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Projection methods for the incompressible Navier-Stokes equations (NSE) are efficient, but introduce numerical boundary layers and have limited temporal accuracy due to their fractional step nature. The Pressure Poisson Equation (PPE) reformulations represent a class of methods that replace the incompressibility constraint by a Poisson equation for the pressure, with a suitable choice of the boundary condition so that the incompressibility is maintained. PPE reformulations of the NSE have important advantages: the pressure is no longer implicitly coupled to the velocity, thus can be directly recovered by solving a Poisson equation, and no numerical boundary layers are generated; arbitrary order time-stepping schemes can be used to achieve high order accuracy in time. In this thesis, we focus on numerical approaches of the PPE reformulations, in particular, the Shirokoff-Rosales (SR) PPE reformulation. Interestingly, the electric boundary conditions, i.e., the tangential and divergence boundary conditions, provided for the velocity in the SR PPE reformulation render classical nodal finite elements non-convergent. We propose two alternative methodologies, mixed finite element methods and meshfree finite differences, and demonstrate that these approaches allow for arbitrary order of accuracy both in space and in time. / Mathematics

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The thesis reports improvements in the characterization techniques for stress and texture in crystalline materials by x-ray and neutron powder diffraction. Furthermore, advances are made in texture evolution modelling and validation against experimental observations. In the beginning, the fundamental assumption of diffraction strain analysis is numerically examined and verified, namely, that the lattice parameter value determined from fitting the diffraction pattern is equal to the average lattice parameter within the gauge volume. Next, the task of shear strain determination from powder diffraction measurements is addressed. A method is developed and implemented for the complete 2D strain tensor determination from the multi-directional energy-dispersive x-ray diffraction patterns. The method not only offers a way to evaluate the shear strain, but also provides a better overall strain averaging approach. Rotation and translation of sample and/or detectors in powder diffraction mode can effectively increase the pole figure coverage and thus the accuracy of texture determination. However, the movements also introduce uncertainties and aberrations into data analysis due to the changes in the diffraction volume and transmitted intensity. In order to overcome these problems, accurate <strong>single exposure</strong> texture characterization techniques are proposed based on several different powder diffraction setups. Numerical analyses are carried out to prove that any simple texture in cubic polycrystals can be effectively determined using single exposure Debye-Scherrer diffraction pattern analysis. Several experiments are reported on collecting Debye-Scherrer diffraction patterns, multi-directional energy-dispersive x-ray diffraction patterns and multi-directional TOF neutron setup. Efficient data processing procedures of the diffraction patterns for ODF determination are presented. Crystal plasticity finite element models are developed to model the texture evolution in polycrystalline engineering samples during manufacturing. In the present thesis, quantitative measures extracted from orientation distribution function are employed to make precise comparison between the model and experiment. Unlike the simple uni-axial compression and tension considered in the literature, in the present thesis the complex texture evolution during linear friction welding is modelled as a sequence of different shear deformations.

O trabalho de doutorado teve como objetivo desenvolver um modulador óptico baseado em filme magnetostrictivo para aplicação como magnetômetro. A modelagem e simulação do dispositivo foi realizada utilizando software com cálculo por método dos elementos finitos (MEF) e teve como finalidade auxiliar iterativamente os processos de projeto e fabricação do modulador. A originalidade da proposta baseia-se na construção de um guia de onda em óptica integrada recoberto por um filme magnetostrictivo para permitir a modulação , via efeito elasto-óptico, da onda guiada pela aplicação de campos magnéticos externos. O campo magnético aplicado provoca a deformação o material magnetostrictivo que induz uma modificação no perfil de esforço aplicado ao substrato. O substrato tem suas propriedades ópticas alteradas devido ao efeito elasto-óptico, o que provoca mudanças nas propriedades da luz transmitida. O trabalho tem seu início com o estudo e a caracterização de filmes magnetostrictivos de Tb25F275 e Tb23Co77 depositados por sputtering sobre substratos de silício. Uma técnica para preparação das amostras e medição da magnetostricção foi estabelecida e os coeficientes de magnetostrição dos filmes foram determinados a partir das medições diretas dos deslocamentos das amostras, em função dos campos magnéticos aplicados, utilizando a técnica de Atomic Force Microscopy (AFM). Os resultados experimentais obtidos permitiram a realização de simulações por MEF para verificação dos modos de guiamento da luz gerados pelo perfil de esforços induzidos termicamente no processo de deposição do filme magnetostrictivo sobre substrato de B12GeO4 (BGO). Foi modelado e simulado também o efeito da aplicação do campo magnético sobre o guia óptico obtido inicialmente pelo efeito de esforço térmico. No resultado das simulações foi possível verificar as alterações do índice de refração efetivo e da intensidade óptica do modo guiado em função de campos magnéticos aplicados ao modulador. Ao final do trabalho realizaram-se a fabricação de alguns protótipos. Os resultados das caracterizações dos moduladores construídos permitirão, no futuro, ajustar os modelos de simulação elaborados. / The doctoral work aims are the development and simulation of an optical modulator based on the effect of magnetostriction for application as magnetometer. The multiphysics simulations were performed using the Finite Elements Method (FEM). In the manufacturing process of optical modulator integrated optics techniques were applied. The originality of the proposal is based on the construction of an integrated optical waveguide covered by a magnetostrictive film to allow the modulation of the guided wave, through the elasto-optical effect, by the application of external magnetic fields. The applied magnetic field causes deformation of the magnetostrictive material that induces a modification of the stress profile produced in substrate. The substrate has its optical properties altered due to the elasto-optical effect, which causes changes in the properties of transmitted light. The work begins with the study and characterization of TbFe and TbCo2 magnetostrictive films deposited by sputtering on silicon substrates. A method for sample preparation and measurement of magnetostriction was established. The magnetostrictive coefficient of the films was determined from the direct measurement of displacements of samples by AFM technique for magnetic fields applied. The experimental results obtained allowed to perform MEF simulations to verify the light guided modes generated by the profile of thermally induced stress created by deposition process of magnetostrictive film on B12GeO4 (BGO) substrate. It was also modeled and simulated the effect of the application of magnetic field on the optical guide obtained initially by the effect of thermal stress. In simulation results, it was possible to verify the changes of effective refractive index and optical intensity of guided modes as functions of magnetic fields applied to the modulator. At the end of the work, some prototypes were fabricated. The results of characterizations of the built modulators will allow, in the future, adjustments in simulation models.

Made available in DSpace on 2015-03-04T18:51:00Z (GMT). No. of bitstreams: 1 Tese-anariodoce.pdf: 2089941 bytes, checksum: e12d7ae40046ae6cfc796af142908753 (MD5) Previous issue date: 2008-05-19 / Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Most marine benthic invertebrates have a complex life cycle in which the adult phase is preceded by a planktonic larval phase. The passive nature of larval dispersal of these species results in a larval transport governed by hydrodynamic processes like advection and eddy diffusion. The recruitment depends on a variety of physical and biological factors, which include spawning, larval dispersal and survival, larval settlement, metamorphosis, post-settlement events, inter-specific and intra-specific competitions. In order to assess interactions between oceanographic and biological processes that determine the population dynamics of marine organisms with a sessile adult phase restricted to the coastline and a planktonic larval phase, we develop a stage-structured finite element model for the barnacle Balanus glandula that inhabits the rocky intertidal zone of central California, USA. As the larval dispersal depends on knowing the flow pattern, we also develop a numerical procedure to couple physical and biological models in a very simple way when the velocity flow field is known of some discrete points of the domain of interest and at a given time. We investigate the effects of different flow patterns and velocity speeds on the abundance and the distribution of this organism as well as the influence of other abiotic interactions such as temperature and habitat quality. The interplay of different intra- and inter-specific competitions is also addressed. / A maioria das espécies marinhas possui um ciclo de vida complexo em que a fase adulta é precedida por uma fase larval pelágica. Os adultos produzem larvas que são soltas na coluna d'água onde elas são influenciadas por processos hidrodinâmicos como advecção e difusão turbulenta. Para os organismos que na maturidade são fixos a um substrato, como as cracas em particular, estudos mostram que estes processos podem afetar diretamente o assentamento das larvas e a dinâmica das populações de adultos. Neste trabalho apresentamos um modelo em Elementos Finitos que permite estudar as interações entre os processos biológicos e oceanográficos na dinâmica de um organismo marinho (craca Balanus glandula) com uma fase adulta séssil restrita à linha costeira e uma fase larval planctônica. Alguns cenários são investigados no estudo da variação, ao longo do tempo e do espaço, do número de indivíduos e da distribuição desta população, com o objetivo de entender, explicar e predizer como os fatores abióticos e bióticos afetam tais variações. O modelo considerou a dinâmica da população estágio-estruturada tanto de uma única espécie quanto de duas espécies, diferentes padrões idealizados de correntes marinhas, qualidade do habitat, influência da temperatura e reconstrução do campo de velocidades a partir de dados locais.

Submitted by Maria Cristina (library@lncc.br) on 2017-04-06T18:57:20Z No. of bitstreams: 1 thesisVolpatto.pdf: 4316650 bytes, checksum: 70380eace3eba66de52728f9d1d7ff89 (MD5) / Approved for entry into archive by Maria Cristina (library@lncc.br) on 2017-04-06T18:57:31Z (GMT) No. of bitstreams: 1 thesisVolpatto.pdf: 4316650 bytes, checksum: 70380eace3eba66de52728f9d1d7ff89 (MD5) / Made available in DSpace on 2017-04-06T18:57:40Z (GMT). No. of bitstreams: 1 thesisVolpatto.pdf: 4316650 bytes, checksum: 70380eace3eba66de52728f9d1d7ff89 (MD5) Previous issue date: 2016-06-14 / Agência Nacional do Petróleo, Gás Natural e Biocombustíveis / The present work aims at constructing a new sequential hydro-mechanical model of gas reservoirs. The new aspect of the proposed model lies on the derivation of new source terms in the subsystems of hydrodynamics and geomechanics. When compared with the fully-coupled formulation, where the two systems are solved simultaneously, the proposed formulation allows to explore the difference in the time-scales of the two phenomena. In addition the sequential formulation can be naturally extended to treat impermeable adjacent rocks and overcomes the problem of lack of stability in the impermeable regions of the geological formation. The formulation proposed based on the fixed stress split algorithm is unconditionally stable in the iterative procedure for coupling the two subsystems. This continuum problem is discretized by the Galerkin method coupled with fixed point algorithms to handle non-linearities present in the equation of state of the gas and in the coupling between the two subsystems. Numerical simulations are performed to illustrate the influence of geomechanical effects upon gas production. Comparisons between the well known one and two-way formulations are also presented. / O presente trabalho objetiva a construção de um novo modelo de acoplamento hidro-mecânico em reservatórios de gás. O aspecto inovador do modelo proposto reside na natureza sequencial do acoplamento, caracterizado pela decomposição do operador acoplado, levando ao surgimento de termos de fonte entre os subsistemas hidrodinâmica e geomecânico. Quando comparado com a formulação completamente acoplada, onde os dois sistemas são resolvidos simultaneamente, a formulação proposta permite a adoção de diferentes passos de tempo, extensão natural para descrever rochas adjacentes ao reservatório produtivo e não sofre de carência de estabilidade nas zonas impermeáveis da formação geológica. A formulação proposta, baseada no algoritmo “fixed stress split”, apresenta a propriedade de ser incondicionalmente estável no processo iterativo adotado na resolução dos dois subsistemas. A formulação sequencial é discretizada pelo método de Galerkin aliada com algoritmo de ponto fixo para tratar as não-linearidades presentes na equação de estado do gás e no acoplamento entre os dois subsistemas. Simulações numéricas são realizadas para ilustrar os efeitos geomecânicos sobre a produção de gás em reservatórios não convencionais de gás em folhelho. Comparações entre as formulações em uma-via e duas-vias, comumente discutidas em geomecânica de reservatórios, são apresentadas.