Orientador: Luiz Felipe Mendes de Moura / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-18T04:18:01Z (GMT). No. of bitstreams: 1 Barros_TiagoRodriguesde_M.pdf: 8532346 bytes, checksum: 17a941d128ad1bcad0846f1722bc6270 (MD5) Previous issue date: 2011 / Resumo: Este trabalho tem como objetivo a simulação numérica de um sensor de tomografia capacitiva elétrica, em função da permissividade elétrica relativa das fases presentes dentro da tubulação, com a finalidade de determinar a melhor geometria do sensor para a geração de imagem de escoamentos numa mistura bifásica ar-água, levando em consideração fluidos com efeito da condutividade nula. A simulação numérica do sensor de tomografia capacitiva é de crucial importância para o desenvolvimento de um tomógrafo capacitivo usado em aplicações específicas, como é o caso do monitoramento de escoamentos bifásicos. A tomografia capacitiva elétrica é uma tecnologia recente que vem se desenvolvendo desde o início de 1980, quando começou a ser utilizada para análise de processos industriais, principalmente em escoamentos multifásicos. Ela é utilizada para gerar uma imagem do interior da tubulação de acordo com a permissividade relativa das fases ali presentes, sendo atualmente o tipo de tomografia de processos mais utilizada. Após a determinação de algumas premissas do projeto como, o diâmetro da tubulação que foi simulada na horizontal, o comprimento dos eletrodos que seriam montados do lado externo da tubulação, as simulações bidimensionais foram realizadas para se obter o melhor espaçamento entre os doze eletrodos do sensor e a distância ideal da blindagem externa. Com as simulações tridimensionais, foi investigada a necessidade de utilização dos eletrodos de guarda, assim como, foi realizada a simulação da geometria final do sensor numa mudança dos componentes de ar para água no interior da tubulação. Os resultados obtidos neste trabalho permitiram determinar a geometria mais adequada do sensor para a situação proposta, assim como, obter o valor das capacitâncias para diferentes condições de escoamento. Os resultados das simulações tridimensionais apontaram as principais limitações de uma análise bidimensional / Abstract: This study was aimed to realize numerical simulations of a capacitive electrical tomography sensor, depending on the relative permittivity of the phases inside the pipe, in order to determine the best geometry of the sensor to generate the image of the flow in the air-water two-phase flow, taking into account the effect of conductivity zero in the fluids. Numerical simulation of the ECT sensor is of crucial importance to develop a capacitive tomograph used in specific applications such as monitoring biphasic flow. Electrical capacitance tomography is a new technology that has been developed since early 1980, when it began to be used in industrial processes, mainly in multiphase flows. It is used to generate an image from inside the pipe according to the relative permittivity of the phases present there, and is currently the type of process tomography procedures most commonly used. After the determination of some assumptions of the project as the diameter of the pipe that was simulated in the horizontal, the length of the electrodes that must be assembled outside the pipe, the two-dimensional simulations were performed to obtain the best spacing between the twelve electrodes of the sensor and the ideal distance of the outer shield. With the three-dimensional simulations, we investigated the necessity of use guard electrodes, as well as, it was realized the simulation of the final geometry of the sensor components in a change of air to water inside the pipe. The results of this study allow us to determine the most suitable sensor geometry for the proposed situation, as well as obtaining the value of capacitance for different flow conditions. The results of three-dimensional simulations showed the main limitations of a two dimensional analysis / Mestrado / Termica e Fluidos / Mestre em Engenharia Mecânica

Orientador: Samuel Rocha de Oliveira / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-08T22:23:20Z (GMT). No. of bitstreams: 1 D'Afonseca_LuisAlberto_D.pdf: 4257675 bytes, checksum: 54debc66eff41b6c8b450adbcfc3bab6 (MD5) Previous issue date: 2007 / Resumo: Nesse trabalho delineamos a teoria clássica para o campo de Einstein-Yang-Mills e elaboramos um conjunto particular de equações para obtermos soluções numéricas. Estudamos dois casos com simetria espaço-temporal: Simetria esférica com campo auto-gravitante e simetria axial no espaço-tempo de Minkowski. Utilizamos métodos numéricos das linhas para fazer a evolução temporal dos campos discretizados. No caso com simetria esférica, os campos são discretizados por diferenças finitas e no caso da simetria axial comparamos as discretizações por métodos Pseudo-Espectrais e por diferenças finitas. Para evolução temporal um método auto-adaptativo de Runge-Kutta é empregado. Na simulação dos campos de Yang-Mills auto-gravitantes com simetria esférica mostramos a evolução da implosão e explosão de uma casca energética sem formação de buraco negro nem de corpo estável. No caso com simetria axial além da implosão e explosão de pulsos de cores diferentes dos campos de Yang-Mills, geramos também várias soluções dinâmicas em que vemos o transiente do intercâmbio de energia entre essas cores / Abstract: In this work we outline the classic theory of Einstein-Yang-Mills fields and work out a set of particular equations suited for numerical simulations. We consider two special cases with space-time symmetries: self-gravitating spherical symmetric and axially symmetric field on a Minkowski space-time. We use the numerical method of lines for time evolution of discretized fields. On the spherical symmetric case, the fields are discretized by finite differences and on the axial symmetric case we compare the field discretization by the pseudo-spectral method and finite differences method. For time stepping we use a self-adaptive Runge-Kutta method. In the simulation of Yang-Mills self-gravitating fields with spherical symmetry we show the evolution of implosion and explosion of a energetic shell without black hole or stable body formation. In the axial symmetric case besides implosion and explosion of pulses of different colours of Yang-Mills fields, we also generate several dynamic solutions that display the transient of the energy exchange among these colours / Doutorado / Fisica-Matematica / Doutor em Matemática Aplicada

PhD (Applied Mathematics) / Department of Mathematics and Applied Mathematics / The work presented in this thesis is the application of the recently introduced numerical techniques, namely the spectral quasi-linearization method (SQLM) and the bivariate spectral quasi-linearization method (BSQLM), in solving problems arising in fluid flow. Firstly, we use the SQLM to solve the highly non-linear one dimensional Bratu problem. The results obtained are compared with exact solution and previously published results using the B-spline method, Picard’s Green’s Embedded Method and the iterative finite difference method. The results obtained show that the SQLM is highly accurate and computationally efficient. Secondly, we use the bivariate spectral quasi-linearization method to solve the two dimensional Bratu problem. Since the exact solution of the two-dimensional Bratu problem is unknown, the results obtained are compared with those previously published results using the finite difference method and the weighted residual method. Thirdly, we use the BSQLM to study numerically the boundary layer flow of a third grade non-Newtonian fluid past a vertical porous plate. We use the Jeffrey fluid as a typical fluid which shows non-Newtonian characteristics. Similarity transformations are used to transform a system of coupled nonlinear partial differential equations into a system of linear partial differential equations which are then solved using BSQLM. The influence of some thermo-physical parameters namely, the ratio relaxation to retardation times parameter, Prandtl number, Schmidt number and the Deborah number is investigated. Also investigated is the influence of the ratio of relaxation to retardation times, Schmidt number and the Prandtl number on the skin friction, heat transfer rate and the mass transfer rate. The results obtained show that increasing the Schmidt number decelerates the fluid flow, reduces the skin friction, heat and mass transfer rates and strongly depresses the fluid concentration whilst the temperature is increased. The fluid velocity, the skin friction, heat and mass transfer rates are increased with increasing values of the relaxation to retardation parameter whilst the fluid temperature and concentration are reduced. Using the the solution based errors, it was shown that the BSQLM converges to the solution only after 5 iterations. The residual error infinity norms showed that BSQLM is very accurate by giving an error of order of 10−4 within 5 iterations. Lastly we propose a model of the non-Newtonian fluid flow past a vertical porous plate in the presence of thermal radiation and chemical reaction. Similarity transformations are used to transform a system of coupled nonlinear partial differential equations into a system of linear partial differential equations. The BSQLM is used to solve the system of equations. We investigate the influence of the ratio of relaxation to retardation parameter, Schmidt number, Prandtl number, thermal radiation parameter, chemical reaction iv parameter, Nusselt number, Sherwood number, local skin fiction coefficient on the fluid concentration, fluid temperature as well as the fluid velocity. From the study, it is noted that the fluid flow velocity, the local skin friction coefficient, heat and mass transfer rate are increased with increasing ratio of relaxation to retardation times parameter whilst the fluid concentration is depressed. Increasing the Prandtl number causes a reduction in the velocity and temperature of the fluid whilst the concentration is increased. Also, the local skin friction coefficient and the mass transfer rates are depressed with an increase in the Prandtl number. An increase in the chemical reaction parameter decreases the fluid velocity, temperature and the concentration. Increasing the thermal radiation parameter has an effect of decelerating the fluid flow whilst the temperature and the concentration are slightly enhanced. The infinity norms were used to show that the method converges fast. The method converges to the solution within 5 iterations. The accuracy of the solution is checked using residual errors of the functions f, and . The errors show that the BSQLM is accurate, giving errors of less than 10−4, 10−7 and 10−8 for f, and , respectively, within 5 iterations. / NRF

High Mach number, low-Reynolds number (high-altitude) reentry flowfield predictions are an important problem area in computational aerothermodynamics. Available numerical tools for handling such flows are very few and significantly limited in their applicability. A new implicit fully-iterative Parabolized Navier-Stokes (PNS) scheme is developed to accurately predict such low-Reynolds number flows. In this new approach the differential equations governing the conservation of mass, momentum and energy, and the algebraic equation of state for a perfect gas are solved simultaneously in a coupled manner. The idea is presented that by treating the governing equations in this manner (rather than eliminating the pressure terms in the governing equations by using appropriate differentiated forms of the equation of state) it may be possible to have an unconditionally time-like numerical scheme. The stability of a simplified version of this new PNS scheme is also studied, and it is demonstrated that these simplified equations are unconditionally time-like in the subsonic as well as the supersonic flow regions. A pseudo-time integration approach is used in addition to a new second-order accurate fully-implicit smoothing, to improve the efficiency of the solution algorithm. The new PNS scheme is used to predict the flowfield around a seven-deg sphere-cone vehicle under high- and low-Reynolds number conditions. Two test case, Case A and Case B, are chosen such that Case A has a large freestream Reynolds number (2.92x10⁵), whereas Case B has a freestream Reynolds number of 1.72x10³, which is smaller than the usual limit of applicability of the non-iterative PNS schemes (Re~10⁴ or larger). Comparisons are made with other available numerical schemes, and the results substantiate the stability, accuracy and efficiency claims of the new Parabolized Navier-Stokes scheme. / Ph. D.

In this thesis I study a variety of two-dimensional turbulent systems using a mixed analytical, phenomenological and numerical approach. The systems under consideration are governed by the two-dimensional Navier-Stokes (2DNS), surface quasigeostrophic (SQG), alpha-turbulence and magnetohydrodynamic (MHD) equations. The main analytical focus is on the number of degrees of freedom of a given system, defined as the least value $N$ such that all $n$-dimensional ($n$ ≥ $N$) volume elements along a given trajectory contract during the course of evolution. By equating $N$ with the number of active Fourier-space modes, that is the number of modes in the inertial range, and assuming power-law spectra in the inertial range, the scaling of $N$ with the Reynolds number $Re$ allows bounds to be put on the exponent of the spectrum. This allows the recovery of analytic results that have until now only been derived phenomenologically, such as the $k$[superscript(-5/3)] energy spectrum in the energy inertial range in SQG turbulence. Phenomenologically I study the modal interactions that control the transfer of various conserved quantities. Among other results I show that in MHD dynamo triads (those converting kinetic into magnetic energy) are associated with a direct magnetic energy flux while anti-dynamo triads (those converting magnetic into kinetic energy) are associated with an inverse magnetic energy flux. As both dynamo and anti-dynamo interacting triads are integral parts of the direct energy transfer, the anti-dynamo inverse flux partially neutralises the dynamo direct flux, arguably resulting in relatively weak direct energy transfer and giving rise to dynamo saturation. These theoretical results are backed up by high resolution numerical simulations, out of which have emerged some new results such as the suggestion that for alpha turbulence the generalised enstrophy spectra are not closely approximated by those that have been derived phenomenologically, and new theories may be needed in order to explain them.

La première partie de cette thèse traite du développement du code de simulation numérique directe YWC, principalement du développement des conditions aux limites. En effet, une forte contribution scientifique a été apportée aux conditions aux limites appelées "Three dimensional Navier-Stokes characteristic boundary condtions" (3D-NSCBC). Premièrement, la formulation de ces conditions aux arêtes et coins a été complétée, ensuite une extension de la formulation a été proposée pour supprimer les déformations observées en sortie dans le cas d'écoulements non-perpendiculaires à la frontière. <p>De plus, ces conditions ont été étendues au cas des gaz réels et une nouvelle définition du facteur de relaxation pour la pression a été proposée. Ce nouveau facteur de relaxation permet de supprimer les déformations observées en sortie pour des écoulements transcritiques. <p>Les résultats obtenus avec le code YWC ont ensuite été utilisés dans la seconde partie de la thèse pour développer une nouvelle méthode de tabulation basée sur l'analyse en composantes principales. Par rapport aux méthodes existante telles que FPI ou SLFM, la technique proposée, permet une identification automatique des variables à transporter et n'est, de plus, pas lié à un régime de combustion spécifique. Cette technique a permis d'effectuer des calculs d'interaction flamme-vortex en ne transportant que 5 espèces à la place des 9 requises pour le calcul en chimie détaillée complète, sans pour autant perdre en précision. <p>Finalement, dans le but de réduire encore le nombre d'espèces transportées, les techniques T-BAKED et HT-BAKED PCA ont été introduites. En utilisant une pondération des points sous-représentés, ces deux techniques permettent d'augmenter la précision de l'analyse par composantes principales dans le cadre des phénomènes de combustion.<p> / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

This thesis is concerned with the development of numerical techniques to simulate compressible multi-phase flows, in particular a high-accuracy numerical approach with mesh adaptivity. The Discontinuous Galerkin (DG) method was chosen as the framework for this work for being characterized for its high-order of accuracy -thus low numerical diffusion- and being compatible with mesh adaptivity due to its locality. A DG solver named DiGGIT (Discontinuous Galerkin at the Georgia Institute of Technology) has been developed and several aspects of the method have been studied. The Local Discontinuous Galerkin (LDG) method -an extension of DG for equations with high-order derivatives- was extended to solve multiphase flows using Diffused Interface Methods (DIM). This multi-phase model includes the convection of the volume fraction, which is treated as a Hamilton-Jacobi equation. This is the first study, to the author's knowledge, in which the volume fraction of a DIM is solved using the DG and the LDG methods. The formulation is independent of the Equation of State (EOS) and it can differ for each phase. This allows for a more accurate representation of the different fluids by using cubic EOSs, like the Peng-Robinson and the van der Waals models. Surface tension is modeled with a new numerical technique appropriate for LDG. Spurious oscillations due to surface tension are common to all the capturing schemes, and this new approach presents oscillations comparable in magnitude to the most common schemes. The moment limiter (ML) was generalized for non-uniform grids with hanging nodes that result from adaptive mesh refinement (AMR). The effect of characteristic, primitive, or conservative decomposition in the limiting stage was studied. The characteristic option cannot be used with the ML in multi-dimensions. In general, primitive variable decomposition is a better option than with conservative variables, particularly for multiphase flows, since the former type of decomposition reduces the numerical oscillations at material discontinuities. An additional limiting technique was introduced for DIM to preserve positivity while minimizing the numerical diffusion, which is especially important at the interface. The accuracy-preserving total variation diminishing (AP-TVD) marker for ``troubled-cell' detection, which uses an averaged-derivative basis, was modified to use the Legendre polynomial basis. Given that the latest basis is generally used for DG, the new approach avoids transforming to the averaged-derivative basis, what results in a more efficient technique. Furthermore, a new error estimator was proposed to determine where to refine or coarsen the grid. This estimator was compared against other estimator used in the literature and it showed an improved performance. In order to provide equal order of accuracy in time as in space, the commonly used 3rd-order TVD Runge-Kutta (RK) scheme in the DG method was replaced in some cases by the Spectral Deferred Correction (SDC) technique. High orders in time were shown to only be required when the error in time is significant. For instance, convection-dominated compressible flows require for stability a time step much smaller than is required for accuracy, so in such cases 3rd-order TVD RK resulted to be more efficient than SDC with higher orders. All these new capabilities were included in DiGGIT and have provided a generalized approach capable of solving sub- and super-critical flows at sub- and super-sonic speeds, using a high-order scheme in space and time, and with AMR. Canonical test cases are presented to verify and validate the formulation in one, two, and three dimensions. Finally, the solver is applied to practical applications. Shock-bubble interaction is studied and the effect of the different thermodynamic closures is assessed. Interaction between single-drops and a wall is simulated. Sticking and the onset of splashing are observed. In addition, the solver is used to simulate turbulent flows, where the high-order of accuracy clearly shows its benefits. Finally, the methodology is challenged with the simulation of a liquid jet in cross flow.

M. Tech. : Mathematical Technology. / Attempts will be made to extend the elementary quarter-mass models (for instance Gillepse, 1992, [5]; Kiecke & Nielsen, 2000, [6] and Singiresu, 2004, [7]) of a motor vehicle suspension system to include the radial vibrations of a rubber tyre in the model. Tangential vibrations of the tyre surface were investigated by Bekker (2009, [8]) and the possible incorporation of such vibrations into a suspension model invites the possibility of future study.

This thesis is devoted to solving the inverse source problem arising in image reconstruction problems. In general, the solution is non-unique and the problem is severely ill-posed. Therefore, small perturbations, such as the noise in the data, and the modeling error in the forward problem, will cause huge errors in the computations. In practice, the most widely used method to tackle the problem is based on Tikhonov-type regularizations, which minimizes a cost function combining a regularization term and a data fitting term. However, because the two tasks, namely regularization and data fitting, are coupled together in Tikhonov regularization, they are difficult to solve. It happens even if each task can be efficiently solved when they are separate. We propose a method to overcome the major difficulties, namely the non-uniqueness of the solution and noisy data fitting, separately. First we find a particular solution called the orthogonal solution that satisfies the data fitting term. Then we add to it a correction function in the kernel space so that the final solution fulfills the regularization and other physical requirements. The key idea is that the correction function in the kernel has no impact to the data fitting, and the regularization is imposed in a smaller space. Moreover, there is no parameter needed to balance the data fitting and regularization terms. As a case study, we apply the proposed method to Fluorescence Tomography (FT), an emerging imaging technique well known for its ill-posedness and low image resolution in existing reconstruction techniques. We demonstrate by theory and examples that the proposed algorithm can drastically improve the computation speed and the image resolution over existing methods.

CAPES / A resolução de equações polinomiais com coeficientes racionais consiste em parte significativa da história do desenvolvimento da álgebra. O problema era encontrar fórmulas que expressassem uma raiz por meio de operações aritméticas efetuadas sobre a equação original, isto é, determinar a resolubilidade por radicais da equação. O trabalho de vários matemáticos culminou, no século XVI, com a obtenção das fórmulas para a resolução de equações polinomiais de grau menor ou igual a 4. Três séculos depois, Niels Abel mostrou que não é possível obter uma fórmula para a equação geral de grau 5. Finalmente, Evariste Galois resolveu completamente o problema estudando o grupo de permutação das raízes e estabelecendo as condições exatas para a resolubilidade de uma equação polinomial. Neste trabalho apresentamos um breve histórico da obtenção de fórmulas para as raízes das equações de grau menor ou igual a 4 e a essência da matemática envolvida no estudo da resolubilidade por radiciais de equações polinomiais de grau maior ou igual a 5. / The solvability by radicals of polynomial equations with rational coefficients is an important part of the history of algebra. The problem was to express a root by means of basic arithmetic operations and radicals. Formulas to solve polynomial equations of degree lower than or equal to 4 were obtained in XVIth century. About three centuries later, Niels Abel showed that it is not possible to find a formula for the general equation of degree 5. Finally, Evariste Galois solved the problem by studying the permutations groups, establishing the exact conditions for the solvability of a polynomial equation. In this work we present a brief history of the classic formulas for the roots of equations with degree lower or equal to 4. Then we study solvability by radicals of polynomial equations of degree higher than or equal to 5.