Radio-frequency microelectromechanical systems (RF MEMS) are widely used for contact actuators and capacitive switches. These devices typically consist of a metallic membrane which is activated by a time-periodic electrostatic force and makes periodic contact with a contact pad. The increase in switch capacitance at contact causes the RF signal to be deflected and the switch thus closes. Membrane motion is damped by the surrounding gas, typically air or nitrogen. As the switch opens and closes, the flow transitions between the continuum and rarefied regimes. Furthermore, creep is a critical physical mechanism responsible for the failure in these devices, especially those operating at high RF power. Simultaneous and accurate modeling of all these different physics is required to understand the dynamical membrane response in these devices and to estimate device lifetime and to improve MEMS reliability. It is advantageous to model fluid and structural mechanics and electrostatics within a single comprehensive numerical framework to facilitate coupling between them. In this work, we develop a single unified finite volume method based numerical framework to study this multi-physics problem in RF MEMS. Our objective required us to develop structural solvers, fluid flow solvers, and electrostatic solvers using the finite volume method, and efficient mechanisms to couple these different solvers. A particular focus is the development of flow solvers which work efficiently across continuum and rarefied regimes. A number of novel contributions have been made in this process. Structural solvers based on a fully implicit finite volume method have been developed for the first time. Furthermore, strongly implicit fluid flow solvers have also been developed that are valid for both continuum and rarefied flow regimes and which show an order of magnitude speed-up over conventional algorithms on serial platforms. On parallel platforms, the solution techniques developed in this thesis are shown to be significantly more scalable than existing algorithms. The numerical methods developed are used to compute the static and dynamic response of MEMS. Our results indicate that our numerical framework can become a computationally efficient tool to model the dynamics of RF MEMS switches under electrostatic actuation and gas damping. / text

Virtual knot theory, introduced by Kauffman, is a generalization of classical knot theory of interest because its finite-type invariant theory is potentially a topological interpretation of Etingof and Kazhdan's theory of quantization of Lie bi-algebras. Classical knots inject into virtual knots}, and flat virtual knots is the quotient of virtual knots which equates the real positive and negative crossings, and in this sense is complementary to classical knot theory within virtual knot theory. We classify flat virtual tangles with no closed components and give bases for its ``infinitesimal'' algebras. The classification of the former can be used as an invariant on virtual tangles with no closed components and virtual braids. In a subsequent paper, we will show that the infinitesimal algebras are the target spaces of any universal finite-type invariants on the respective variants of the flat virtual tangles.

Cette thèse a pour objectif de comprendre la dynamique d’une sphère traversant une interface liquide-liquide. Cette situation, se rencontre dans de nombreuses applications, allant du cycle du carbone dans l’océan (sédimentation de neige marine), aux procédés d’enrobage, en passant par la détection de phase dans l’industrie pétrolière. Pour étudier cette configuration, trois approches sont privilégiées. Un dispositif expérimental muni d’une caméra haute fréquence est utilisé de manière à explorer la dynamique conjointe de la sphère et de l’interface sur une large gamme de paramètres. Le couplage entre une méthode Volume of Fluid (VoF) et une méthode de frontières immergées (IBM) est réalisé et validé dans le but de simuler numériquement ce problème. Enfin des modèles théoriques sont mis en place de manière à interpréter physiquement les différents comportements observés. Ces trois démarches complémentaires permettent de caractériser le passage d’une configuration de flottaison à l’entraînement colonnaire notamment en fonction du rapport entre effets gravitationnels et capillaires. La dynamique de la colonne emportée est très riche (instabilité capillaire, visqueuse, fragmentation, ...). Le bon accord entre les expériences et les simulations numériques permet d’évaluer avec confiance l’influence de chaque paramètre sans dimension (au nombre de 5) à l’aide d’une étude paramétrique numérique. / The goal of this work is to understand the dynamics of a sphere passing through a liquid-liquid interface. Such a configuration is met in different applications, such as oceanic carbon cycle (sedimentation of marine snow), coating processes and phase detection in oil industry. To this aim, three different aproaches are employed. An experimental device, in which various sets of fluids and spheres are used, has been designed to analyze different types of configuration. A combination of an Immersed Boundary Method (IBM) with a Volume of Fluid (VoF) method is used to compute the flow field. Finally theoretical models are derived to better understand the observed behaviours. These three approaches give insights to understand whether a sphere can float or sink. The behaviour of the tail of light fluid towed by the sphere appears to be extremely rich (capillary and viscous instabilities, fragmentation, ...). The agreement between experimental and numerical results allows us to perform an extensive numerical study of the influence of all dimensionless parameters

Doctor of Philosophy / Department of Mechanical and Nuclear Engineering / Mingjun Wei / In this study, a global Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order model (ROM) is proposed. It is extended from usual fixed-domain problems to more general fluid-solid systems with moving boundaries/interfaces. The idea of the extension is similar to the immersed boundary method in numerical simulations which uses embedded forcing terms to represent boundary motions and domain changes. This immersed boundary method allows a globally defined fixed domain including both fluid and solid, where POD-Galerkin projection can be directly applied. However, such a modified approach cannot get away with the unsteadiness of boundary terms which appear as time-dependent coefficients in the new Galerkin model. These coefficients need to be pre-computed for prescribed periodic motion, or worse, to be computed at each time step for non-prescribed (e.g. with fluid-structure interaction) or non-periodic situations. Though computational time for each unsteady coefficient is smaller than the coefficients in a typical Galerkin model, because the associated integration is only in the close neighborhood of moving boundaries. The time cost is still much higher than a typical Galerkin model with constant coefficients. This extra expense for moving-boundary treatment eventually undermines the value of using ROMs. An aggressive approach is to decompose the moving boundary/domain to orthogonal modes and derive another low-order model with fixed coefficients for boundary motion. With this domain decomposition, an approach including two coupled low-order models both with fixed coefficients is proposed. Therefore, the new global ROM with decomposed approach is more efficient. Though the model with the domain decomposition is less accurate at the boundary, it is a fair trade-off for the benefit on saving computational cost. The study further shows, however, that the most time-consuming integration in both approaches, which come from the unsteady motion, has almost negligible impact on the overall dynamics. Dropping these time-consuming terms reduces the computation cost by at least one order while having no obvious effect on model accuracy. Based on this global POD-Galerkin based ROM with forcing term, an improved ROM which can handle the parametric variation of body motions in a certain range is also presented. This study shows that these forcing terms not only represent the moving of the boundary, but also decouple the moving parameters from the computation of model coefficients. The decoupling of control parameters provides the convenience to adapt the model for the prediction on states under variation of control parameters. An improved ROM including a shit mode seems promising in model adaptation for typical problems in a fixed domain. However, the benefit from adding a shit mode to model diminishes when the method is applied to moving-boundary problems. Instead, a combined model, which integrates data from a different set of parameters to generate the POD modes, provides a stable and accurate ROM in a certain range of parametric space for moving-boundary problems. By introducing more data from a different set of parameters, the error of the new model can be further reduced. This shows that the combined model can be trained by introducing more and more information. With the idea of the combined model, the improved global ROM with forcing terms shows impressive capability to predict problems with different unknown moving parameters, and can be used in future parametric control and optimization problems.

Cette thèse concerne le développement de méthodes de détection et de diagnostic des défauts de surface dans les structures immergées. Les structures étudiées sont formées de plaques métalliques. Les méthodes proposées sont basées sur une analyse de mesures acoustiques ultrasonores issues d’échographie sous-marine. Cette analyse combine des outils usuels du traitement du signal et des méthodes de classification à base de réseaux de neurones gaussiens. Des variantes avec et sans modèle de référence sont proposées. Les techniques usuelles d’évaluation par contact montrent leurs limites pour le diagnostic des structures telles que les hydroliennes. Le présent travail de recherche consiste à utiliser un seul et unique transducteur sans contact sous différents angles contrairement à d’autres techniques qui nécessitent un grand nombre de capteurs et une connaissance précise de leur positionnement. Notre étude utilise les ondes de Lamb car elles sont très sensibles aux anomalies structurelles. Les principales étapes et outils utilisés sont les suivants : - 1. Utilisation d’un dispositif de génération et d’acquisition d’ondes de Lamb. - 2. Étude de la propagation d’ondes de Lamb dans les structures en immersion, en particulier dans les plaques métalliques immergées dans l’eau. - 3. Caractérisation des signaux pour différents types de défauts. - 4. Estimation de l’angle d’acquisition et de la distance du transducteur par rapport au centre de la plaque. / This study concerns the damages detection and diagnosis for immersed structure. The structures are metallic plates. The proposed method focuses on the analysis of ultrasonic acoustic measurements obtained by submarine echography. It combines signal processing tools and Gaussian neural networks for classification purpose. Methods with and without reference models are proposed. The usual detection technics with contact are not applicable for the considered systems like stream turbines. This research consists to use a single and a single transducer under different incidence angles opposed to others technics using numerous sensors and their accurate location. The present research use Lamb wave according to their sensibility to the structural damages. The different stages are the following : - 1. Experimental setup for Lamb wave generation and acquisition. - 2. Study of the Lamb wave processing on immersed structures, in particular in metallic plate immersed in water. - 3 .Signal characterization for different types of damages. - 4. Estimation of the angle and lift-off distance.

Problemas de interface do tipo elípticos são frequentemente encontrados em dinâmicas de fluidos, ciências dos materiais, mecânica e outros campos de estudo. Em particular, o clássico Método de Interface Imersa (IIM) figura como uma das abordagens numéricas mais robustas para resolver problemas dessa categoria, o qual tem sido empregado recorrentemente para simular o comportamento de fluxos sobre corpos imersos em malhas cartesianas. Embora esse método seja eficiente e robusto, técnicas construídas com base no IIM impõem como restrições matemáticas diversos tipos de condições de salto na interface a fim de serem passíveis de utilização na prática. Nesta tese, introduzimos um novo método de Interface Imersa para resolver problemas elípticos com coeficientes descontínuos em malhas cartesianas. Diferentemente da maioria das formulações existentes que dependem de vários tipos de condições de salto para produzirem uma solução para o problema elíptico, o esquema aqui proposto reduz significativamente o número de restrições ao solucionar a EDP estudada, isto é, apenas os saltos de ordem zero das incógnitas devem ser fornecidos. A técnica apresentada combina esquemas de Diferenças Finitas, abordagem do Ponto Fantasma, modelos de correções e regras de interpolação em uma metodologia única e concisa. Além disso, o método proposto é capaz de produzir soluções de alta ordem, incluindo cenários onde há poucos dados disponíveis onde o quesito alta precisão é indispensável. A robustez e a precisão do método proposto são verificadas através de uma variedade de experimentos numéricos envolvendo diversos problemas elípticos com interfaces arbitrárias. Finalmente, a partir dos testes numéricos conduzidos, é possível concluir que o método projetado produz aproximações de alta ordem a partir de um número muito condensado de restrições matemáticas. / Elliptic interface problems are often encountered in fluid dynamics, material sciences, mechanics and other relevant fields of study. In particular, the well-known Immersed Interface Method (IIM) figures among the most effective approaches for solving non-trivial problems, where the method is traditionally used to simulate the flow behavior over complex bodies immersed in a cartesian mesh. Although their powerfulness and versatility, techniques that are built in light of the IIM impose as constraints different types of jump conditions at the interface in order to be properly managed and applicable for specific purposes. In this thesis, we introduce a novel Immersed Interface Method for solving Elliptic problems with discontinuous coefficients on cartesian grids. Different from most existing formulations that rely on various jump conditions types to get a valid solution, the present scheme reduces significatively the number of constraints when solving the PDE problem, i.e., only the ordinary jumps of the unknowns are required to be given, a priori. Our technique combines Finite Difference schemes, Ghost node strategy, correction models, and interpolation rules into a unified and concise methodology. Moreover, the method is capable of producing high-order solutions, succeeding in many practical scenarios with little available data wherein high precision is indispensable. We attest the robustness and the accuracy of the proposed method through a variety of numerical experiments involving several Elliptic problems with arbitrary interfaces. Finally, from the conducted numerical tests, we verify that the designed method produces high-order approximations from a very limited number of valid jump constraints.

Un large spectre d’applications en ingénierie est concerné par les écoulements de fluides en interaction avec des structures poreuses, allant de problèmes à petite échelle jusqu’à des problématiques de plus grande échelle. Ces structures poreuses, souvent à géométries complexes, peuvent se déplacer ou se déformer en réponse au forçage exercé par l’écoulement environnant.Le but de ce travail est de proposer un modèle numérique pour la simulation macroscopique d’écoulements de fluide interagissant avec des milieux poreux mobiles à géométries complexes, qui soit facile d’implémentation et pouvant être utilisé dans une large gamme d’applications. Pour atteindre cet objectif, la méthode de Lattice Boltzmann est utilisée pour résoudre l’écoulement dans des milieux poreux à l’échelle d’un volume représentatif élémentaire. Pour l’implémentation du mouvement désiré, le concept de frontières immergées est adopté. Dans ce contexte, un nouveau modèle est proposé pour traiter des milieux poreux en volume, dont la résistance à l’écoulement environnant est modélisé par la loi de Brinkman-Forchheimer-Darcy étendue.L’algorithme est d’abord testé sur l’écoulement à travers un cylindre fixe. La simplicité de ce cas test académique permet de caractériser finement la précision de la méthode. Le modèle est ensuite utilisé pour simuler des écoulements de fluide autour et à travers des corps poreux mobiles, à la fois pour des géométries confinées et pour des écoulements ouverts. L’invariance Galiléenne des équations moyennées macroscopiques gouvernant la dynamique du fluide est démontrée. D’excellents accords avec les résultats de référence sont obtenus pour les différents cas testés. / A wide spectrum of engineering problems is concerned with fluid flows in interaction with porous structures, ranging from small length-scale problems to large ones. These structures, often of complex geometry, may move/deform in response to the forces exerted by the surrounding flow. Despite the advancements in computational fluid dynamics, the numerical simulation of such configurations - a valuable tool for the study of the flow physics involved - remains a challenging task.The aim of the present work is to propose a numerical model for the macroscopic simulation of fluid flows interacting with moving porous media of complex geometry, that is easy to implement and can be used in a range of applications. To achieve this, the Lattice Boltzmann method is employed for solving the flow in porous media at the representative elementary volume scale. For the implementation of the desired body motion, the concept of the Immersed Boundary method is adopted. In this context, a novel model is proposed for dealing with moving volumetric porous media, whose resistance to the surrounding flow obeys the Brinkman-Forchheimer-extended Darcy law. The algorithm is initially tested for flow past a static cylinder. The simplicity of this academic test case allows us to assess in detail the accuracy of the proposed method. The model is later used to simulate fluid flows around and through moving porous bodies, both in a confined geometry and in open space. We are able to demonstrate the Galilean invariance of the macroscopic volume-averaged flow governing equations. Excellent agreement with reference results is obtained in all cases.

Dans cette thèse, nous nous intéressons à la simulation numérique d’écoulements compressibles comportant des interfaces. Ces interfaces peuvent séparer un fluide et un solide rigide, deux fluides de lois d’état différentes ou encore un fluide et un solide élastique. Dans un premier temps, nous avons élaboré une méthode de type frontières immergées afin d’imposer une condition de glissement au bord d’un obstacle rigide de manière précise. Nous avons ensuite étudié et validé un schéma de type interface non diffuse pour les écoulements multi-matériaux en vue d’appliquer la méthode de frontières immergées aux solides déformables. / We are interested in numerical simulation of compressible flows with interfaces. Theses interfaces can separatea fluid and a rigid solid, two fluids with differents constitutive law, or a fluid and an elastic solid. First, we havedevelopped an immersed boundary method to impose precisely a non penetration condition at the border of anobstacle. Then, a sharp interface method for compressible multimaterials have been studied and validated. Theimmersed boundary method of the first part is applied in this context.

Le travail de cette thèse est consacré à la simulation aux grandes échelles (LES) et à la modélisationde la combustion supersonique, dont l’application est rencontrée dans les moteurs detype scramjet. Dans ce contexte, une étude LES appliquée au cas d’une flamme supersoniquehydrogène-air (flamme de Cheng) a été effectuée sur trois niveaux de raffinements de maillage.Les résultats en termes de profils moyens et fluctuations de composition et de température sontconfrontés aux mesures expérimentales, et l’impact du raffinement de maillage est établi. Parailleurs, à partir des données issues de cette étude LES, une modélisation de la combustionturbulente dans un milieu fortement compressible est proposée sur la base d’une approche tabuléede la chimie. Une analyse temporelle des interactions choc/flamme a ensuite été menée,permettant de mettre en évidence la présence de structures transitoires ayant une influence surles processus de stabilisation de la flamme. / This PhD study is focused on the large eddy simulation (LES) and on the modelisation of supersonic combustion as encountered in scramjet types engines. In this context, a LES study was performed for an hydrogen-air supersonic flame (Cheng’s flame) with three mesh refinement levels. The results obtained for mean and fluctuations of composition and temperature are compared to experimental measurements, and the impact of the grid resolution is established. Moreover, a modelisation of turbulent combustion in highly compressible flows is proposed based of tabulated chemistry approach. An analysis of the dynamics of shock/flame interaction was then conducted, and the presence of transient structures, which impact the flame stabilisation processes, was emphasized.

The objective of this work is to develop a novel 3-D biological particulate dynamics framework to simulate blood flow in the micro circulation. This entails the amalgamation of concepts from various fields namely blood flow dynamics, solid mechanics, fluid-structure interaction and computational data structures. It is envisioned that this project will serve as a harbinger for implementing a multi-scale simulation model with applications in a vast array of situations from blood flows in heart valves to studying cancer metastasis. The primary motivation for this work stems from the need for establishing a simple, effective and holistic framework for performing blood flow simulations, taking into account the extremely 3-D nature of flow, the particle interactions and fluid structure interaction between blood and its constituent elements. Many current models to simulate blood cells rely on finite element methods which render large scale simulations extremely computationally intensive. The development of a framework for simulating blood flow is tied together with achieving a framework for performing an investigation of cancer metastasis. Cancer initially develops at a primary site and spreads through the body to secondary sites using the circulatory systems of the body - the blood circulatory system and the lymphatic system. It is known that all the cancer cells that enter into the circulation do not survive the harsh environment, though the exact cause of this is still undetermined. Moreover, the mechanical properties of cancer cells are not well documented and appropriate computational models require that experiments be conducted to determine the same. Thus the end goal of this work is to establish a system to analyze and simulate 3-D blood particulate dynamics, including cancer cells, from a holistic standpoint in order to understand more about the phenomenon of blood flow as a whole, and cancer metastasis in particular.