacional do fluido se resume a uma malha não estruturada maior ou igual ao domínio inicial do fluido e a interface fluido-casca dentro da malha do fluido é identificada por meio de curvas de nível da função distância assinalada do contorno. Ambos os modelos são testados através de exemplos numéricos mostrando robustez e eficiência. Finalmente, como uma sugestão para o futuro desenvolvimento desta pesquisa, iniciaram-se estudos relativos a funções B-splines. O uso desse tipo de funções deverá resolver problemas de estabilidade relativos a oscilações espúrias devidas ao uso de polinômios de Lagrange para a representação de descontinuidades. / This work consists of the development of computational tools for nonlinear geometric fluid-shell interaction analysis using the Finite Element Method (FEM). The fluid solver is explicit and its time integration based on characteristics. The computational code is able to simulate the Navier-Stokes equations for compressible flows written in the Eulerian description as well as in the arbitrary Lagrangian-Eulerian (ALE) description, enabling movements prescription for the fluid mesh. The structure is modeled in a total Lagrangian description, using a FEM formulation to deal with geometrical nonlinear dynamics of shells based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors, not displacements and rotations, avoiding the use of large rotation approximations. Two partitioned coupling models are developed. The first model, ideal for simulations where the displacements scale is not very large compared to the fluid domain, is based on the ALE description and the coupling between the two different meshes is done by mapping the fluid boundary nodes local positions over the shell elements and vice-versa, avoiding the need for matching fluid and shell nodes. The fluid mesh is adapted using a simple approach based on shell nodal positions and velocities. The second model, ideal for problems with large scales of displacements such as inflatable structures, is based on immersed boundary and consists of a robust level-set based approach that integrates the Lagrangian shell finite and the Eulerian finite element high speed fluid flow solver, with no need for mesh adaptation, where the fluid representation relies on a fixed unstructured mesh larger or equal to the initial fluid domain and the fluid-shell interface inside the fluid mesh is tracked with level sets of a boundary signed distance function. Both models are tested with numerical examples, showing efficiency and robustness. Finally, as a suggestion for future development of this research, we started studies relatives to B-Spline functions. The use of this kind of functions should solve stability problems related to spurious oscillations due to the use of Lagrange polynomials for representing discontinuities.

"Fluid-structure interaction arises in a wide array of technological applications including naval and marine hydrodynamics, civil and wind engineering and flight vehicle aerodynamics. When a fluid flows over a bluff body such as a circular cylinder, the periodic vortex shedding in the wake causes fluctuating lift and drag forces on the body. This phenomenon can lead to fatigue damage of the structure due to large amplitude vibration. It is widely believed that the wake structures behind the structure determine the hydrodynamic forces acting on the structure and control of wake structures can lead to vibration control of the structure. Modeling this complex non-linear interaction requires coupling of the dynamics of the fluid and the structure. In this thesis, however, the vibration of the flexible cylinder is prescribed, and the focus is on modeling the fluid dynamics in its wake. Low-dimensional iterative circle maps have been found to predict the universal dynamics of a two-oscillator system such as the rigid cylinder wake. Coupled map lattice (CML)models that combine a series of low-dimensional circle maps with a diffusion model have previously predicted qualitative features of wake patterns behind freely vibrating cables at low Reynolds number. However, the simple nature of the CML models implies that there will always be unmodelled wake dynamics if a detailed, quantitative comparison is made with laboratory or simulated wake flows. Motivated by a desire to develop an improved CML model, we incorporate self-learning features into a new CML that is trained to precisely estimate wake patterns from target numerical simulations and experimental wake flows. The eventual goal is to have the CML learn from a laboratory flow in real time. A real-time self-learning CML capable of estimating experimental wake patterns could serve as a wake model in a future anticipated feedback control system designed to produce desired wake patterns. A new convective-diffusive map that includes additional wake dynamics is developed. Two different self-learning CML models, each capable of precisely estimating complex wake patterns, have been developed by considering additional dynamics from the convective-diffusive map. The new self-learning CML models use adaptive estimation schemes which seek to precisely estimate target wake patterns from numerical simulations and experiments. In the first self-learning CML, the estimator scheme uses a multi-variable least-squares algorithm to adaptively vary the spanwise velocity distribution in order to minimize the state error (difference between modeled and target wake patterns). The second self-learning model uses radial basis function neural networks as online approximators of the unmodelled dynamics. Additional unmodelled dynamics not present in the first self-learning CML model are considered here. The estimator model uses a combination of a multi-variable normalized least squares scheme and a projection algorithm to adaptively vary the neural network weights. Studies of this approach are conducted using wake patterns from spectral element based NEKTAR simulations of freely vibrating cable wakes at low Reynolds numbers on the order of 100. It is shown that the self-learning models accurately and efficiently estimate the simulated wake patterns within several shedding cycles. Next, experimental wake patterns behind different configurations of rigid cylinders were obtained. The self-learning CML models were then used for off-line estimation of the stored wake patterns. With the eventual goal of incorporating low-order CML models into a wake pattern control system in mind, in a related study control terms were added to the simple CML model in order to drive the wake to the desired target pattern of shedding. Proportional, adaptive proportional and non-linear control techniques were developed and their control efficiencies compared."

Neste trabalho, a resposta dinâmica de um riser marítimo devido à geração e desprendimento alternado de vórtices é investigada numericamente. O riser é dividido em seções bidimensionais ao longo de seu comprimento. O Método dos Vórtices Discretos é empregado para a determinação das forças hidrodinâmicas que agem nestas seções bidimensionais. As seções hidrodinâmicas são resolvidas independentemente, e o acoplamento entre as mesmas é feito através da solução da estrutura no domínio do tempo pelo Método dos Elementos Finitos. Os resultados numéricos são comparados com resultados obtidos experimentalmente. Processamento paralelo é empregado para melhorar a performance do método. As simulações são realizadas através de uma metodologia mestre-escravo, utilizando MPI Message Passing Interface para explorar o paralelismo. A escalabilidade do algoritmo é mostrada e discutida. Este trabalho representa o desenvolvimento de um simulador que permite, efetivamente, a análise dinâmica de um riser com características e dimensões representativas das condições reais encontradas em campo, a um custo computacional factível para seu uso como uma ferramenta de engenharia. Isto é obtido por meio da técnica de processamento paralelo, aliada à solução do escoamento através de um método eficiente de CFD Método dos Vórtices Discretos e à solução da estrutura através do Método dos Elementos Finitos. / In this work the dy6namic response of a marine riser due to vortex shedding is numerically investigated. The riser is divided in two-dimensional sections along the riser length. The Discrete Vortex Method is employed for the assessment of the hydrodynamic forces acting on these two-dimensional sections. The hydrodynamic sections are solved independently, and the coupling among the sections is taken into account by the solution of the structure in the time domain by the Finite Element Method. The numerical results are compared with results obtained experimentally. Parallel processing is employed to improve the performance of the method. The simulations are carried out through a master-slave approach using MPI Message Passing Interface to exploit the parallelism. Scalability of the algorithm is shown and discussed. This work represents the development of a simulator that effectively allows the dynamic analysis of a riser with representative characteristics and dimensions of real field conditions, with a feasible computational cost for its use as an engineering tool. This is obtained by means of the parallel processing technique, together with an efficient CFD solution of the flow with de Discrete Vortex Method and the solution of the structure with the Finite Element Method.

Dans cette thèse, nous étudions des modèles mathématiques concernant certains problèmes d'écoulement de fluide à densité variable. Le premier chapitre résume l'ensemble de la thèse et se concentre sur les résultats obtenus, la nouveauté et la comparaison avec la littérature existante. Dans le deuxième chapitre, nous étudions la stabilisation locale des équations non homogènes de Navier-Stokes dans un canal 2d autour du flot de Poiseuille. Nous concevons un contrôle feedback de la vitesse qui agit sur l'entrée du domaine de sorte que la vitesse et la densité du fluide soient stabilisées autour du flot de Poiseuille, à condition que la densité initiale soit donnée par une constante additionnée d'une perturbation dont le support se situe loin du bord latéral du canal. Dans le troisième chapitre, nous étudions un système couplant les équations de Navier-Stokes compressibles à une structure élastique située à la frontière du domaine fluide. Nous prouvons l'existence locale de solutions solides pour ce système couplé. Dans le quatrième chapitre, notre objectif est d'étudier la nulle- contrôlabilité d'un problemè d'interaction fluide-structure linéarisé dans un canal bi dimensional. L'écoulement du fluide est ici modélisé par les équations de Navier-Stokes compressibles. En ce qui concerne la structure, nous considérons une poutre de type Euler-Bernoulli amortie située sur une partie du bord. Dans ce chapitre, nous établissons une inégalité d'observabilité pour le problème considéré d'interaction fluid-structure linéarisé qui constitue le premier pas vers la preuve de la nulle contrôlabilité du système. / In this thesis we study mathematical models concerning some fluid flow problems with variable density. The first chapter is a summary of the entire thesis and focuses on the results obtained, novelty and comparison with the existing literature. In the second chapter we study the local stabilization of the non-homogeneous Navier-Stokes equations in a 2d channel around Poiseuille flow. We design a feedback control of the velocity which acts on the inflow boundary of the domain such that both the fluid velocity and density are stabilized around Poiseuille flow provided the initial density is given by a constant added with a perturbation, such that the perturbation is supported away from the lateral boundary of the channel. In the third chapter we prove the local in time existence of strong solutions for a system coupling the compressible Navier-Stokes equations with an elastic structure located at the boundary of the fluid domain. In the fourth chapter our objective is to study the null controllability of a linearized compressible fluid structure interaction problem in a 2d channel where the structure is elastic and located at the fluid boundary. In this chapter we establish an observability inequality for the linearized fluid structure interaction problem under consideration which is the first step towards the direction of proving the null controllability of the system.