Simulação de fluidos tem sido um dos focos principais de pesquisa em computação gráfica nos últimos anos. O interesse por tal assunto é motivado pelas aplicações na indústria cinematográfica, jogos e sistemas voltados para simulação de fenômenos físicos realísticos em tempo real. Neste trabalho atacamos um problema ainda pouco explorado pela comunidade de computação gráfica, a simulação de fluidos em imagens digitais. Adotamos uma abordagem relacionando fluidos multifásicos, onde propriedades da imagem são incorporadas às equações de Navier-Stokes a fim de permitir que objetos contidos nas imagens \"escoem\" interagindo a forças que agem no sistema / In the last years, fluid simulation has been one of the main focus in Computer Graphics. Such a reason is related to applications to film industry, games and frameworks for realtime physical problem simulations. In this work we aim at accessing a problem which is not so much explored in Computer Graphics: fluid simulation in digital images. We adopt a approach related to multiphase fluids, where properties of the image are set to the Navier-Stokes equations in order to allow that objects into the images \"flow\"in accordance to the forces in the system

O estudo do transporte de sedimentos, partindo da estimativa de estruturas turbulentas relevantes, constituiu o principal foco deste trabalho. Assim, a equação de transporte de massa (advecção-difusão) foi aplicada em conjunto com as equações de Navier-Stokes e da continuidade filtradas. Neste contexto, houve a necessidade de uma descrição conveniente da turbulência, o que ocorreu mediante a aplicação da simulação de grandes escalas acoplada a modelos de viscosidade turbulenta sub-malha. O método de fronteira imersa foi utilizado na modelação da interface sólido/fluido, representada pela geometria de fundo dos canais. As equações de Navier-Stokes filtradas e da continuidade foram resolvidas numericamente pelo método de passos fracionados, o qual estabeleceu o almejado acoplamento entre ambas. Na discretização das equações governantes foi utilizado o método de diferenças finitas, aplicado sobre malhas deslocadas. Os esquemas explícitos de Adams-Bashforth (de segunda e quarta ordens) foram utilizados no avanço temporal das velocidades do escoamento e das concentrações de sedimentos. Uma nova formulação para a velocidade de sedimentação foi desenvolvida analiticamente, enquanto que eventuais fluxos de ressuspensão foram impostos como condição de contorno no fundo do canal. Todos os códigos computacionais, que estabeleceram as diretrizes e a lógica de cálculo, foram criados no contexto deste trabalho. Os resultados obtidos indicam que a simulação de grandes escalas, associada ao método de fronteira imersa, considerando velocidade de sedimentação conforme aqui modelada, e ainda utilizando a equação de advecção-difusão para o transporte de massa, constituem ferramentas altamente adequadas à estimativa do transporte de sedimentos pela água. / The goal of this work is the research of sediment transport phenomena, deriving from outstanding turbulent eddies estimative. Thus, the mass transport equation (advection-diffusion) was connected with the filtered Navier-Stokes and continuity equations. In this context, the large-eddy simulation and sub-grid viscosity modeling established a convenient description of turbulence effects. The immersed boundary method was applied to model solid/fluid interface, represented here by the shapes of channel bottom. The filtered Navier-Stokes and continuity equations were solved by the fractional step method. The equations were discretized with the finite difference method, applied over staggered grids, whereas explicit Adams-Bashforth schemes (second and forth orders) were used in temporal advancement of velocities and sediment concentration fields. A new analytical formulation for settling velocity was obtained, while fortuitous re-suspension flux was applied like a boundary condition in the channel bottom. The computational code was totally developed in this work. The results of present simulations show that large-eddy simulation coupled to the immersed boundary method, considering, yet, the settling velocity of particles and the advection-diffusion equation for mass transport, constitute potential tools for sediment transport evaluation in water flows.

O estudo do transporte de sedimentos, partindo da estimativa de estruturas turbulentas relevantes, constituiu o principal foco deste trabalho. Assim, a equação de transporte de massa (advecção-difusão) foi aplicada em conjunto com as equações de Navier-Stokes e da continuidade filtradas. Neste contexto, houve a necessidade de uma descrição conveniente da turbulência, o que ocorreu mediante a aplicação da simulação de grandes escalas acoplada a modelos de viscosidade turbulenta sub-malha. O método de fronteira imersa foi utilizado na modelação da interface sólido/fluido, representada pela geometria de fundo dos canais. As equações de Navier-Stokes filtradas e da continuidade foram resolvidas numericamente pelo método de passos fracionados, o qual estabeleceu o almejado acoplamento entre ambas. Na discretização das equações governantes foi utilizado o método de diferenças finitas, aplicado sobre malhas deslocadas. Os esquemas explícitos de Adams-Bashforth (de segunda e quarta ordens) foram utilizados no avanço temporal das velocidades do escoamento e das concentrações de sedimentos. Uma nova formulação para a velocidade de sedimentação foi desenvolvida analiticamente, enquanto que eventuais fluxos de ressuspensão foram impostos como condição de contorno no fundo do canal. Todos os códigos computacionais, que estabeleceram as diretrizes e a lógica de cálculo, foram criados no contexto deste trabalho. Os resultados obtidos indicam que a simulação de grandes escalas, associada ao método de fronteira imersa, considerando velocidade de sedimentação conforme aqui modelada, e ainda utilizando a equação de advecção-difusão para o transporte de massa, constituem ferramentas altamente adequadas à estimativa do transporte de sedimentos pela água. / The goal of this work is the research of sediment transport phenomena, deriving from outstanding turbulent eddies estimative. Thus, the mass transport equation (advection-diffusion) was connected with the filtered Navier-Stokes and continuity equations. In this context, the large-eddy simulation and sub-grid viscosity modeling established a convenient description of turbulence effects. The immersed boundary method was applied to model solid/fluid interface, represented here by the shapes of channel bottom. The filtered Navier-Stokes and continuity equations were solved by the fractional step method. The equations were discretized with the finite difference method, applied over staggered grids, whereas explicit Adams-Bashforth schemes (second and forth orders) were used in temporal advancement of velocities and sediment concentration fields. A new analytical formulation for settling velocity was obtained, while fortuitous re-suspension flux was applied like a boundary condition in the channel bottom. The computational code was totally developed in this work. The results of present simulations show that large-eddy simulation coupled to the immersed boundary method, considering, yet, the settling velocity of particles and the advection-diffusion equation for mass transport, constitute potential tools for sediment transport evaluation in water flows.

Most realistic fluid flow problems are characterised by high Reynolds numbers and complex boundaries. Over the last ten years, immersed boundary methods (IBM) that are able to cope with realistic geometries have been applied to Lattice- Boltzmann methods (LBM). These methods, however, have normally been applied to low Reynolds number problems. In the present work, an iterative direct forcing IBM has been successfully coupled with a multi-domain cascaded LBM in order to investigate viscous flows around rigid, moving and wilfully deformed boundaries at a wide range of Reynolds numbers. The iterative force-correction immersed boundary method of (Zhang et al., 2016) has been selected due to the improved accuracy of the computation, while the cascaded LB formulation is used due to its superior stability at high Reynolds numbers. The coupling is shown to improve both the stability and numerical accuracy of the solution. The resulting solver has been applied to viscous flow (up to a Reynolds number of 100000) passed a NACA-0012 airfoil at a 10 degree angle of attack. Good agreement with results obtained using a body-fitted Navier-Stokes solver has been obtained. At moving or deformable boundary applications, emphasis should be given on the influence of the internal mass on the computation of the aerodynamic forces, focusing on deforming boundary motions where the rigid body approximation is no longer valid. Both the rigid body and the internal Lagrangian points approximations are examined. The resulting solver has been applied to viscous flows around an in-line oscillating cylinder, a pitching foil, a plunging SD7003 airfoil and a plunging and flapping NACA-0014 airfoil. Good agreement with experimental results and other numerical schemes has been obtained. It is shown that the internal Lagrangian points approximation accurately captures the internal mass effects in linear and angular motions, as well as in deforming motions, at Reynolds numbers up to 4 • 104. Finally, an expanded higher-order immersed boundary method which addresses two major drawbacks of the conventional IBM will be presented. First, an expanded velocity profile scheme has been developed, in order to compensate for the discontinuities caused by the gradient of the velocity across the boundary. Second, a numerical method derived from the Navier-Stokes equations in order to correct the pressure distribution across the boundary has been examined. The resulting hybrid solver has been applied to viscous flows around stationary and oscillating cylinders and examined the hovering flight of elliptical wings at low Reynolds numbers. It is shown that the proposed scheme smoothly expands the velocity profile across the boundary and increases the accuracy of the immersed boundary method. In addition, the pressure correction algorithm correctly expands the pressure profile across the boundary leading to very accurate pressure coefficient values along the boundary surface. The proposed numerical schemes are shown to be very efficient in terms of computational cost. The majority of the presented results are obtained within a few hours of CPU time on a 2.8 GHz Intel Core i7 MacBook Pro computer with a 16GB memory.

The main contribution of the present work is the proposition of a framework for analysis of active suspensions using the Caenorhabditis elegans nematode as the living model. To do so, five different perspectives are used: kinematics, macro-reological, numerical, theoretical and micro-reological. First, a theoretical and experimental analysis of the kinematic motion of the nematodes suspended in a biological fluid is presented. Two different populations are examined: starving and well fed nematodes. We show that the relationship between the length of an individual nematode and the wavelength of its movement is linear and can be adjusted by a theoretical prediction proposed in this work. A deep discussion on propulsive mechanics based on a scale analysis that identifies three major forces acting on an individual nematode is made. In addition, we investigated the shear viscosity of Caenorhabditis elegans suspensions. The oscillatory shear experiments revealed an anomalous viscosity behavior with the variation of the volumetric fraction of suspension, ?. The effective viscosity of the suspension decreased with increasing nematode volumetric fraction at low concentrations. Based on the experimental data, a phenomenological equation for the effective viscosity of the suspension as a function of the volumetric fraction of particles is proposed. The collective behavior of the nematodes is also observed in linear regime through the difference of normal stresses. Finally, step strain tests are conducted to obtain the relaxation times. The presence of a negative active stress due to the nematoid driving behavior persists for a period of time, leading to a negative undershoot and an oscillatory behavior in the relaxation function. In order to propose a rheological model, simplifications are made in the model and immersed boundary method simulations are conducted in a flexible filament, varying the type of movement that it performs. It is observed that the presence of asymmetries in its undulating movement generates drastic changes on its kinematic responses. A rheological model as a function of filament orientation is proposed and validated with experimental data in linear regime. After validation of the proposed constitutive equation, the model is observed under the nonlinear regime of oscillatory shear, in which the rheological characterizations are made based on existing frameworks using Lissajous-Bowditch curves and Pipkin diagrams. Finally, a protocol for analysis of suspensions in a microrheometer is presented. Particles are added and tracked as unidirectional oscillatory shear (pulsatile flow) is applied. The velocity and shear rate profiles are obtained, as well as the rheological signals equivalent to the strain rate and stress. Signal analysis tools are used and an artificial intelligence system is proposed to remove the component added to the signal by unidirectional shear, aiming to reconstruct the signal with null temporal average and allowing the application of well known rheological theories, such as the decomposition of stresses in coefficients of Chebyshev, for the calculation of viscommetric quantities of compliances and fluidities. The major contribution of the study concerns the observation, characterization, modeling and simulation of a microsized animal that moves in different fashion, depending on the environment, and the surrounding fluid. The rheological properties analyzed, simuations performed and model proposed can be used for both production of artifitial microorganisms and control of living organisms. Moreover, this combination of analyses and techniques can be used to study any type of passive and active suspension providing new and conclusive results regarding the rheological characterization and the physical behavior of the particles. / A principal contribuição do presente trabalho é a proposição de um framework de análise de suspensões ativas utilizando como modelo vivo o nematoide Caenorhabditis elegans. Para tanto, cinco perspectivas diferentes são utilizadas: cinemática, macrorreológica, numérica, teórica e microrreológica. Primeiramente, uma análise teórica e experimental do movimento cinemático das partículas ativas suspensas em um fluido biológico é apresentada. Duas populações diferentes são examinadas: na ausência de alimento e com nematoides bem alimentados. Mostramos que a relação entre o comprimento de um nematoide individual e o comprimento de onda de seu movimento é linear e pode ser ajustada por uma previsão teórica proposta neste trabalho. Uma profunda discussão sobre a mecânica de propulsão com base em uma análise de escala que identifica três forças principais que atuam em um nematoide individual é feita. Além disso, investigamos a viscosidade de cisalhamento das suspensões de Caenorhabditis elegans. Os experimentos em cisalhamento oscilatório revelaram um comportamento anômalo da viscosidade com a variação da fração volumétrica de suspensão, ?. A viscosidade efetiva da suspensão diminuiu com o aumento da fração volumétrica do nematoide para pequenas concentrações. Baseando-se nos dados experimentais, uma equação fenomenológica para a viscosidade efetiva da suspensão em função da fração volumétrica de partículas é proposta. O comportamento coletivo dos nematoides é também observado, em regime linear, pela diferença de tensões normais. Finalmente, o teste de step strain é conduzido para obter os tempos de relaxação. A presença de uma tensão ativa negativa devido ao comportamento impulsor do nematoide persiste por um certo período, levando a um undershoot negativo e a um comportamento oscilatório na função de relaxação. A fim de propor um modelo reológico, simplificações são efetuadas no modelo e simulações usando o método de fronteira imersa são conduzidas em um filamento flexível, variando o tipo de movimento que este realiza. Observa-se que a presença de assimetrias em seu movimento ondulatório gera drásticas mudanças em suas respostas cinemáticas. Um modelo reológico em função da orientação do filamento é proposto e validado com os dados experimentais em regime linear. Após a validação da equação constitutiva proposta, o modelo é observado sob o regime não-linear do cisalhamento oscilatório, no qual as caracterizações reológicas são feitas com base nos frameworks existentes, utilizando curvas de Lissajous-Bowditch e diagramas de Pipkin. Por fim, é apresentado um protocolo de análise de suspensões em um microrreômetro. Partículas são adicionadas e rastreadas à medida que um cisalhamento unidirecional (escoamento pulsátil) é aplicado. Os perfis de velocidade e taxa de cisalhamento são obtidos, assim como os sinais reológicos equivalentes à taxa de deformação e tensão. Ferramentas de análise de sinais são utilizadas e um sistema de inteligência artificial é proposto para remoção da componente constante do sinal adicionada pelo cisalhamento unidirecional, visando reconstruir o sinal com média temporal nula e possibilitando a aplicação de teorias reológicas já conhecidas, como a decomposição de tensões em coeficientes de Chebyshev para o cálculo das quantidades viscométricas de conformidade e fluidez. A principal contribuição do estudo diz respeito à observação, caracterização, modelagem e simulação de um animal microscópico que se movimenta de maneira diferente dependendo do ambiente e do fluido circundante. As propriedades reológicas analisadas, as simulações realizadas e o modelo proposto podem ser utilizados tanto para a produção de microorganismos artificiais quanto para o controle de organismos vivos. Além disso, essa combinação de análises e técnicas pode ser usada para estudo de qualquer tipo de suspensão ativa e passiva, fornecendo resultados novos e conclusivos em relação à caracterização reológica e ao comportamento físico das partículas.

The ultimate goal of this research is to develop the capability of direct numerical simulation of a flow containing numerous rigid finite size particles. In order to reach this goal, we have implemented the smoothed profile method (SPM) in the University of Iowa in-house solver, pELAFINT3D and overcame several challenges related to the method. This includes a proposed formulation for the interface thickness and many validations and comparisons with experimental data as well as with a second-order accurate sharp interface method. As one of the issues related to low-density particles is the instability, SPM has been improved by developing to a fully implicit scheme. Moreover, use of higher order integration formulation and implementation of Euler parameters have been shown to be helpful in stabilization of the calculations. To preserve the efficiency when the number of the particles increases, local mesh refinement is shown to be a very effective tool. A revised version of SPM that has only one projection step is proposed to improve the efficiency of the method. A comprehensive efficiency study is performed and it has been shown that the new method is less expensive in problems with high added mass effect when strongly coupled fluid-structure interaction schemes are used. Moreover, the code is massively parallelized using MPI and PETSc libraries. The parallelization includes I/O, operations leading to construction of the linear solver as well as the solver itself. Simulation of a particle laden flow involves particles collisions. Two novel collision models are suggested which are able to avoid particle overlapping for arbitrary shape particles. The methods are efficient as they are not involved with extra grid refinement related to implementing lubrication forces. The issue of handling continuously changing number of particles in a particle laden flow is solved by implementation of a linked list data structure for the particles. By studying a flow over a constricted region we showed that the platelets’ activation is more likely to happen for the particles that pass from the middle of the upper bump region because those particles will have longer exposure time to the high shear flow behind the bump. PDF contour of particles’ presence show the more concentrated presence of the particles near the bump. Moreover, the interaction of RBCs and platelets pushes the platelets toward the wall after the bottom wall.

This thesis presents an automatic animation system for jellyfish that is based on a physical simulation of the organism and its surrounding fluid. Our goal is to explore the unusual style of locomotion, namely jet propulsion, which is utilized by jellyfish. The organism achieves this propulsion by contracting its body, expelling water, and propelling itself forward. The organism then expands again to refill itself with water for a subsequent stroke. We endeavor to model the thrust achieved by the jellyfish, and also the evolution of the organism's geometric configuration. <p> We restrict our discussion of locomotion to fully grown adult jellyfish, and we restrict our study of locomotion to the resonant gait, which is the organism's most active mode of locomotion, and is characterized by a regular contraction rate that is near one of the creature's resonant frequencies. We also consider only species that are axially symmetric, and thus are able to reduce the dimensionality of our model. We can approximate the full 3D geometry of a jellyfish by simulating a 2D slice of the organism. This model reduction yields plausible results at a lower computational cost. From the 2D simulation, we extrapolate to a full 3D model. To prevent our extrapolated model from being artificially smooth, we give the final shape more variation by adding noise to the 3D geometry. This noise is inspired by empirical data of real jellyfish, and also by work with continuous noise functions from the graphics community. <p> Our 2D simulations are done numerically with ideas from the field of computational fluid dynamics. Specifically, we simulate the elastic volume of the jellyfish with a spring-mass system, and we simulate the surrounding fluid using the semi-Lagrangian method. To couple the particle-based elastic representation with the grid-based fluid representation, we use the immersed boundary method. We find this combination of methods to be a very efficient means of simulating the 2D slice with a minimal compromise in physical accuracy.

This thesis presents an automatic animation system for jellyfish that is based on a physical simulation of the organism and its surrounding fluid. Our goal is to explore the unusual style of locomotion, namely jet propulsion, which is utilized by jellyfish. The organism achieves this propulsion by contracting its body, expelling water, and propelling itself forward. The organism then expands again to refill itself with water for a subsequent stroke. We endeavor to model the thrust achieved by the jellyfish, and also the evolution of the organism's geometric configuration. <p> We restrict our discussion of locomotion to fully grown adult jellyfish, and we restrict our study of locomotion to the resonant gait, which is the organism's most active mode of locomotion, and is characterized by a regular contraction rate that is near one of the creature's resonant frequencies. We also consider only species that are axially symmetric, and thus are able to reduce the dimensionality of our model. We can approximate the full 3D geometry of a jellyfish by simulating a 2D slice of the organism. This model reduction yields plausible results at a lower computational cost. From the 2D simulation, we extrapolate to a full 3D model. To prevent our extrapolated model from being artificially smooth, we give the final shape more variation by adding noise to the 3D geometry. This noise is inspired by empirical data of real jellyfish, and also by work with continuous noise functions from the graphics community. <p> Our 2D simulations are done numerically with ideas from the field of computational fluid dynamics. Specifically, we simulate the elastic volume of the jellyfish with a spring-mass system, and we simulate the surrounding fluid using the semi-Lagrangian method. To couple the particle-based elastic representation with the grid-based fluid representation, we use the immersed boundary method. We find this combination of methods to be a very efficient means of simulating the 2D slice with a minimal compromise in physical accuracy.

Fluid-structure interaction (FSI) is an important physical phenomenon in many applications and across various disciplines including aerospace, civil and bio-engineering. In civil engineering, applications include the design of wind turbines, pipelines, suspension bridges and offshore platforms. Ocean structures such as drilling risers, mooring lines, cables, undersea piping and tension-leg platforms can be subject to strong ocean currents, and such structures may suffer from Vortex-Induced Vibrations (VIV's), where vortex shedding of the flow interacts with the structural properties, leading to large amplitude vibrations in both in-line and cross-flow directions. Over the past years, many experimental and numerical studies have been conducted to comprehend the underlying physical mechanisms. However, to date there is still limited understanding of the effect of oscillatory interactions between fluid flow and structural behavior though such interactions can cause large deformations. This research proposes a mathematical framework to accurately predict FSI for elastically supported rigid structures. The numerical method developed solves the Navier-Stokes (NS) equations for the fluid and the Equation of Motion (EOM) for the structure. The proposed method employs Finite Differences (FD) on Cartesian grids together with an improved, efficient and oscillation-free Immersed Boundary Method (IBM), the accuracy of which is verified for several test cases of increasing complexity. A variety of two and three dimensional FSI simulations are performed to demonstrate the accuracy and applicability of the method. In particular, forced and a free vibration of a rigid cylinder including Vortex-Induced Vibration (VIV) of an elastically supported cylinder are presented and compared with reference simulations and experiments. Then, the interference between two cylinders in tandem arrangement at two different spacing is investigated. In terms of VIV, three different scenarios were studied for each cylinder arrangement to compare resonance regime to a single cylinder. Finally, the IBM is implemented into a three-dimensional Large-Eddy Simulation (LES) method and two high Reynolds number (Re) flows are studied for a stationary and transversely oscillating cylinder. The robustness, accuracy and applicability of the method for high Re number flow is demonstrated by comparing the turbulence statistics of the two cases and discussing differences in the mean and instantaneous flows.

Resumo: A compreensão do escoamento em válvulas de compressores herméticos alternativos é de fundamental importância para introduzir modificações no projeto delas de maneira a aumentar a performance dos compressores, e por fim, dos ciclos de refrigeração. A válvula do compressor é um dispositivo ímpar, umas vez que seu funcionamento se dá pela ação da pressão exercida pelo escoamento, caracterizando um problema de forte interação fluido- estrutura. O uso da modelagem numérica através das ferramentas da mecânica dos fluidos computacional (CFD) tem se destacado como a alternativa mais dinâmica para o estudo do fenômeno. O trabalho desenvolvido foi voltado para o estudo numérico do escoamento através do difusor radial, o qual é um modelo simplificado da válvula, com o emprego do Método da Fronteira Imersa com Modelo Físico Virtual para a modelagem do disco superior do difusor (palheta). O ponto forte desta metodologia é que a representação de regiões sólidas é feita pelo cálculo de um campo de força, o qual é introduzido nas equações das células na vizinhança do sólido. Este procedimento dispensa o uso de malhas que se adaptam ao corpo, possibilitando o uso de malhas cartesianas convencionas para modelar geometrias complexas e móveis. A metodologia foi acoplada com a solução das equações governantes do escoamento em coordenadas cilíndricas através do Método dos Volumes Finitos. Inicialmente, a metodologia foi validada, utilizando como dados de referência resultados provenientes de estudos numéricos e experimentais, e foi avaliada a influência dos parâmetros do procedimento na qualidade final dos resultados. Na segunda etapa foram desenvolvidos estudos preliminares referentes ao movimento do disco superior, com a imposição artificial dos processos de abertura e fechamento da válvula. Os resultados obtidos mostraram que a metodologia adotada ... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The fully understanding of the flow through automatic valves of alternative hermetic compressors is essentiall to introduce modifications in its project aiming the improvement of the compressor performance and, also, the refrigeration cycle. The compressor valve is a singular device, once its operation is ruled by the flow pressure, characterizing a case with a strong fluid-structure interaction. The using of numerical tools trough the methods of computational fluid dynamics (CFD) has gained especial attention due to its flexibility to study the phenomenon. The present work was developed to study numerically the flow through the radial diffuser, which is a simplified model of the valve, with the employment of the Immersed Boundary Method with Virtual Physical Model to modeling the superior disk (valve reed). The main advantage of this methodology is that the modeling of solid boundaries is performed with the calculus of a force field, which is introduced in the cells equations nearby the solid. This procedure dispenses the using of body-fitted meshes, enabling the adoption of conventional Cartesian meshes to model complex and moving geometries. The methodology was coupled with the solution of the governing equations in cylindrical coordinates though the Finite Volume Method. Firstly, the methodology was validated, confronting the results obtained with data from numerical and experimental studies, where the influence of the main parameters in the quality of the final results was evaluated. In the second step were developed preliminary studies concerning the movement of the superior disk, whose opening and closing movements were artificially imposed. The results obtained showed that the adopted methodology is quit promising and flexible, and can be employed in more refined studies to the comprehension of the flow through the valve regarding the fluid-structure interaction that rules the problem / Orientador: José Luiz Gasche / Coorientador: Júlio Militzer / Banca: Cassio Roberto Macedo Maia / Banca: Elie Luis Martinez Padilla / Mestre