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.

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.

Para uma análise mais exata do sistema estrutural, é necessário um estudo do comportamento interativo entre as diversas partes que o compõe, entre eles, destaca-se a interação entre os elementos de fundação e o maciço de solos. Neste trabalho foram desenvolvidas formulações numéricas para a análise da interação estaca-solo via acoplamento entre diferentes métodos numéricos: método dos elementos de contorno, método dos elementos finitos e método das diferenças finitas. As estacas podem estar submetidas a carregamentos horizontais, verticais e momentos aplicados em seu topo. Nestas formulações foram utilizadas, além das equações integrais de deslocamentos, as equações de suas derivadas, levando a um grau maior de singularidade, porém permitindo a adoção de aproximações mais refinadas para os deslocamentos e tensões ao longo da estaca. Todos os deslocamentos e suas derivadas referentes à estaca foram compatibilizados com os correspondentes do solo. Desenvolvidas as formulações, feito o devido acoplamento entre eles, foram analisados exemplos, que foram comparados com os resultados obtidos por outros pesquisadores, demonstrando sua validade. / For a more accurate analysis of the structural system, it is necessary to study the interactive behavior between the various parts that compose it, among them, there is the interaction between the foundation elements and massive soil. In this work, numerical formulations were developed for the analysis of pile-soil interaction by coupling between different numerical methods: the boundary element method, finite element method and finite difference method. Piles can be subjected to horizontal loads, vertical and moments applied on its top. In these formulations were used in addition to the displacement integral equations, the equations of their derivatives, leading to a higher degree of uniqueness but allowing the adoption of more sophisticated approaches to displacements and contact tractions along the pile. All displacements and their derivatives relating to the pile were matched with the corresponding soil. Developed formulations made due coupling between them were analyzed examples, which were compared with results obtained by other authors, demonstrating its validity.

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.

Landslides cause significant damage to property and human lives throughout the world. Rainfall is the most common triggering factor for the occurrence of landslides. This dissertation presents two novel methodologies for assessment of rainfall-triggered shallow landslide hazard. The first method focuses on using remotely sensed soil moisture and soil surface properties in developing a framework for real-time regional scale landslide hazard assessment while the second method is a deterministic approach to landslide hazard assessment of the specific sites identified during first assessment. In the latter approach, landslide inducing transient seepage in soil during rainfall and its effect on slope stability are modeled using numerical analysis. Traditionally, the prediction of rainfall-triggered landslides has been performed using pre-determined rainfall intensity-duration thresholds. However, it is the infiltration of rainwater into soil slopes which leads to an increase of porewater pressure and destruction of matric suction that causes a reduction in soil shear strength and slope instability. Hence, soil moisture, pore pressure and infiltration properties of soil must be direct inputs to reliable landslide hazard assessment methods. In-situ measurement of pore pressure for real-time landslide hazard assessment is an expensive endeavor and thus, the use of more practical remote sensing of soil moisture is constantly sought. In past studies, a statistical framework for regional scale landslide hazard assessment using remotely sensed soil moisture has not been developed. Thus, the first major objective of this study is to develop a framework for using downscaled remotely sensed soil moisture available on a daily basis to monitor locations that are highly susceptible to rainfall- triggered shallow landslides, using a well-structured assessment procedure. Downscaled soil moisture, the relevant geotechnical properties of saturated hydraulic conductivity and soil type, and the conditioning factors of elevation, slope, and distance to roads are used to develop an improved logistic regression model to predict the soil slide hazard of soil slopes using data from two geographically different regions. A soil moisture downscaling model with a proven superior prediction accuracy than the downscaling models that have been used in previous landslide studies is employed in this study. Furthermore, this model provides satisfactory classification accuracy and performs better than the alternative water drainage-based indices that are conventionally used to quantify the effect that elevated soil moisture has upon the soil sliding. Furthermore, the downscaling of soil moisture content is shown to improve the prediction accuracy. Finally, a technique that can determine the threshold probability for identifying locations with a high soil slide hazard is proposed. On the other hand, many deterministic methods based on analytical and numerical methodologies have been developed in the past to model the effects of infiltration and subsequent transient seepage during rainfall on the stability of natural and manmade slopes. However, the effects of continuous interplay between surface and subsurface water flows on slope stability is seldom considered in the above-mentioned numerical and analytical models. Furthermore, the existing seepage models are based on the Richards equation, which is derived using Darcy’s law, under a pseudo-steady state assumption. Thus, the inertial components of flow have not been incorporated typically in modeling the flow of water through the subsurface. Hence, the second objective of this study is to develop a numerical model which has the capability to model surface, subsurface and infiltration water flows based on a unified approach, employing fundamental fluid dynamics, to assess slope stability during rainfall-induced transient seepage conditions. The developed model is based on the Navier-Stokes equations, which possess the capability to model surface, subsurface and infiltration water flows in a unified manner. The extended Mohr-Coulomb criterion is used in evaluating the shear strength reduction due to infiltration. Finally, the effect of soil hydraulic conductivity on slope stability is examined. The interplay between surface and subsurface water flows is observed to have a significant impact on slope stability, especially at low hydraulic conductivity values. The developed numerical model facilitates site-specific calibration with respect to saturated hydraulic conductivity, remotely sensed soil moisture content and rainfall intensity to predict landslide inducing subsurface pore pressure variations in real time.

In mammalian hearts, initiation of the heartbeat occurs in a region of specialised pacemaker cells known as the sinoatrial node (SAN). The SAN is a highly complex spatially distributed structure which displays considerable cellular heterogeneity and is subject to complex electrotonic interactions with the surrounding atrial tissue. In this study, biophysically detailed ionic models of central and peripheral SAN pacemaker cells are described. These models are able to accurately reproduce experimental recordings of the membrane potential from central and peripheral SAN tissue. These models are used to investigate frequency synchronisation of electrically coupled cardiac pacemaker cells. Based on simulation results presented, it is proposed that cellular heterogeneity in the SAN plays an important role in achieving rhythm coordination and possibly contributes to the efficient activation of the surrounding atrial myocardium. This represents an important, previously unexplored, mechanism underlying pacemaker synchronisation and cardiac activation in vivo. A spatial-gradient model of action potential heterogeneity within the SAN is then formulated using a large-scale least squares optimisation technique. This model accurately reproduces the smooth spatial variation in action potential characteristics observed in the SAN. One and two dimensional models of the intact SAN are then formulated and three proposed models of SAN heterogeneity are investigated: 1) the discrete-region model, in which the SAN consists of a compact central region surrounded by a region of transitional pacemaker cells, 2) the gradient model, in which cells of the SAN exhibit a smooth variation in properties from the centre to the periphery of the SAN, and 3) the mosaic model, in which SAN and atrial cells are scattered throughout the SAN region with the proportion of atrial cells increasing towards the periphery. Simulation results suggest that the gradient model achieves frequency entrainment more easily than the other models of SAN heterogeneity. The gradient model also reproduces action potential waveshapes and a site of earliest activation consistent with experimental observations in the intact SAN. It is therefore proposed that the gradient model of SAN heterogeneity represents the most plausible model of SAN organisation.

A hybrid FEM/FDM algorithm for particle migration of quasi-steady flow in concentrated suspension materials is proposed in this study. This hybrid FEM/FDM algorithm in which the planar variables, such as pressure field, are described in terms of finite element method, and gapwise variables of temperature, density concentration and time derivatives are expressed by finite difference method. The particle concentration inhomogeneities can be predicted, which is ignored by the existing injection molding simulation packages. Simulation results indicated that powder concentration variation could be significant in practical processing in PIM. / Singapore-MIT Alliance (SMA)

Liquid sloshing with unrestrained free surface in a moving container is associated with various engineering problems, such as tankers on highways, liquid oscillations in large storage tanks caused by earthquakes, sloshing of liquid cargo in ocean-going vessels, and the motion of liquid fuel in aircraft and spacecraft. The purpose of this study is to develop a three-dimensional (3D) numerical wave tank with or without internal structures to investigate the mechanism of liquid sloshing and the interaction between the fluid and internal structures. The developed 3D time-independent finite difference method is applied on solving liquid sloshing in tanks with or without the influence of baffles under the ground motion of six-degrees of freedom. The 3D Navier-Stokes equations were solved and transformed to a tank-fixed coordinate system, and the fully nonlinear kinematic and dynamic free surface boundary conditions for fluid sloshing in a rectangular tank with a square base were considered. The fluid is assumed incompressible in this study. The complicated interaction in the vicinity of the fluid-structure interface was solved by implementing one dimensional ghost cell approach and the stretching grid technique near the fluid-structure boundaries were used to catch the detailed evolution of local flow field. A PC-cluster was established by linking several single computers to reduce the computational times due to the implementation of the 3D numerical model. The Message Passing Interface (MPI) parallel language and MPICH2 software were utilized to code the computer codes and to carry out the circumstance of parallel computation, respectively. The developed numerical scheme was verified by rigorous benchmark tests. Not only the reported analytical, numerical and experimental studies were compared with the present numerical results, the experimental investigation was also involved in the present work to further validate the accuracy of the numerical scheme. All the benchmark tests of this study showed excellent accuracy of the developed numerical scheme. For a tank without internal structures, the coupled motions of surge and sway are simulated with various excitation angles, excitation frequencies and water depths. The characteristics of sloshing waves are dissected in terms of the classification of sloshing wave types, sloshing amplitude, beating phenomenon, sloshing-induced forces and energy transfer of sloshing waves. Six types of sloshing waves, named single-directional, diagonal, square-like, swirling-like, swirling and irregular waves, were found and classified in the present study and the occurrence of these waves are tightly in connection with the excitation frequency of the tank. The effect of excitation angle on the characteristics of sloshing waves is explored and discussed, especially for swirling waves. The spectral analyses of sloshing displacement of various sloshing waves are examined and a clear evidence of the correlation between sloshing wave patterns and resonant modes of sloshing waves are demonstrated. The mechanism of switching direction of swirling waves is discussed by investigating the situation of circulatory flow, the instantaneous free surface, the gravitational effect and the instantaneous direction of external forcing. The coupling effects of heave, surge and sway motions were also included in this study and the result showed an unstable influence of heave motion on the kinematic and dynamic characteristics of sloshing waves when the vertical excitation frequency of the tank is twice as large as the fundamental natural frequency. Except irregular waves, the other types of sloshing waves are converted into swirling waves due to the effect of heave motion. The study related to tuned liquid damper (TLD) in 2D and 3D tanks were considered. A comprehensive investigation for a 2D tank with vertically tank bottom-mounted baffles (baffled tank) are demonstrated and discussed with respect to the influence of baffle height on the natural mode of the tank, the evolution of vortices and vortex shedding phenomenon, the relationship between the vortex shedding frequency and the excitation frequency of the tank, the vortex size generated in the vicinity of the baffle tip, the interaction of vortices inside the tank. The baffle height shows a significant influence on the shift of the first natural frequency of the baffled tank and the liquid depth also plays an important part in determining this influence. In other words, the shift of the first natural mode due to various baffle height is varied with water depths. The design of two baffles separated by 0.2 times the tank breadth is an efficient tool to not only reduce the sloshing amplitude but switch the first natural frequency of the tank. The sloshing displacement is affected distinctly by different numbers of baffles mounted vertically on the tank bottom. The more baffles mounted onto the tank bottom, the smaller the sloshing displacement is presented in both the transient and steady-state periods. The processes of the evolution of vortices near the baffle tip are categorized into four phases: the formation of separated shear layer and generation of vortices, the formation of a vertical jet and shedding of vortices, the interaction between shedding vortices and sloshing flow (the generation of snaky flow) and the interaction between snaky flow and sloshing waves. Vortex shedding phenomenon due to stronger vertical jets occurs when the excitation frequency is close to the first natural mode of the baffled tank. The size of the vortex generated near the baffle tip is discussed and the vortex size is closely correlated with the baffle height. Two types of 3D tuned liquid dampers, a vertically tank bottom-mounted baffle and a vertical plate, are discussed for a tank under coupled surge-sway motions. The wave types of diagonal and single-directional waves switch to the swirling type due to the influence of the baffle. The phenomenon of square-like waves or irregular waves coexisting with swirling waves is found in the baffled tank under diagonal excitation. The baffle and the vertical plate mounted parallel to the east (west) wall of the tank can effectively reduce the sloshing amplitude when the excitation angle is between 0 degree and 10 degree and the corresponding sloshing displacement in the sway (z) direction becomes more dominant with the increase of the excitation angle. The shift of the first natural mode of the baffled tank due to various baffle heights in the x direction is dominated in this design of baffled tank. The length of the plate can cause a significant influence on not only the variation of the natural frequencies but the type of the sloshing waves. The influence of the vertical plate on the irregular waves is insignificant and several peaks appear in the spectral analysis of the sloshing displacement for the irregular waves and the numbers of peaks are more than that of the baffled tank.

In geothermal reservoirs and unconventional gas reservoirs with very low matrix permeability, fractures are the main routes of fluid flow and heat transport, so the fracture permeability change is important. In fact, reservoir development under this circumstance relies on generation and stimulation of a fracture network. This thesis presents numerical simulation of the response of a fractured rock to injection and extraction considering the role of poro-thermoelasticity and joint deformation. Fluid flow and heat transport in the fracture are treated using a finite difference method while the fracture and rock matrix deformation are determined using the displacement discontinuity method (DDM). The fractures response to fluid injection and extraction is affected both by the induced stresses as well as by the initial far-field stress. The latter is accounted for using the non-equilibrium condition, i.e., relaxing the assumption that the rock joints are in equilibrium with the in-situ stress state. The fully coupled DDM simulation has been used to carry out several case studies to model the fracture response under different injection/extractions, in-situ stresses, joint geometries and properties, for both equilibrium and non-equilibrium conditions. The following observations are made: i) Fluid injection increases the pressure causing the joint to open. For non-isothermal injection, cooling increases the fracture aperture drastically by inducing tensile stresses. Higher fracture aperture means higher conductivity. ii) In a single fracture under constant anisotropic in-situ stress (non-equilibrium condition), permanent shear slip is encountered on all fracture segments when the shear strength is overcome by shear stress in response to fluid injection. With cooling operation, the fracture segments in the vicinity of the injection point are opened due to cooling-induced tensile stress and injection pressure, and all the fracture segments experience slip. iii) Fluid pressure in fractures increases in response to compression. The fluid compressibility and joint stiffness play a role. iv) When there are injection and extraction in fractured reservoirs, the cooler fluid flows through the fracture channels from the injection point to extraction well extracting heat from the warmer reservoir matrix. As the matrix cools, the resulting thermal stress increases the fracture apertures and thus increases the fracture conductivity. v) Injection decreases the amount of effective stress due to pressure increase in fracture and matrix near a well. In contrast, extraction increases the amount of effective stress due to pressure drop in fracture and matrix.