O objetivo deste trabalho é estudar e desenvolver procedimentos numéricos adequados para a análise de problemas da Engenharia do Vento Computacional (EVC). O escoamento é analisado a partir das equações de Navier-Stokes para um fluido Newtoniano e de uma equação de conservação de massa considerando a hipótese de pseudo-compressibilidade, ambas em um processo isotérmico. Na presença de escoamentos turbulentos emprega-se a Simulação de Grandes Escalas (“LES”) com os modelos clássico e dinâmico de Smagorinsky para as escalas inferiores à resolução da malha. Dois modelos numéricos de Taylor-Galerkin para a análise do escoamento são estudados: o esquema explícito de dois passos e o esquema explícito-iterativo. O Método dos Elementos Finitos (MEF) é empregado para a discretização do domínio espacial utilizando o elemento hexaédrico trilinear isoparamétrico com integração reduzida das matrizes em nível de elemento. Em problemas envolvendo efeitos de interação fluido-estrutura emprega-se um esquema de acoplamento particionado com características superiores de conservação, permitindo, inclusive, o uso de subciclos entre as análises do fluido e da estrutura e de malhas não compatíveis na interface. A estrutura é considerada como um corpo deformável constituído de um material elástico linear com a presença de nãolinearidade geométrica. O MEF é também usado para a discretização da estrutura, empregando-se para tanto o elemento hexaédrico trilinear isoparamétrico com integração reduzida e controle de modos espúrios. A equação de equilíbrio dinâmico é integrada no tempo utilizando o método implícito de Newmark no contexto do método de estabilização α- Generalizado. Na presença de estruturas deformáveis, o escoamento é descrito através de uma formulação arbitrária Lagrangeana-Euleriana (ALE). Ao final, comparações com exemplos numéricos e experimentais são apresentadas para demonstrar a viabilidade dos algoritmos desenvolvidos, seguindo-se com as conclusões do trabalho e as sugestões para trabalhos futuros. / Analysis and development of numerical tools to simulate Computational Wind Engineering (CWE) problems is the main goal of the present work. The isothermal flow is analyzed using the Navier-Stokes equations for viscous fluids and a mass conservation equation obtained according to the pseudo-compressibility assumption. Turbulent flows are simulated employing Large Eddy Simulation (LES) with the classical and dynamic Smagorinsky’s models for subgrid scales. Two Taylor-Galerkin models for the flow analysis are investigated: the explicit two-step scheme and the explicit-iterative scheme. The Finite Element Method (MEF) is employed for spatial discretizations using the eight-node hexahedrical isoparametric element with one-point quadrature. Fluid-structure interaction problems are analyzed with a coupling model based on a conservative partitioned scheme. The Finite Element Method (MEF) is employed for spatial discretizations using the eight-node hexahedrical isoparametric element with one-point quadrature. Fluid-structure interaction problems are analyzed with a coupling model based on a conservative partitioned scheme. Subcycling and nonmatching meshes for independent discretizations of the fluid and structure domains are also available. The structure is considered as a deformable body constituted by a linear elastic material with geometrically nonlinear effects. The FEM is used for the spatial discretization of the structure as well. Eight-node hexahedrical isoparametric elements with one-point quadrature and hourglass control are adopted in this process. The implicit Newmark algorithm within the framework of the α-Generalized method is employed for the numerical integration of the dynamic equilibrium equation. An arbitrary Lagrangean-Eulerian (ALE) description is adopted for the kinematic description of the flow when deformable structures are analyzed. Numerical and experimental examples are simulated in order to demonstrate the accuracy of the developed algorithms. Concluding remarks and suggestions for future works are pointed out in the last chapter of the present work.

Cette thèse traite plusieurs aspects scientifiques inhérents à la simulation numérique de problèmes d'interaction fluide-structure impliquant de fines membranes déformables. Deux cas spécifiques relatifs à la biomécanique cardiovasculaire sont considérés : l'interaction de l'écoulement sanguin avec la valve aortique (qui se produit à l'échelle macroscopique), et l'interaction de la membrane des globules rouges avec ses fluides interne et externe (qui se produit à l'échelle microscopique). Dans les deux cas, le couplage fluide-structure est géré par l'intermédiaire d'un formalisme de frontières immergées, en représentant la membrane par un maillage Lagrangien se mouvant au travers d'un maillage fluide Eulérien. Lorsque l'on traite la dynamique des globules rouges, la membrane est considérée comme étant une structure sans masse et infiniment fine. La première question à laquelle on s'intéresse dans cette thèse est la manière de modéliser la microstructure complexe de la membrane des globules rouges. Un moyen possible pour caractériser un modèle de membrane adapté est de simuler l'expérience des pinces optiques, qui consiste en une configuration expérimentale bien contrôlée qui permet d'étudier la mécanique individuelle d'un globule rouge isolé dans une large gamme de déformations. Plusieurs modèles pertinents sont identifiés, mais les caractéristiques de déformation mesurées durant l'expérience des pinces optiques se révèlent n'être pas assez sélectives pour être utilisées dans un contexte de validation. Des mesures de déformation additionnelles sont proposées, qui pourraient permettre une meilleure caractérisation de la mécanique de la membrane des globules rouges. En ce qui concerne les configurations macroscopiques, une méthode numérique innovante est proposée afin de gérer des simulations numériques de membranes 3D continues, en conservant le formalisme de frontières immergées. Dans cette méthode, appelée méthode des frontières immergées épaisses, la membrane a une épaisseur finie. La précision et la robustesse de la méthode sont démontrées par l'intermédiaire d'une variété de cas tests bien choisis. La méthode proposée est ensuite appliquée à un problème d'interaction fluide-structure réaliste, à savoir l'interaction d'un écoulement (sanguin) pulsé avec une valve aortique biomimétique. Une étude combinée expérimentale et numérique est menée, montrant que la méthode est capable de capturer la dynamique globale de la valve, ainsi que les principales caractéristiques de l'écoulement en aval de la valve. Tous les développements ont été effectués dans le solveur YALES2BIO (http://www.math.univ-montp2.fr/~yales2bio/) développé à l'IMAG, qui est donc disponible pour toutes autres améliorations, validations et études applicatives. / This thesis deals with several scientific aspects inherent to the numerical simulation of fluid-structure interaction problems involving thin deformable membranes. Two specific cases relevant to cardiovascular biomechanics are considered: the interaction of the blood flow with the aortic valve (which occurs at the macroscopic scale), and the interaction of the red blood cells membrane with its inner and outer fluids (which occurs at the microscopic scale). In both cases, the fluid-structure interaction coupling is handled using an immersed boundary formalism, representing the membrane by a Lagrangian mesh moving through an Eulerian fluid mesh.When dealing with red blood cells dynamics, the membrane is considered to be an infinitely thin and massless structure. The first question which is addressed in the present thesis work is how to model the complex microstructure of the red blood cells membrane. A possible way to characterize a suitable membrane model is to simulate the optical tweezers experiment, which is a well-controlled experimental configuration enabling to study the individual mechanics of an isolated red blood cell in a large range of deformation. Some relevant membrane models are identified, but the deformation characteristics measured during the optical tweezers experiment reveal to be not selective enough to be used in a validation context. Additional deformation measurements are proposed, which could allow a better characterization of the red blood cell membrane mechanics.Regarding the macroscopic configurations, an innovative numerical method is proposed to handle numerical simulations of 3D continuum membranes, still within the immersed boundary formalism. In this method, called immersed thick boundary method, the membrane has a finite thickness. The accuracy and robustness of the method are demonstrated through a variety of well-chosen test cases. Then, the proposed method is applied to a realistic fluid-structure interaction problem, namely the interaction of a pulsatile (blood) flow with a biomimetic aortic valve. A combined experimental and numerical study is led, showing that the method is able to capture the global dynamics of the valve, as well as the main features of the flow downstream of the valve.All the developments were performed within the YALES2BIO solver (http://www.math.univ-montp2.fr/~yales2bio/) developed at IMAG, which is thus available for further improvements, validations and applicative studies.

Cette thèse porte sur l’analyse mathématique de l’interaction d’un fluide non-visqueux avec des structures immergées. Plus précisément, elle est structurée autour de deux axes principaux. L’un d’eux est l’analyse asymptotique du mouvement d’une particule infinitésimale en milieu liquide. L’autre concerne l’interaction entre des vagues et une structure immergée. La première partie de la thèse repose sur l’analyse mathématique d’un système d’équations différentielles ordinaires non-linéaires d’ordre 2 modélisant le mouvement d’un solide infiniment petit dans un fluide incompressible en 2D. Les inconnues du modèle décrivent la position du solide, c’est-à-dire la position du centre de masse et son angle de rotation. Les équations proviennent de la deuxième loi de Newton avec un prototype de force de type Kutta-Joukowski. Plus précisément, nous étudions la dynamique de ce système lorsque l’inertie du solide tend vers 0. Les principaux outils utilisés sont des développements asymptotiques multiéchelles en temps. Pour la dynamique de la position du centre de masse, l’étude met en évidence des analogies avec le mouvement d’une particule chargée dans un champ électromagnétique et la théorie du centre-guide. En l’occurrence, le mouvement du centreguide est donné par une équation de point-vortex. La dynamique de l’angle est quant à elle donnée par une équation de pendule non-linéaire lentement modulée. Des régimes très différents se distinguent selon les données initiales. Pour de petites vitesses angulaires initiales la méthode de Poincaré-Lindstedt fait apparaitre une modulation des oscillations rapides, alors que pour de grandes vitesses angulaires initiales, un movement giratoire bien plus irrégulier est observé. C’est une conséquence particulière et assez spectaculaire de l’enchevêtrement des trajectoires homocliniques. La deuxième partie de la thèse porte sur le problème des vagues dans le cas où le domaine occupé par le fluide est à surface libre et avec un fond plat sur lequel un objet solide se translate horizontalement sous l’effet des forces de pression du fluide. Nous avons étudié deux systèmes asymptotiques qui décrivent le cas d’un fluide parfait incompressible en faible profondeur. Ceux-ci correspondent respectivement aux équations de Saint-Venant et de Boussinesq. Grâce à leur caractère bien-posé en temps long, les modèles traités permettent de prendre en compte certains effets de la mécanique du solide, comme les forces de friction, ainsi que les effets non-hydrostatiques. Notre analyse théorique a été complétée par des études numériques. Nous avons développé un schéma de différences finies d’ordre élevé et nous l’avons adapté à ce problème couplé afin de mettre en évidence les effets d’un solide (dont le mouvement est limité à des translations sur le fond) sur les vagues qui passent au dessus de lui. A la suite de ces travaux, nous avons souligné l’influence des forces de friction sur ce genre de systèmes couplés ainsi que sur le déferlement des vagues. Quant à l’amortissement dû aux effets hydrodynamiques, une vague ressemblance avec le phénomène de l’eau morte est mise en évidence. / This PhD thesis concerns the mathematical analysis of the interaction of an inviscid fluid with immersed structures. More precisely it revolves around two main problems: one of them is the asymptotic analysis of an infinitesimal immersed particle, the other one being the interaction of water waves with a submerged solid object. Concerning the first problem, we studied a system of second order non-linear ODEs, serving as a toy model for the motion of a rigid body immersed in a two-dimensional perfect fluid. The unknowns of the model describe the position of the object, that is the position of its center of mass and the angle of rotation; the equations arise from Newton’s second law with the consideration of a Kutta-Joukowski type lift force. It concerns the detailed analysis of the dynamic of this system when the solid inertia tends to 0. For the evolution of the position of the solid’s center of mass, the study highlights similarities with the motion of a charged particle in an electromagnetic field and the wellknown “guiding center approximation”; it turns out that the motion of the corresponding guiding center is given by a point-vortex equation. As for the angular equation, its evolution is given by a slowly-in-time modulated non-linear pendulum equation. Based on the initial values of the system one can distinguish qualitatively different regimes: for small angular velocities, by the Poincaré-Lindstedt method one observes a modulation in the fast time-scale oscillatory terms, for larger angular velocities however erratic rotational motion is observed, a consequence of Melnikov’s observations on the presence of a homoclinic tangle. About the other problem, the Cauchy problem for the water waves equations is considered in a fluid domain which has a free surface on the upper vertical limit and a flat bottom on which a solid object moves horizontally, its motion determined by the pressure forces exerted by the fluid. Two shallow water asymptotic regimes are detailed, well-posedness results are obtained for both the Saint-Venant and the Boussinesq system coupled with Newton’s equation characterizing the solid motion. Using the particular structure of the coupling terms one is able to go beyond the standard scale for the existence time of solutions to the Boussinesq system with a moving bottom. An extended numerical study has also been carried out for the latter system. A high order finite difference scheme is developed, extending the convergence ratio of previous, staggered grid based models. The discretized solid mechanics are adapted to represent important features of the original model, such as the dissipation due to the friction term. We observed qualitative differences for the transformation of a passing wave over a moving solid object as compared to an immobile one. The movement of the solid not only influences wave attenuation but it affects the shoaling process as well as the wave breaking. The importance of the coefficient of friction is also highlighted, influencing qualitative and quantitative properties of the coupled system. Furthermore, we showed the hydrodynamic damping effects of the waves on the solid motion, reminiscent of the so-called dead water phenomenon.

Dans ce travail, une méthode basée sur les éléments finis ondulatoires - Wave Finite Elements (WFE) - est proposée en vue de prédire le rayonnement acoustique de conduites axisyrnétriques de longueur finie, comportant un fluide interne, et immergées dans un fluide acoustique de dimensions infinies. La condition de rayonnement de Sommerfeld est prise en compte en entourant le fluide extérieur d'un perfectly matched layer (PML), c'est-à-dire une couche d'éléments absorbants dans laquelle les ondes acoustiques incidentes sont progressivement amorties. Dans le cadre de l'approche WFE, la conduite, le fluide qu'elle contient, le fluide extérieur et le PML constituent un guide d'ondes multiphysique qui est discrétisé par un maillage éléments finis périodique, et peut être ainsi modélisé comme un assemblage de sous-systèmes identiques de faible longueur. Une base d'ondes se propageant le long de la conduite, calculée à partir du modèle éléments finis d'un sous-système, est utilisée afin de prédire le comportement vibroacoustique de guides d'ondes de longueur finie à moindre coût. Des simulations numériques sont réalisées pour des cas de conduites de structure homogène ou multi-couches. La précision et l'efficacité de la méthode WFE sont clairement établies en comparaison avec la méthode des éléments finis conventionnelle. / In this work, a wave finite element (WFE) method is proposed to predict the sound radiation of finite axisymmetric fluid-filled pipes immersed in an external acoustic fluid of infinite extent, The Sommerfeld radiation condition is taken into account by means of a perfectly matched layer (PML) around the external fluid. Within the WFE framework, the fluid-filled pipe, the surrounding fluid and the PML constitute a multiphysics waveguide that is discretized by means of a periodic finite element mesh, and is treated as an assembly of identical subsystems of small length. Wave modes are computed from the FE model of a multi-physics subsystem and used as a representation basis to assess the vibroacoustic behavior of the finite waveguide at a low computational cost. Numerical experiments are carried out in the cases of axisymmetric pipes of either homogeneous or multi-layered crosssections, The accuracy and efficiency of the proposed approach are dearly highlighted in comparison with the conventional FE method.

Le sujet de la thèse est le développement d'un outil numérique qui permet de modéliser l'écoulement autour des pales d'éoliennes. Nous nous sommes intéressés à la résolution des équations de Navier-Stokes en incompressible sur des maillages de type octree où les échelles plus petites en proche parois ont été modélisées par la méthode dite des wall functions. Un procédé d'adaptation automatique du maillage (AMR) a été développé pour affiner le maillage dans les zones où la vorticité est plus importante. Le modèle de structure d'une pale d'éolienne a été également implémenté et couplé avec le modèle fluide car une application de l'outil numérique est l'étude des effets des rafales de vent sur les pales d'éolienne. Un travail expérimental a été mené sur une éolienne avec une mesure de vent en amont. Ces données permettent ainsi de calibrer et valider les modèles numériques développés dans la thèse. / The subject of the thesis is the development of a numerical tool that allows to model the flow around wind blades. We are interested in the solving of incompressible Navier-Stokes equations on octree grids, where the smallest scales close to the wall have been modelled by the use of the so-called Wall Functions. An automatic Adaptive Mesh Refinement (AMR) process has been developed in order to refine the mesh in the areas where the vorticity is higher. The structural model of a real wind blade has also been implemented and coupled with the fluid model. Indeed, an application of the numerical tool is the study of the effects of wind gusts on blades. An experimental work has been conducted with an in-service wind turbine with the measurement of wind speed upstream. This data will allow to calibrate and validate the numerical models developed in the thesis.

We study the turbulent flow of a fluid over a canopy, that we model as a deformable porous medium. This porous medium is more precisely a carpet of fibres that bend under the hydrodynamic load, hence initiating a fluid-structure coupling at the scale of a fibre's height (honami). The objective of the thesis is to develop a macroscopic model of this fluid-structure interaction in order to perform numerical simulations of this process. The volume averaging method is implemented to describe the large scales of the flow and their interaction with the deformable porous medium. An hybrid approach is followed due to the non-local nature of the solid phase; While the large scales of the flow are described within an Eulerian frame by applying the method of volume averaging, a Lagrangian approach is proposed to describe the ensemble of fibres. The interface between the free-flow and the porous medium is handle with a One-Domain- Approach, which we justify with the theoretical development of a mass- and momentum- balance at the fluid/porous interface. This hybrid model is then implemented in a parallel code written in C$++$, based on a fluid- solver available from the \openfoam CFD toolbox. Some preliminary results show the ability of this approach to simulate a honami within a reasonable computational cost. Prior to implementing a macroscopic model, insight into the small-scale is required. Two specific aspects of the small-scale are therefore studied in details; The first development deals with the inertial deviation from Darcy's law. A geometrical parameter is proposed to describe the effect of inertia on Darcy's law, depending on the shape of the microstructure of the porous medium. This topological parameter is shown to efficiently characterize inertia effects on a diversity of tested microstructures. An asymptotic filtration law is then derived from the closure problem arising from the volume averaging method, proposing a new framework to understand the relationship between the effect of inertia on the macroscopic fluid-solid force and the topology of the microstructure of the porous medium. A second research axis is then investigated. As we deal with a deformable porous medium, we study the effect of the pore-scale fluid-structure interaction on the filtration law as the flow within the pores is unsteady, inducing time-dependent fluidstresses on the solid- phase. For that purpose, we implement pore-scale numerical simulations of unsteady flows within deformable pores, focusing for this preliminary study on a model porous medium. Owing to the large displacements of the solid phase, an immersed boundary approach is implemented. Two different numerical methods are compared to apply the no-slip condition at the fluid-solid interface: a diffuse interface approach and a sharp interface approach. The objective is to find the proper method to afford acceptable computational time and a good reliability of the results. The comparison allows a cross-validation of the numerical results, as the two methods compare well for our cases. This numerical campaign shows that the pore-scale deformation has a significant impact on the pressure drop at the macroscopic scale. Some fundamental issues are then discussed, such as the size of a representative computational domain or the form of macroscopic equations to describe the momentum transport within a soft deformable porous medium.

Cette thèse aborde la résolution des problèmes d'interaction fluide-structure par un algorithme consistant en un couplage entre deux solveurs : un pour le fluide et un pour la structure. Pour assurer la cohérence entre les maillages fluide et structure, on considère également une discrétisation de chaque domaine par volumes finis. En raison des difficultés de décomposition du domaine en sous-domaines, nous considérons pour chaque environnement un algorithme parallèle de multi-splitting (ou multi-décomposition) qui correspond à une présentation unifiée des méthodes de sous-domaines avec ou sans recouvrement. Cette méthode combine plusieurs applications de points fixes contractantes et nous montrons que, sous des hypothèses appropriées, chaque application de points fixes est contractante dans des espaces de dimensions finies normés par des normes hilbertiennes et non-hilbertiennes. De plus, nous montrons qu'une telle étude est valable pour les résolutions parallèles synchrones et plus généralement asynchrones de grands systèmes linéaires apparaissant lors de la discrétisation des problèmes d'interaction fluide-structure et peut être étendue au cas où le déplacement de la structure est soumis à des contraintes. Par ailleurs, nous pouvons également considérer l’analyse de la convergence de ces méthodes de multi-splitting parallèles asynchrones par des techniques d’ordre partiel, lié au principe du maximum discret, aussi bien dans le cadre linéaire que dans celui obtenu lorsque les déplacements de la structure sont soumis à des contraintes. Nous réalisons des simulations parallèles pour divers cas test fluide-structure sur différents clusters, en considérant des communications bloquantes et non bloquantes. Dans ce dernier cas nous avons eu à résoudre une difficulté d'implémentation dans la mesure où une erreur irrécupérable survenait lors de l'exécution ; cette difficulté a été levée par introduction d’une méthode assurant la terminaison de toutes les communications non bloquantes avant la mise à jour du maillage. Les performances des simulations parallèles sont présentées et analysées. Enfin, nous appliquons la méthodologie présentée précédemment à divers contextes d'interaction fluide-structure de type industriel sur des maillages non structurés, ce qui constitue une difficulté supplémentaire. / This thesis deals with the solution of fluid-structure interaction problems by an algorithm consisting in the coupling between two solvers: one for the fluid and one for the structure. In order to ensure the consistency between fluid and structure meshes, we also consider a discretization of each domain by finite volumes. Due to the difficulties of decomposing the domain into sub-domains, we consider a parallel multi-splitting algorithm for each environment which represents a unified presentation of sub-domain methods with or without overlapping. This method combines several contracting fixed point mappings and we show that, under appropriate assumptions, each fixed point mapping is contracting in finite dimensional spaces normalized by Hilbertian and non-Hilbertian norms. In addition, we show that such a study is valid for synchronous parallel solutions and more generally asynchronous of large linear systems arising from the discretization of fluidstructure interaction problems and can be extended to cases where the displacement of the structure is subject to constraints. Moreover, we can also consider the analysis of the convergence of these asynchronous parallel multi-splitting methods by partial ordering techniques, linked to the discrete maximum principle, both in the linear frame and in the one obtained when the structure's displacements are subjected to constraints. We carry out parallel simulations for various fluidstructure test cases on different clusters considering blocking and non-blocking communications. In the latter case, we had to solve an implementation problem due to the fact that an unrecoverable error occurred during execution; this issue has been overcome by introducing a method to ensure the termination of all non-blocking communications prior to the mesh update. Performances of parallel simulations are presented ans analyzed. Finally, we apply the methodology presented above to various fluid-structure interaction cases on unstructured meshes, which represents an additional difficulty.

O presente trabalho tem por objetivo desenvolver uma formulação numérica baseada em Análise Isogeométrica para o estudo de problemas de interação fluido-estrutura (IFE) em aplicações envolvendo corpos rígidos submersos, onde escoamentos incompressíveis de fluidos Newtonianos com superfície livre são considerados. Propõe-se o emprego da Análise Isogeométrica por permitir a unificação entre os procedimentos de pré-processamento e análise, melhorando assim as condições de continuidade das funções de base empregadas tanto na discretização espacial do problema como na aproximação das variáveis do sistema de equações. O sistema de equações fundamentais do escoamento é formado pelas equações de Navier-Stokes e pela equação da conservação de massa, descrita segundo a hipótese de pseudo-compressibilidade, em uma formulação cinemática ALE (Arbitrary Lagrangean- Eulerian). A consideração da superfície livre no escoamento se dá tratando o fluido como um meio bifásico, através do método Level Set. O corpo rígido apresenta não linearidade na rotação e restrições representadas por vínculos elásticos e amortecedores viscosos, sendo a equação de equilíbrio dinâmico resolvida através do método de Newmark. O esquema de acoplamento sólido-fluido adotado é o particionado convencional, que impõe condições de compatibilidade cinemáticas e de equilíbrio sobre a interface sólido-fluido, analisando ambos os meios de maneira sequencial. A discretização das equações governantes é realizada através do esquema explícito de dois passos de Taylor-Galerkin, aplicado no contexto da Análise Isogeométrica. Por fim, são analisados alguns problemas da Dinâmica de Fluidos Computacional, de onde se concluiu que os resultados obtidos são bastante consistentes com os fenômenos envolvidos, com as ferramentas exclusivas da Análise Isogeométrica, como o refinamento k, melhorando a convergência dos resultados. Para escoamentos bifásicos, verificou-se que o método Level Set obteve resultados bastante promissores apresentando, entretanto, uma dissipação numérica excessiva. Propõe-se, para estudos futuros, a elaboração de esquemas numéricos que conservem melhor o volume da fase líquida do escoamento. / The present work aims to development of a numerical formulation based on Isogeometric Analysis for the study of Fluid-Structure Interaction problems in applications involving rigid bodies submerged, considering incompressible Newtonian flows with free surface. The use of the Isogeometric Analysis allows unification between the preprocessing and analysis steps, improving then the continuity of the base functions employed, both in the spatial discretization and approximation of the variables in the system of equations. The fundamental flow equations are formed by the Navier-Stokes and the mass conservation, described by de pseudo-compressibility hypothesis, in an ALE (Arbitrary Lagrangean-Eulerian) kinematic formulation. The free surface consideration of the flow is handled treating the fluid like a two- phase medium, using the Level Set method. The rigid body considers nonlinearity in rotation, and restrictions represented by elastic springs and viscous dampers, with the dynamic equilibrium equation being resolved using the Newmark’s method. The solid-fluid coupling scheme is the conventional partitioned, which imposes kinematics and equilibrium compatibility conditions on the solid-fluid interface, analyzing both mediums in a sequential manner. The governing equations are discretized using the explicit two step Taylor-Galerkin method, applied in an Isogeometric Analisys context. Finally, some Computational Fluid Dinamics problems are analysed, from which it was concluded that the results obtained are quite consistent with phenomena involved, with the unique tools of Isogeometric Analysis, such as k-refinement, improving the convergence of the results. For biphasic flows, it was verified that the Level Set method obtained very promising results, presenting, however, an excessive numerical dissipation. For future studies, it is proposed the elaboration of numerical schemes that better preserve the volume of the liquid phase of the flow.

Orientador: Prof. Dr. André Fenili / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Engenharia Mecânica, 2015. / No presente trabalho, é investigado o modelo matemático de uma viga não linear com seção retangular em rotação. Foi considerado, no modelo, curvatura linear e condições de contorno de viga livre-engastada. Para simulação, considera-se ainda ângulo de ataque constante e as não linearidades resultantes do acoplamento entre a velocidade angular do eixo de rotação e vibração transversal da viga. As forças externas de arrasto e sustentação ao longo do comprimento da viga foram modeladas utilizando teoria de faixas. Estas forças são funções não lineares da velocidade transversal da viga e da velocidade angular do eixo de rotação. As equações de governo para a viga foram discretizadas no espaço utilizando-se o método das diferenças finitas. Isso resulta em uma sistema de equações diferenciais para os valores nodais da discretização espacial da viga. Esse conjunto de equações diferenciais é integrado numericamente no domínio do tempo utilizando-se um método de Runge-Kutta de quarta ordem. / In this work, we investigate the mathematical model of a nonlinear beam with rectangular cross section in rotation. It was considered, in the model, linear curvature and boundary conditions of clamped-free. To simulation, still considered constant attack angle and the nonlinearities resulting from the coupling between the angular velocity of the rotation axis and transverse vibration of the beam. The external drag and lift forces along the length of the beam were modeled as turbulent drag and potential generated by the lift force. These forces are dependent on the speed of nonlinear excitations acting on the beam. The solution in space wasobtained from the finite difference method using 5 points, and the solution in the time from the Runge- Kutta method of 4th order.

Orientador: Prof. Dr. Juan Pablo Julca Avila / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Engenharia Mecânica, 2015. / Atualmente, os risers rígidos em catenária ou SCRs (Steel Catenary Risers), que são tubos longos de aço, apresentam-se como a melhor solução técnico-econômica na transferência de petróleo e gás desde o solo marinho até uma plataforma flutuante. Os SCRs são de fácil fabricação, resistem altas pressões internas e hidrostáticas e também resistem altas temperaturas. Porém, cuidado especial deve-se tomar no cálculo dos momentos fletores e força axial interna no ponto de contato com o solo marinho, sendo estes parâmetros cruciais no projeto. Por outro lado, devido a que os SCRs interagem com o solo marinho, a plataforma à qual está conectada, correntezas e com o escoamento interno, a teoria de SCRs é complexa e não tem sido totalmente desenvolvida, requerendo para seu estudo a teoria de vigas curvas, tópicos de mecânica dos sólidos e dos fluidos, dinâmica não-linear, mecânica de ondas e mecânica dos solos. Este trabalho tem como principal objetivo o desenvolvimento e implementação de uma ferramenta computacional para análise estática e dinâmica bidimensional de risers rígidos e flexíveis dispostos em catenária em contato com o solo marinho. A discretização espacial do riser é feita usando elementos finitos não lineares tipo de viga, incluindo grandes deslocamentos e rotações. A formulação co-rotacional é utilizada para o tratamento da não linearidade geométrica. O método iterativo-incremental de Newton-Raphson é usado para resolver as equações de equilíbrio estático e dinâmico. A integração no tempo das equações dinâmicas é feita usando o esquema implícito de Newmark. A fim de garantir a estabilidade do esquema numérico implementado quando são impostos deslocamentos no topo do riser pelo método de penalização, é introduzido nas equações dinâmicas um termo de amortecimento estrutural para a filtragem das frequências espúrias induzidas por este tipo de excitação. O solo marinho é modelado como uma fundação elástica-linear do tipo Winkler e o método de penalização é usado para a imposição da condição de não penetração. Simulações estáticas e dinâmicas de problemas geometricamente não lineares foram conduzidas para a avaliação do elemento de viga plana implementado neste trabalho. Os resultados obtidos foram comparados com resultados da literatura para a validação do código. A ferramenta computacional foi aplicada satisfatoriamente para resolver problemas estáticos e dinâmicos de risers rígidos e flexíveis. / Steel catenary risers (SCR) are slender steel pipes that hang free in the ocean, this represents the best technical and economical solution for the oil and gas transfer from the seabed to the floating platform. SCRs are of easy manufacturing, high internal and external pressure resistance and also high temperature resistance. Special care should be taken in the calculation of the bending and tension stresses at the touch down point (TDP) as this parameters are of main importance in the calculation of fatigue resistance. On the other side, as the riser interacts with many other elements as seawater currents, internal flow, floating platform and seabed SCRs theory is complex and is not yet well developed, requiring for its study deep knowledge of curved beam theory, solid and fluid mechanics, non-linear dynamics, wave theory and soil mechanics. The main objective of this work is the development and implementation of a computational tool for the static and dynamic two-dimensional analysis of steel catenary and flexible risers, special attention is given to the seabed contact phenomena, to this end, numerical methods for the solution of dynamic equations were implemented into a MATLAB code. The spacial discretization of the riser geometric domain was made by finite element procedures, the large deflections and rotations, inherent to risers geometric non linearity, were treated by means of the co-rotational formulation. The incremental-iterative Newton-Raphson scheme is used to solve the equations of static and dynamic equilibrium. Time domain integration is made using Newmarks implicit method. To guarantee the numerical stability of the implemented code when imposed a time-varying nodal displacement by the penalty method an structural damping is introduced. This damping filters spurious frequencies induced by the penalty method. The seabed is modeled as an elastic foundation of Winkler type, once again the penalty method is used to enforce the non-penetration condition. Static and dynamic simulations of beams with geometrical non linearity were conducted in order to test the stability and accuracy of the implemented code. These results were compared with those available in specialized literature in order to validate the code. This computational tool was successfully applied to the static and dynamic analysis of steel catenary risers.