A interação entre as ondas vibratórias geradas pela resposta estrutural de uma placa e os modos acústicos de uma cavidade, que é uma das principais fontes de ruído no interior de cabines de automóveis, é estudada empregando técnicas computacionais e experimentais. Para investigar este fenômeno foi construído um protótipo que consiste de uma cavidade feita de acrílico que simula o interior de um veículo. O teto deste modelo pode ser substituído por uma placa de alumínio flexível, para que se possa gerar efeitos de acoplamento entre o campo acústico e a resposta estrutural. Inicialmente, foi feito um estudo analítico do modelo, empregando-se técnicas de elementos finitos com o objetivo de extrair as freqüências naturais e modos vibroacústicos em uma faixa de freqüência abaixo de 300 Hz, em dois casos diferentes: com e sem a presença de assentos dentro da cavidade. Depois disso, o modelo foi submetido a vários testes experimentais, para se obterem as funções de resposta em freqüência, as freqüências naturais vibroacústicas e os modos acústicos e estruturais, usando excitação acústica e estrutural e empregando métodos padrões de análise modal. Para fins de comparação, as FRF\'s vibroacústicas foram obtidas de duas maneiras diferentes: com excitação estrutural e resposta acústica e com excitação acústica e resposta estrutural. As freqüências naturais e os modos vibroacústicos foram medidos usando excitação acústica e estrutural. Neste caso, é mostrada a importância do controle da força excitadora. Alguns parâmetros experimentais foram variados, tais como posicionamento das excitações acústica e estrutural e o tipo de suspensão. Finalmente, é apresentada uma compilação das diferentes técnicas para a extração dos parâmetros modais vibroacústicos, propondo novas metodologias para a medição dos modos acústicos e estruturais em freqüências abaixo de 70 Hz, controlando a força excitadora e utilizando métodos de ajuste de curvas. É mostrado que o uso de excitação acústica e estrutural merece alguns cuidados, visto que a aplicação dos métodos traz restrições de acordo com a faixa de freqüência e a escolha da melhor forma de extração dos modos vibroacústicos depende da freqüência estudada. / The interaction between the vibration waves generated by the structural response of a plate and the acoustic modes of a cavity, which is one of the main noise sources in automobile passenger cabin, is addressed employing both computational and experimental techniques. In order to investigate this phenomenon a prototype which consists of a cavity made of acrylic that resembles a vehicle interior was built. The roof of this model can be replaced by a flexible aluminum plate in order to generate coupling effects between the acoustic field and the structural response. Initially an analytical study was performed on the model employing finite element techniques with the aim of extracting the vibroacoustic natural frequencies and mode shapes in a frequency range below 300 Hz in two different cases: with and without the presence of seats inside the cavity. After that, the model was submitted to several experimental tests in order to obtain the frequency response functions, vibroacoustic natural frequencies and mode shapes, using acoustic and structural excitation and employing standard modal testing methods. For comparison purposes, the vibroacoustic FRF\'s were obtained in two different manners: with the structural excitation and acoustic response and with acoustic excitation and structural response. The vibroacoustic natural frequencies and mode shapes were measured employing both acoustic and structural excitation. In this case, it is shown the importance of the control of the exciting force. Some experimental parameters were varied, such as positioning of the acoustic and structural sources and the suspension type. Finally, a compilation of different techniques for the vibroacoustic modal parameters extraction is presented, proposing new methodologies for the acoustic and structural modes measurements in frequencies below 70 Hz, using force control and curve fitting methods. It is shown that both acoustic and structural excitations have restrictions concerning the frequency range and the choice of the better method for the extraction of the vibroacoustic mode shapes and natural frequencies depends on it.

Um dos grandes desafios enfrentados pelos fabricantes de turbinas hidráulicas é prevenir o aparecimento de vibrações induzidas pelo escoamento nas travessas do pré-distribuidor e pás do rotor. Considerando apenas as travessas, e atribuídos a tais vibrações, foram relatados 28 casos de trincas ou ruídos anormais nas últimas décadas, que acarretaram enormes prejuízos associados a reparos, atrasos e perda de geração. O estado da arte na prevenção destes problemas baseia-se na utilização de sofisticados, e caros, programas comerciais de dinâmica dos fluidos computacional para o cálculo transiente do fenômeno. Este trabalho faz uma ampla revisão bibliográfica e levantamento de eventos de trincas ou ruídos ocorridos em travessas nos últimos 50 anos. Propõe, então, um enfoque alternativo, baseado exclusivamente em ferramentas de código aberto. A partir de hipóteses simplificadoras devidamente justificadas, o problema é formulado matematicamente de forma bidimensional, no plano da seção transversal da travessa, levando em conta a interação fluido-estrutura. Nesta estratégia, as equações de Navier-Stokes são resolvidas pelo método dos elementos finitos por meio da biblioteca gratuita oomph-lib. Um código especial em C++ é desenvolvido para o problema de interação fluido-estrutura, no qual o fenômeno de turbulência é levado em consideração por meio de um algoritmo baseado no modelo de Baldwin-Lomax. O método proposto é validado por meio da comparação dos resultados obtidos com referências e medições disponíveis na literatura, que tratam de problemas de barras retangulares suportadas elasticamente. O trabalho finaliza com a aplicação do método a um estudo de caso envolvendo uma travessa particular. / One of the biggest challenges for hydraulic turbine manufacturers is to prevent vortex-induced vibration on the stay vanes and runner blades. Only regarding stay vanes, 28 cases of cracks or unusual noises attributed to such vibrations were reported in the past decades leading to huge costs due to repair, delays and lack of generation. The state of the art today is to use powerful and expensive commercial computational fluid dynamics software to address the required transient phenomena. The present work carries out a comprehensive survey on occurred events in stay vanes during the last 50 years. Then, an alternative approach, based only on free open-source tools, is proposed. From due justified simplifying assumptions, the problem is formulated two-dimensionally, in the stay vane cross section plane, taking the fluid-structure interaction into account. In such a strategy, the Navier-Stokes equations are solved using oomph-lib, an object-oriented, finite-element library. A special C++ computational code is developed to deal with the fluid-structure interaction problem, in which turbulence is considered through a special algorithm, based on the Baldwin-Lomax model. The proposed method is validated through comparisons with an aerodynamics benchmark and an experimental measurement of oscillating rectangular bars both available in the literature. The method is finally applied to a case study of a particular stay vane. Keywords: Hydraulic turbine. Fluid-structure interaction. Vortex-induced vibration.

Introduction. Atherosclerotic plaque rupture may occur without warning leading to severe clinical events such as heart attack and stroke. The mechanisms causing plaque rupture are not well understood. It is hypothesized that mechanical forces may play an important role in the plaque rupture process and that image-based computational mechanical analysis may provide useful information for more accurate plaque vulnerability assessment. The objectives of this dissertation are: a) develop in vivo magnetic resonance imaging (MRI)-based 3D computational models with fluid-structure Interactions (FSI) for human atherosclerotic carotid plaques; b) perform mechanical analysis using 3D FSI models to identify critical stress/strain conditions which may be used for possible plaque rupture predictions. Data, Model, and Methods. Histological, ex vivo/ in vivo MRI data of human carotid plaques were provided by the University of Washington Medical School and Washington University Medical School. Blood flow was assumed to be laminar, Newtonian, viscous and incompressible. The Navier-Stokes equations with arbitrary Lagrangian-Eulerian (ALE) formulation were used as the governing equations for the flow model. The vessel and plaque components were assumed to be hyperelastic, isotropic, nearly-incompressible and homogeneous. The nonlinear Mooney-Rivlin model was used to describe the nonlinear properties of the materials with parameter values chosen to match available experimental data. The fully-coupled FSI models were solved by a commercial finite element software ADINA to obtain full 3D flow and stress/strain distributions for analysis. Validation of the computational models and Adina software were provided by comparing computational solutions with analytic solutions and experimental data. Several novel methods were introduced to address some fundamental issues for construction of in vivo MRI-based 3D FSI models: a) an automated MRI segmentation technique using a Bayes theorem with normal probability distribution was implemented to obtain plaque geometry with enclosed components; b) a pre-shrink process was introduced to shrink the in vivo MRI geometry to obtain the no-load shape of the plaque; c) a Volume Component-Fitting Method was introduced to generate a 3D computational mesh for the plaque model with deformable complex geometry, FSI and inclusions; d) a method using MRI data obtained under in vitro pressurized conditions was introduced to determine vessel material properties. Results. The effects of material properties on flow and wall stress/strain behaviors were evaluated. The results indicate that a 100% stiffness increase may decrease maximal values of maximum principal stress (Stress-P1) and maximum principal strain (Strain-P1) by about 20% and 40%, respectively; flow Maximum-Shear-Stress (FMSS) and flow velocity did not show noticeable changes. By comparing ex vivo and in vivo data of 10 plaque samples, the average axial (25%) and inner circumferential (7.9%) shrinkages of the plaques between loaded and unloaded state were obtained. Effects of the shrink-stretch process on plaque stress/strain distributions were demonstrated based on six adjusted 3D FSI models with different shrinkages. Stress-P1 and Strain-P1 increased 349.8% and 249% respectively with 33% axial stretch. The effects of a lipid-rich necrotic core and fibrous cap thickness on structure/flow behaviors were investigated. The mean values of wall Stress-P1 and Strain-P1 from lipid nodes from a ruptured plaque were significantly higher than those from a non-ruptured plaque (112.3 kPa, 0.235 & 80.1 kPa, 0.185), which was 40.2% and 26.8% higher, respectively (p<0.001). High stress/strain concentrations were found at the thin fibrous cap regions. These results indicate that high stress concentrations and thin fibrous cap thickness might be critical indicators for plaque vulnerability. Conclusion. In vivo image-based 3D FSI models and mechanical image analysis may have the potential to provide quantitative risk indicators for plaque vulnerability assessment.

La méthode Smoothed Particle Hydrodynamics (SPH) est une méthode lagrangienne, sans maillage développée initialement pour des simulations de phénomènes astrophysiques. Depuis, elle a connu de nombreuses applications, notamment pour la simulation des écoulements des fluides. Contrairement aux méthodes utilisant un maillage, la méthode SPH peut gérer de manière naturelle et sans traitement spécifique les simulations des écoulements à sur- face libre et multiphasiques avec interface subissant de grandes déformations. Dans cette thèse, une modélisation SPH des écoulements des fluides multiphasiques a été réalisée en tenant compte de différentes complexités (écoulements à surface libre et multiphasiques interfacials) et de natures d'écoulement (si- mulation des fluides, des sols et les deux en interactions). Un modèle SPH faiblement compressible (WCSPH) a été proposé pour simuler les écoulements des fluides multiphasiques avec interface comprenant plus de deux phases de fluide. Ce modèle inclut le développement d’une nouvelle formulation de force de tension de surface en utilisant un opérateur SPH consistant de premier ordre. Une modification de condition généralisée aux parois solides a été apportée pour qu’elle soit appliquée sur les écoulements des fluides multiphasiques avec des rapports de densité et de viscosité élevés. Une nouvelle loi de comportement dépendant de la pression nommée RBMC-αμ ( Regularized Bingham Mohr Coulomb où αμ est un paramètre libre) a également été développée. Cette loi peut simuler les fluides (Newtonien, Binghamien), les sols (cohésif, frictionnel) et les deux en interactions. La loi précédente étant sensible à la pression, une extension du terme diffusif δ-SPH a été faite pour le cas des écoulements des fluides multiphasiques afin de réduire les oscillations de pression à haute fréquence qui sont dues à l’utilisation d’une équation d’état. La validation et l’application des modèles développés dans cette thèse sont montrées à travers plusieurs cas tests de difficulté croissante. / Smoothed Particle Hydrodynamics (SPH) is a Lagrangian gridless method developed initially to simulate astrophysical phenomena, and since it has been known for a large number of applications, especially for fluid flow simulations. Contrary to the grid-based method, the SPH method can handle free surface and interfacial fluid flow simulation including large deformations naturally and without the need for any specific treatment. In this thesis a SPH modeling of multiphase fluid flows has been achieved with consideration of different complexities ( free surface and interfacial fluid flows) and natures (simulation of fluids, soil and both in interactions). A consistent weakly compressible SPH model (WCSPH) has been proposed to simulate interfacial multiphase fluid flows with more than two fluid phases. This model includes a new expression of the surface tension force using a first order consistency SPH operator. A modification to the well known generalized wall boundary condition have been brought in order to be applied to multiphase fluid flow with large density and viscosity ratios. A new pressure-based constitutive law named RBMC-αμ (Regularized Bingham Mohr Coulomb with αμ is free parameter) has been developed in this thesis. This model can simulate fluids (Newtonian, Binghamton), soils (cohesive, frictional) and both in interactions. Because the previous model is pressure sensitive, an extension of δ-SPH diffusive term has been proposed for multiphase fluid flows to overcome the hight frequency pressure oscillations due to the determination of pressure from an equation of state. The validation and application of the developed models have been shown in this thesis through several test-cases of increasing difficulty.

Many cells exploit the bending or rotation of flagellar filaments in order to self-propel in viscous fluids. Often swimming occurs in complex, nonlinear fluids, e.g. mucus. Futhermore even in simple Newtonian fluids, if swimming appendages are deformable then locomotion is subject to fluid-structure interactions. The fundamental question addressed in this thesis is how exactly locomotion is impacted, in particular if it is faster or slower, with or without these effects. First we study locomotion in shear-thinning and viscoelastic fluids with rigid swimming appendages. Following the introductory Chapter, in Chapter 2 we propose empirical extensions of the classical Newtonian resistive-force theory to model the waving of slender filaments in non-Newtonian fluids, based on experimental measurements for the motion of rigid rods in non-Newtonian fluids and on the Carreau fluid model. We then use our models to address waving locomotion in shear-thinning fluids, and show that the resulting swimming speeds are systematically lowered a result which we are able to capture asymptotically and to interpret physically. In Chapter 3 we consider swimming using small-amplitude periodic waves in a viscoelastic fluid described by the Oldroyd-B constitutive relationship. Using Taylor’s swimming sheet model, we show that if all travelling waves move in the same direction, the locomotion speed of the organism is systematically decreased. However, if we allow waves to travel in two opposite directions, we show that this can lead to enhancement of the swimming speed, which is physically interpreted as due to asymmetric viscoelastic damping of waves with different frequencies. A change of the swimming direction is also possible. Secondly we consider the affect of fluid-structure interactions. In Chapter 4, we use Taylor’s swimming sheet model to describe an active swimmer immersed in an Oldroyd-B fluid. We solve for the shape of an active swimmer as a balance between the external fluid stresses, the internal driving moments, and the passive elastic resistance. We show that this dynamic balance leads to a generic transition from hindered rigid swimming to enhanced flexible locomotion. The results are physically interpreted as due to a viscoelastic suction increasing the swimming amplitude in a non-Newtonian fluid and overcoming viscoelastic damping. In Chapter 5 we consider peritrichously flagellated bacteria, such as Escherichia coli. The rotation of each motor is transmitted to a flexible rod called the hook which in turns transmits it to a helical filament, leading to swimming. The motors are randomly distributed over the body of the organism, and thus one expects the propulsive forces from the filament to almost cancel out leading to negligible swimming. We show that the transition to swimming is an elasto-hydrodynamic instability arising when the flexibility of the hook is below a critical threshold.

L'athérosclérose est une maladie inflammatoire qui commence quand les lipoprotéines de faible densité (LDL) entrent dans l'intima du vaisseau sanguin où elles sont oxydées (ox-LDL). Le ox-LDL est considéré comme un agent dangereux par le système immunitaire provoquant ainsi une réponse immunitaire. Cette réponse immunitaire déclenche le recrutement des monocytes dans l'intima où elles se transforment en macrophages et ensuite en cellules spumeuses. Ce dernier amplifie la production des cytokines inflammatoires et davantage de recrutement des monocytes. Ce processus auto-amplifié est compensé par la sécrétion de cytokines anti-inflammatoires (anti-inflammation biochimique) et la migration des cellules musculaires lisses pour former une chape fibreuse qui couvre le noyau lipidique. Cette chape fibreuse avec le noyau lipidique s'appellent la plaque d'athérosclérose. Celle-ci change la géométrie du vaisseau sanguin en le rétrécissant et interagit avec du flux sanguin. Cette interaction peut avoir des conséquences dangereuses liées à la rupture de plaque ou à la formation du caillot de sang. La thèse est consacrée à la modélisation mathématique de ces phénomènes. Elle est composée de deux parties : Nous développons des modèles mathématiques basés sur des équations de réaction diffusion afin de décrire le processus inflammatoire. Le premier modèle est unidimensionnel. Il nous permet d'expliquer comment le développement de l'athérosclérose dépend de la concentration en cholestérol (ox-LDL). Si cette concentration dans l'intima est basse, alors la maladie ne se développera pas. Les concentrations intermédiaires de ox-LDL peuvent mener au développement de la maladie dans certaines conditions. Nous montrons que l'inflammation se propage en front d'ondes de réaction-diffusion. Les concentrations élevées de ox-LDL engendre le développement de la maladie. Même une petite perturbation du cas non inflammatoire mène à une propagation d'ondes qui correspond à l'inflammation. Ensuite nous étudions un modèle bidimensionnel qui représente un système d'équations type réaction-diffusion sur une bande. La deuxième dimension correspond à la section transversale de l'intima et une condition aux limites non-linéaire décrit le recrutement des monocytes. Cette condition aux limites est une fonction des concentrations des cytokines. Nous démontrons l'existence des fronts de propagation d'onde et confirmons les résultats précédents qui montrent que l'athérosclérose se développe en tant qu'onde de réaction-diffusion. Les résultats théoriques des deux modèles sont confirmés par des simulations numériques qui montrent que le cas bidimensionnel converge vers le cas unidimensionnel quand l'épaisseur de l'intima tend vers zéro. Une fois la plaque se forme, elle interagit avec le flux sanguin engendrant de différentes conséquences mécaniques et biochimiques. Nous développons un modèle d'interaction fluide-structure. La plaque d'athérome composée d'un dépôt lipidique couvert par une chape fibreuse, les deux étant modélisés en tant que matériaux hyper-élastiques. Le sang est considéré comme un fluide non-Newtonien avec une viscosité variable modélisée selon la loi de Carreau. Les paramètres utilisés dans nos simulations sont tirés de données expérimentales mentionnées dans la littérature. Nous étudions les effets non-Newtoniens sur les recirculations du sang en aval de la plaque d'athérome et aussi sur les contraintes sur celle-ci. Les simulations montrent que le modèle Newtonien surestime les recirculations de manière significative par rapport au modèle non-Newtonien. Elles montrent aussi que le modèle Newtonien sous-estime légèrement les contraintes sur la plaque pour des taux de cisaillement usuels, mais cette sous-estimation devient importante pour des taux de cisaillement bas. / Atherosclerosis is an inflammatory disease which starts when low density lipoproteins (LDL) enter the intima of blood vessel where they are oxidized (ox-LDL). The ox-LDL is considered as a dangerous agent by the immune system provoking an anti-inflammatory response. This immune response triggers the recruitment of monocytes into the intima where they differentiate into macrophages and foam cells. The latter amplifies the production of inflammatory cytokines and further recruitment of monocytes. This auto-amplified process is compensated by the secretion of anti-inflammatory cytokines (biochemical anti-inflammation) and triggers the migration of smooth muscle cells to form a fibrous cap that covers the lipid core. These fibrous caps with the lipid core are called atherosclerosis plaque. It changes the geometry of the blood vessel by narrowing it and interacts with the blood flow. This interaction may have dangerous consequences related to the plaque rupture or to the formation of blood clot. The PhD thesis is devoted to mathematical modelling of these phenomena. It consists of two major parts : We develop mathematical models based on reaction-diffusion equations in order to describe the inflammatory process. The first model is one-dimensional. It allows us to explain how the development of atherosclerosis depends on the cholesterol (ox-LDL) concentration. If its concentration in the intima is low, then the disease will not develop. Intermediate ox-LDL concentrations can lead to the disease development under certain conditions. We show that the inflammation propagates as a reaction-diffusion wave. High ox-LDL concentrations will necessary result in the disease development. Even a small perturbation of the non inflammatory case leads to a travelling wave propagation which corresponds to a chronic inflammatory response. We then study a two-dimensional model which represents a reaction-diffusion system in a strip. The second dimension corresponds to the cross-section of the intima, nonlinear boundary conditions describe the recruitment of monocytes as a function of the cytokines concentration. We prove the existence of travelling waves and confirm our previous results which show that atherosclerosis develops as a reaction-diffusion wave. The theoretical results of the two models are confirmed by numerical simulations that show that the two-dimensional model converge to the one-dimensional one if the thickness of the intima tends to zero. When the plaque is formed, it interacts with blood flow resulting in various mechanical and bio-chemical effects. We develop a fluid-structure interaction model. The atheroma plaque is composed of a lipid pool and a fibrous cap and both are modeled as hyper elastic materials. The blood is supposed to be a non-Newtonian fluid with a variable viscosity modeled by the Carreau law. The parameters used in our simulations are taken from experimental data found in literature. We investigate the non-Newtonian effects on the re circulations downstream of the atheroma plaque and on the stress over the plaque. The simulations show that the Newtonian model significantly overestimates the re circulations in comparison with the non-Newtonian model. They also show that the Newtonian model slightly underestimates the stress over the plaque for usual shear rates, but this underestimation can become significant for low shear rates.

The fluid-structure interactions of wall-mounted slender structures, such as cilia, filaments, flaps, and flags, play an important role in a broad range of physical processes: from the coherent waving motion of vegetation, to the passive flow control capability of hair-like surface coatings. While these systems are ubiquitous, their coupled nonlinear response exhibits a wide variety of behaviours that is yet to be fully understood, especially when multiple structures are considered. The purpose of this work is to investigate, via numerical simulation, the fluid-structure interactions of arrays of slender structures over a range of input conditions. A direct modelling approach, whereby the individual structures and their dynamics are fully resolved, is realised via a lattice Boltzmann-immersed boundary model, which is coupled to two different structural solvers: an Euler-Bernoulli beam model, and a finite element model. Results are presented for three selected test cases - which build in scale from a single flap in a periodic array, to a small finite array of flaps, and finally to a large finite array - and the key behaviour modes are characterised and quantified. Results show a broad range of behaviours, which depend on the flow conditions and structural properties. In particular, the emergence of coherent waving motions are shown to be closely related to the natural frequency of the array. Furthermore, this behaviour is associated with a lock-in between the natural frequency of the array and the predicted frequency of the fluid instabilities. The original contributions of this work are: the development and application of a numerical tool for direct modelling of large arrays of slender structures; the characterisation of the behaviour of slender structures over a range of input conditions; and the exposition of key behaviour modes of slender structures and their relation to input conditions.

A quarter of the world's population experience wheezing. These sounds have been used for diagnosis since the time of the Ebers Papyrus (ca. 1500 BC), but the underlying physical mechanism responsible for the sounds is still poorly understood. The main purpose of this thesis is to change this, developing a theory for the onset of wheezing using both experimental and analytical approaches, with implications for both scientific understanding and clinical diagnosis. Wheezing is caused by a fluid structure interaction between the airways and the air flowing through them. We have developed the first systematic set of experiments of direct relevance to this physical phenomena. We have also developed new tools in shell theory using geometric algebra to improve our physical understanding of the self-excited oscillations observed when air flows through flexible tubes. In shell theory, the use of rotors from geometric algebra has enabled us to develop improved physical understanding of how changes of curvature, which are of direct importance to constitutive laws, come about. This has enabled a scaling analysis to be applied to the self-excited oscillations of flexible tubes, showing for the first time that bending energy is dominated by strain energy. We made novel use of multiple camera reconstruction to validate this scaling analysis by directly measuring the bending and strain energies during oscillations. The dominance of strain energy allows a simplification of the governing shell equations. We have developed the first theory for the onset of self-excited oscillations of flexible tubes based on a flutter instability. This has been validated with our experimental work, and provides a predictive tool that can be used to understand wheezing in the airways of the lung. Our theory for the onset of wheezing relates the frequency of oscillation to the airway geometry and material properties. This will allow diagnoses based on wheezing sounds to become more specific, which will allow the stethoscope, which has changed little in the last 200 years, to be brought into the 21st century.

The present research develops a numerical fluid-structure interaction (FSI) code based on CFDShip-Iowa version 4, a general-purpose URANS/DES overset fluid solver. Linear and nonlinear FSI methods are developed to compute structural responses on surface ships or marine structures. The modal superposition transient analysis and the nonlinear FEM structure solver are used for small and large deformation FSI problems, respectively. The gluing method is applied to transfer the forces and displacements on non-matching grids for fluid and structure domains. The linear FEM solver is applied to deform the boundary layer grid with large deformation in the fluid domain, while the deformation is ignored in small deformation problems. Deformation of an interior point in the boundary layer grid is obtained using linear interpolation in both linear and nonlinear deformation problems. The S175 containership is studied in regular waves as an application example for the linear problem. Heave and pitch responses are compared with the experiments, showing good agreement. Time histories of vertical bending moment (VBM) are calculated using rigid model, one-way coupling, and two-way coupling approaches. The elastic models are able to capture the ringing of the VBM induced by slamming, while the rigid model shows a peak at the moment of slamming without further fluctuations. The two-way coupling method shows the effects of hull deformation on the amplitude and phase of VBM as well as the accelerations of heave and pitch. For the nonlinear deformation problem three sloshing tanks with an elastic bar clamped to its bottom or top are simulated and compared with the experiments and other numerical simulation results. The present simulation results show reasonable agreement with the experiments for bar deformation and free surface elevation. A secondary wave on the free surface is creadted by the vorticity generated from the free surface. The effect of the bar on the sloshing impact is studied comparing dynamic pressure acting on the tank wall without bar, with an elatic bar, and with a rigid bar.

This thesis presents a stable fluid structural interaction technique to simulate the dynamics of tissue valves including bio-prosthetic heart valves and natural heart valves under physiological Reynolds numbers. A partitioned approach is implemented where the equations governing the flow and the displacement of the structure are solved using two distinct solvers. A FEAP based solid solver is strongly coupled to the p-ELAFINT flow solver using subiteration procedure. The flow solver has been massively parallelized so that the domain can be distributed among several processors. The fixed Cartesian method with adaptive mesh refinement in p-ELAFINT enables us to perform fast and efficient flow computations of problem involving moving boundaries such as heart valve leaflets. To capture the structure deformation, Enhanced Assumed Solid shell element has been implemented into the solid solver which is known for its locking free and superior bending characteristics. Aitken Relaxation method which dynamically computes the relaxation parameter is used for relaxing the solid displacement in the FSI coupling. This helps the subiteration procedure to achieve a faster convergence compared to traditional Subiterative procedures with fixed relaxation parameter. Fung type material model with experimentally derived parameters is used as the constitutive model to capture the realistic solid deformation. Opening phase of a bicuspid aortic valve (BAV) model derived from a patient specific data and a pericardial bioprosthetic valve model were simulated using the FSI algorithm with realistic material parameters under physiological flow conditions. It was observed that the valves attained its fully open position under 35 milliseconds which is similar to the physiological opening. The bioprosthetic valve attained a fully circular orifice while the BAV attained an ellipsoidal shaped orifice at its fully open position. In the BAV, strong vortical patterns were observed at peak systole and recirculation zones were observed near the sino-tubular junction. The work presented in this thesis be seen as a platform from which complex patient specific data can be modeled under physiological conditions and as a base to include contact mechanics with which complete cardiac cycle can be simulated.