Geothermal energy is an important source of clean and renewable energy. This project deals with the study of deep geothermal power plants for the generation of electricity. The design involves the extraction of heat from the Earth and its conversion into electricity. This is performed by allowing fluid deep into the Earth where it gets heated due to the surrounding rock. The fluid gets vaporized and returns to the surface in a heat pipe. Finally, the energy of the fluid is converted into electricity using turbine or organic rankine cycle (ORC). The main feature of the system is the employment of side channels to increase the amount of thermal energy extracted. A finite difference computer model is developed to solve the heat transport equation. The numerical model was employed to evaluate the performance of the design. The major goal was to optimize the output power as a function of parameters such as thermal diffusivity of the rock, depth of the main well, number and length of lateral channels. The sustainable lifetime of the system for a target output power of 2 MW has been calculated for deep geothermal systems with drilling depths of 8000 and 10000 meters, and a financial analysis has been performed to evaluate the economic feasibility of the system for a practical range of geothermal parameters. Results show promising an outlook for deep geothermal systems for practical applications.

This is a book on numerical methods for singular perturbation problems - in particular stationary convection-dominated convection-diffusion problems. More precisely it is devoted to the construction and analysis of layer-adapted meshes underlying these numerical methods. An early important contribution towards the optimization of numerical methods by means of special meshes was made by N.S. Bakhvalov in 1969. His paper spawned a lively discussion in the literature with a number of further meshes being proposed and applied to various singular perturbation problems. However, in the mid 1980s this development stalled, but was enlivend again by G.I. Shishkin's proposal of piecewise- equidistant meshes in the early 1990s. Because of their very simple structure they are often much easier to analyse than other meshes, although they give numerical approximations that are inferior to solutions on competing meshes. Shishkin meshes for numerous problems and numerical methods have been studied since and they are still very much in vogue. With this contribution we try to counter this development and lay the emphasis on more general meshes that - apart from performing better than piecewise-uniform meshes - provide a much deeper insight in the course of their analysis. In this monograph a classification and a survey are given of layer-adapted meshes for convection-diffusion problems. It tries to give a comprehensive review of state-of-the art techniques used in the convergence analysis for various numerical methods: finite differences, finite elements and finite volumes. While for finite difference schemes applied to one-dimensional problems a rather complete convergence theory for arbitrary meshes is developed, the theory is more fragmentary for other methods and problems and still requires the restriction to certain classes of meshes.

First we consider implicit finite difference schemes on uniform grids in time and space for second order linear stochastic partial differential equations of parabolic type. Under sufficient regularity conditions, we prove the existence of an appropriate asymptotic expansion in powers of the the spatial mesh and hence we apply Richardson's method to accelerate the convergence with respect to the spatial approximation to an arbitrarily high order. Then we extend these results to equations where the parabolicity condition is allowed to degenerate. Finally, we consider implicit finite difference approximations for deterministic linear second order partial differential equations of parabolic type and give sufficient conditions under which the approximations in space and time can be simultaneously accelerated to an arbitrarily high order.

Le but de ce travail était la modélisation mécanique et thermique du laminage asymétrique. Celle-ci a été effectuée à l'aide de diverses méthodes. Deux approches, l'une analytique et l'autre semi-analytique, ont été utilisées pour la modélisation mécanique et deux autres, celles des différences finies et des éléments finis, pour la modélisation thermique. La première approche est celle des champs uniformes ; on a développé un modèle simple qui peut donner des ordres de grandeurs des différents paramètres du procédé. Une deuxième méthode plus complète mais plus complexe se base sur un champ de vitesse déduit d'une estimation parabolique de la forme des trajectoires. L’avantage de ce modèle est qu’il est capable de prévoir des grandeurs locales. Enfin la méthode des éléments finis a été aussi utilisée pour la modélisation mécanique. Dans un deuxième temps, l’aspect thermique du laminage asymétrique a été étudié. Pour la modélisation du procédé, nous avons alors adopté deux méthodes numériques, les différences finies et les éléments finis, du fait de la complexité de celui-ci. Le modèle thermique développé par différences finies a été ensuite intégré dans notre modèle mécanique (méthode des trajectoires). Celui-ci a donc pu être étendu pour pouvoir utiliser des lois d’écoulement qui dépendent de la température et donc pouvoir simuler le laminage asymétrique à chaud. Les prédictions du champ de température ont été confrontées aux résultats de calculs par éléments finis obtenus avec le code Abaqus. Finalement, une étude simple du développement de la texture cristallographique au cours du laminage a été réalisée. / The aim of this work was to propose a mechanical and thermal modelling of asymmetric rolling. This was achieved using various methods. Two approaches, the first one analytical and the second semi-analytical, were employed for mechanical modeling. Two others methods, the finite difference and finite element methods, were used for thermal modeling. The first analytical model is an upper bound method based on a uniform strain field; a simple model was developed that can give orders of magnitude of the various process parameters. The second model uses a more refined analytical velocity field based on the classical parabolic estimation of the material flow lines in rolling. The advantage of this model is its ability to provide local quantities. Finally, the finite element method was also used for mechanical modeling.The thermal aspects of asymmetric rolling were investigated in turn by two methods. For modeling the process, we adopted two numerical approaches, the finite difference and finite element methods, because of the complexity of the latter. The thermal model developed by finite differences was integrated into our mechanical model (flow line model). It was then extended to investigate asymmetrical hot rolling. The predictions of the temperature field were compared with results from finite element calculations obtained with the Abaqus code. Finally, a simple study of crystallographic texture development was achieved.

Ce travail est motivé par une demande croissante d'informations quantitatives sur l'évolution du littoral. Nous avons étudié deux approches pour l'analyse de la dynamique sédimentaire. Les deux techniques aboutissent à la résolution de modèles non-locaux pour le fond. L'étude mathématique a porté sur l'analyse de l'existence et l'unicité de perturbations autour des ondes progressives solutions du modèle de Fowler. Nous avons montré que les solutions constantes de l'équation de Fowler sont instables. Pour la simulation numérique de ce modèle, nous avons dans un premier temps considéré des schémas aux différences finies explicites pour lesquels nous avons obtenu des critères de stabilité numérique. Dans un second temps, nous avons utilisé une approche par splitting de sorte à pouvoir résoudre la convection, puis la diffusion et l'anti-diffusion fractionnaire de façon exacte. Ensuite, il est apparu que nous pouvions utiliser les principes de minimisation pour décrire l'évolution d'un lit érodable sous l'action de l'eau où le fond est considéré comme une structure déformable de faible rigidité s'adaptant en minimisant une certaine fonctionnelle d'énergie. Il est intéressant de constater que cette seconde approche peut être liée à la première car elle débouche aussi sur une équation de type Exner avec un terme non-local. En nous inspirant du modèle morphodynamique non-local de Fowler, nous concluons cette thèse par une application exotique au traitement de signal où nous proposons une nouvelle méthode de filtrage. / This work is motivated by a growing demand for quantitative information on the evolution of the coastline.We have studied two approaches for the analysis of sand morphodynamics.Both techniques lead to the resolution of nonlocal models for the seabottom.The mathematical study focused on the analysis of the existence and uniqueness of perturbations around the travelling-waves solutions of the Fowler model. We have shown that constant solutions of Fowler's equation are unstable.For the numerical simulation of this model, we have first considered explicit finite difference schemes for which we got numerical stability criteria. We have next used an approach by splitting method in order to solve first the convection, then the diffusion/fractional anti-diffusion exactly. We have also used minimization principles to describe the evolution of an erodible bed sheared by a fluid flow where the seabed is considered as a deformable structure with low stiffness whichadapts itself by minimizing a certain energy functional. It is interesting to note that this secondapproach can be linked to the first one because it also leads to a new Exner equation with a nonlocal term for the flux. Inspired by Fowler's morphodynamical model, we conclude this dissertation with an unexpected application to signal processing.

The aim of this study is to analysis, investigate and find out the solutions for the problems associated with the implementations of antennas RFID Reader and Tag for various applications. In particular, the efficiency of the RFID reader antenna and the detection range of the RFID tag antenna, subject to a small and compact antenna's design configuration have been studied. The present work has been addressed directly to reduce the cost, size and increase the detection range and communication reliability of the RFID framework antennas. Furthermore, the modelling concept of RFID passive tags mounted on various materials including the novel design of RFID reader antenna using Genetic Algorithm (GA) are considered and discussed to maintain reliable and efficient antenna radiation performances. The main benefit of applying GA is to provide fast, accurate and reliable solutions of antenna's structure. Therefore, the GA has been successfully employed to design examples: meander-line, two linear cross elements and compact Helical- Spiral antennas. In addition, a hybrid method to model the human body interaction with RFID tag antenna operating at 900MHz has been studied. The near field distribution and the radiation pattern together with the statistical distribution of the radiation efficiency and the absorbed power in terms of cumulative distribution functions for different orientation and location of RFID's tag antenna on the human body have been demonstrated. Several tag antennas wi th symmetrical and unsymmetrical structure configurations operating in the European UHF band 850-950 MHz have been fabricated and tested. . The measured and simulated results have been found to be in a good agreement with reasonable impedance matching to the typical input impedance of an RFID integrated circuit chip and nominal power gain and radiation patterns.

Cette thèse vise à étudier le couplage entre méthodes de Galerkine discontinue (DG) et méthodes de différences finies (DF) en maillages hybrides non structuré / cartésien, en vue d'applications en aéroacoustique numérique. L'idée d'une telle approche consiste à pouvoir tirer profit localement des avantages respectifs de ces méthodes, soit, en d'autres termes, à pouvoir prendre en compte la présence de géométries complexes par une méthode DG en maillage non structuré, et les zones qui en sont suffisamment éloignées par une méthode DF en maillage cartésien, moins coûteuse. Plus précisément, il s'agit de concevoir un algorithme d'hybridation de ces deux types de schémas pour l'approximation des équations d'Euler linéarisées, puis d'évaluer avec attention le comportement numérique des solutions qui en sont issues. De par le fait qu'aucun résultat théorique ne semble actuellement atteignable dans un cas général, cette étude est principalement fondée sur une démarche d'expérimentation numérique. Par ailleurs, l'intérêt d'une telle hybridation est illustré par son application à un calcul de propagation acoustique dans un cas réaliste / This thesis aims at studying coupling techniques between Discontinuous Galerkin (DG) and finite difference (FD) schemes in a non-structured / Cartesian hybrid-mesh context,in the framework of Aeroacoustics computations. The idea behind such an approach is the possibility to locally take advantage of the qualities of each method. In other words, the goal is to be able to deal with complex geometries using a DG scheme on a non-structured mesh in their neighborhood, while solving the rest of the domain using a FD scheme on a cartesian grid, in order to alleviate the needs in computational resources. More precisely, this work aims at designing an hybridization algorithm between these two types of numerical schemes, in the framework of the approximation of the solutions of the Linearized Euler Equations. Then, the numerical behaviour of hybrid solutions is cautiously evaluated. Due to the fact that no theoretical result seems achievable at the present time, this study is mainly based on numerical experiments. What's more, the interest of such an hybridization is illustrated by its application to an acoustic propagation computation in a realistic case

Aplicações industriais envolvendo escoamentos multifásicos são inúmeras, sendo que, o aprimoramento de alguns desses processos pode resultar em um grande salto tecnológico com significativo impacto econômico. O estudo numérico dessas aplicações é imprescindível, pois fornece informações precisas e mais detalhadas do que a realização de testes experimentais. Um grande desafio é o estudo numérico de escoamentos viscoelásticos multifásicos envolvendo altas taxa de elasticidade, devido às instabilidades causadas por altas tensões elásticas, grandes deformações, e até mudanças topológicas na interface. Assim, a investigação numérica desse tipo de problema exige uma formulação precisa e robusta. No presente trabalho, um novo resolvedor de escoamentos bifásicos envolvendo fluidos complexos é apresentado, com particular interesse em escoamentos com altas taxas de elasticidade. A formulação proposta é baseada no método Volume-of-fluid (VOF) para representação da interface e no algoritmo Continuum Surface Force (CSF) para o balanço de forças na interface. A curvatura e advecção da interface são calculados via métodos geométricos para garantir a precisão dos resultados. Métodos de estabilização são utilizados quando números críticos de Weissenberg (Wi) são encontrados, devido ao famoso problema do alto número de Weissenberg (HWNP). O método da projeção, combinado com um método implícito para solução da equação da quantidade de movimento, são discretizados por um esquema de diferenças finitas em uma malha deslocada. Problemas de benchmarks foram resolvidos para acessar a precisão numérica da formulação em diferentes níveis de complexidade física, tal como representação e advecção da interface, influência das forças interfaciais, e características reológicas do fluido. A fim de demonstrar a capacidade do novo resolvedor, dois problemas bifásicos transientes, envolvendo fluidos viscoelásticos, foram resolvidos: o efeito de Weissenberg e o reômetro extensional (CaBER). O efeito de Weissenberg ou rod-climbing effect consiste em um bastão que gira dentro de um recipiente com fluido viscoelástico e, devido às forças elásticas, o fluido escala o bastão. Os resultados foram comparados com dados teóricos, numéricos e experimentais, encontrados na literatura para pequenas velocidades angulares. Além disso, resultados obtidos com altas velocidades angulares (alta elasticidade) são apresentados com o modelo Oldroyd-B, em que escaladas muito elevadas foram observadas. Valores críticos da velocidade angular foram identificados, e para valores acima foi observada a ocorrência de instabilidades elásticas, originadas pela combinação de tensões elásticas, curvatura interfacial, e escoamentos secundários. Até onde sabemos, numericamente, essas instabilidades nunca foram capturadas antes. O CaBER consiste no comportamento e colapso de um filamento de fluido viscoelástico, formado entre duas placas paralelas devido às forças capilares. Esse experimento envolve consideráveis dificuldades, dentre as quais podemos destacar a grande influência das forças capilares e a diferença de escalas de comprimento no escoamento. Em grande parte dos resultados encontrados na literatura, o CaBER é resolvido por modelos simplificados em uma dimensão. Resultados obtidos foram comparados com tais resultados da literatura e com soluções teóricas, apresentando admirável precisão. / Industrial applications involving multiphase flow are numerous. The improvement of some of these processes can result in a major technological leap with significant economic impact. The numerical study of these applications is essential because it provides accurate and more detailed information than conducting experiments. A challenge is the numerical study of high viscoelastic multiphase flows due to instabilities caused by the high elastic tension, large deformations and even topological changes in the interface. Thus the numerical investigation of this problem requires a robust formulation. In this study a new two-phase solver involving complex fluids is presented, with particular interest in the solution of highly elastic flows of viscoelastic fluids. The proposed formulation is based on the volume-of-fluid method (VOF) to interface representation and continuum surface force algorithm (CSF) for the balance of forces in the interface. The curvature and interface advection are calculated via geometric methods to ensure the accuracy of the results. Stabilization methods are used when critical Weissenberg numbers are found due to the famous high Weissenberg number problem (HWNP). The projection method combined with an implicit method for the solution of the momentum equation are discretized by a finite difference scheme in a staggered grid. Benchmark test problems are solved in order to access the numerical accuracy of different levels of physical complexities, such as the dynamic of the interface and the role of fluid rheology. In order to demonstrate the ability of the new resolver, two-phase transient problems involving viscoelastic fluids have been solved, theWeissenberg effect problem and the extensional rheometer (CaBER). The Weissenberg effect problem or rod-climbing effect consists of a rod that spins inside of a container with viscoelastic fluid and due to the elastic forces the fluid climbs the rod. The results were compared with numerical and experimental data from the literature for small angular velocities. Moreover results obtained for high angular velocities are presented using the Oldroyd-B model, which showed high climbing heights. Critical values of the angular speed have been identified. For values above a critical level were observed the occurrence of elastic instabilities caused by the combination of elastic tension, interfacial curvature and secondary flows. To our knowledge, numerically these instabilities were never captured before. The CaBER consists of the behavior and collapse of a viscoelastic fluid filament formed between two parallel plates due to capillary forces. This experiment involves considerable difficulties, among which we can highlight the great influence of the capillary forces and the difference of the length scales in the flow. In much of the results found in the literature, the CaBER is solved by simplified models. The results were compared with results reported in the literature and theoretical solutions, which showed remarkable accuracy.

O presente trabalho apresenta um método de interação fluido estrutura chamado de fronteira virtual para modelagem de escoamentos sobre geometrias complexas. A principal característica do método é que a condição de contorno interna da superfície do corpo imerso é obtida usando uma função que calcula a força de campo das equações de momentum. Este método de cálculo da força de campo é conhecido como método direto. A principal vantagem do método da fronteira virtual é que se trabalha com duas malhas, uma cartesiana (também conhecida como euleriana) para o fluido e outra curvilínea (também conhecida como malha lagrangiana) para o objeto imerso. Como estas malhas são independentes uma da outra, os algoritmos de geração das malhas são simples em comparação com outros métodos de geração de malha, nos quais a esta precisa se adaptar ao corpo que se quer analisar. Nos métodos de body fitted, algoritmos complexos com custo computacional muito elevado são necessários para se trabalhar com geometrias complexas. Neste trabalho, o método de fronteira virtual é desenvolvido para trabalhar escoamentos compressíveis não viscosos em duas dimensões sobre geometrias complexas, e testado sobre um cilindro de seção circular e sobre uma série de aerofólios NACA da série 4. O regime de principal interesse é o regime transônico, em particular para velocidades abaixo da velocidade do som (Mach entre 0,8 e 1). No entanto, resultados para outros regimes de escoamento (subsônico incompressível, subsônico compressível, transônico e supersônico) também são mostrados. / This work presents a fluid-structure interaction method, known as virtual boundary method, developed for flow modeling, over complex geometries. The main characteristic of the method is that, the internal boundary condition at the surface are created using a function, that compute the body force from the momentum equations. This method is known as direct method. The virtual boundary method main advantage is the easy and quick mesh generation. Due the use two different grids, a Cartesian grid for the fluid and a curvilinear grid for the body that interact with the fluid. As these two grids are independent one of other, the grid generation algorithms are easier compared with other methods on CFD as the body fitted. Where the grid has to be adapted to the body of interest. The body fitted methods are implemented with complex algorithms, and high computational cost, especially when complex geometries are analyzed. In this work, the virtual boundary method are developed in order to work with in viscid compressible flow in two dimensions over complex geometries, tested over a cylinder and several NACA series 4 and critical airfoils. The regime of interest is the transonic, below the speed of sound, nevertheless results for several flow regimens (incompressible subsonic, compressible subsonic, transonic and supersonic) are also presented.

Apresentamos alguns métodos numéricos para a resolução das equações hiperbólicas que regem problemas de transporte de cargas elétricas em isolantes, aplicando-os a quatro problemas específicos: injeção de corrente por um contato ôhmico em uma amostra com voltagem constante aplicada; transporte de um pulso de cargas através de uma amostra em circuito aberto; transporte de um pulso de cargas através de uma amostra submetida a uma diferença de potencial constante (tempo de vôo); e, finalmente, descarga termo-estimulada em circuito aberto. Empregamos, basicamente, dois tipos de métodos: características e diferenças finitas. Concluímos que, quando as descontinuidades são importantes, é mais conveniente usar o método das características; porém, quando não houver descontinuidades ou se estas não forem importantes, alguns métodos de diferenças finitas podem ser utilizados com boa precisão e menores tempos de computação do que aqueles gastos pelos métodos das características. / Numeral methods for solving partial differential equations of the hiperbolic type, governing some problems of transport of electric charge in dielectrics are presented and then applied to four specific problems: injection of charge via an ohmic contact into a sample with a constant applied voltage; transport of a pulse of charge through a sample in the open circuit mode; transport of a pulse of charge through a sample subjected to a constant voltage; and finally, thermally stimulated discharge in open circuit. Essentially two kinds of methods are employed: the method of characteristics and finite-difference methods. It is concluded that when discontinuities are important, the method of characteristics is the most convenient; otherwise, appropriate finite-difference schemes can be used with sufficient precision and less time expenses in computers.