Dissertations / Theses on the topic 'Lagrangian surfaces'

We deal with several problems on the surfaces obtained as second symmetric products of smooth projective curves. In particular, we treat both some attempts at extending the notion of gonality for curves and some classical problems, as the study of the ample cone in the Néron-Severi group. Moreover, we develop a family of examples of Lagrangian surfaces having particular topological properties.

Cette thèse est constituée de quatre chapitres. Le premier contient les notions de base qui permettent d'aborder les divers thèmes qui y sont étudiés. Le second est consacré à l'étude des sous-variétés lagrangiennes d'une variété presque kählérienne. J'y présente les résultats obtenus en collaboration avec Burcu Bektas, Joeri Van der Veken et Luc Vrancken. Dans le troisième, je m'intéresse à un problème de géométrie différentielle affine et je donne une classification des hypersphères affines qui sont isotropiques. Ce résultat a été obtenu en collaboration avec Luc Vrancken. Et enfin dans le dernier chapitre, je présente quelques résultats sur les surfaces de translation et les surfaces homothétiques, objet d'un travail en commun avec Rafael López<br>Abstract in English not available

In this thesis we study the properties of Lagrangian matroids of dessins d'enfants (also known as maps on orientable surfaces) and their behaviour under the action of the absolute Galois group Gal(Q). We show that while the Lagrangian matroid of a dessin itself is not invariant under this action, some of its properties, namely its width and parity, are. We also study the partial duals of a dessin and their Lagrangian matroids and show that certain partial duals can always be defined over their field of moduli. We prove some results on the representations of Lagrangian matroids as well. A relationship between dessins, their partial duals and tropical curves arising from monodromy groups of dessins is observed.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-04-18T13:51:58Z No. of bitstreams: 1 marcusviniciusdesouzaferraz.pdf: 4103901 bytes, checksum: e4adcd64380c6ba8941b29bcc9d0abfd (MD5)<br>Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-04-19T17:48:41Z (GMT) No. of bitstreams: 1 marcusviniciusdesouzaferraz.pdf: 4103901 bytes, checksum: e4adcd64380c6ba8941b29bcc9d0abfd (MD5)<br>Made available in DSpace on 2018-04-19T17:48:41Z (GMT). No. of bitstreams: 1 marcusviniciusdesouzaferraz.pdf: 4103901 bytes, checksum: e4adcd64380c6ba8941b29bcc9d0abfd (MD5) Previous issue date: 2018-02-27<br>CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>O conhecimento da topografia das superfícies e uma compreensão da interação entre elas é essencial para qualquer estudo que envolva os fenômenos de atrito, desgaste e lubrificação. O estudo da relação entre o atrito e os parâmetros de rugosidade é um problema difícil e de interesse tanto industrial como acadêmico e trabalhos experimentais e teóricos têm mostrado que uma película de fluido entre duas superfícies rugosas em movimento relativo impede o contato sólido - sólido e pode proporcionar atrito muito baixo e desgaste desprezível. A modelagem matemática utilizada neste trabalho é baseada em modelos clássicos, tais como a equação de Reynolds para a descrição dos fenômenos hidrodinâmicos e as formulações de Hertz (1896) e Greenwood e Williamson (1966) para a modelagem do contato das asperezas entre as superfícies rugosas. Para tratar a complexidade das interações entre o fluido e os pares sólidos contactados, a descrição Lagrangiana-Euleriana Arbitrária é apresentada nesta pesquisa. Através do Método dos Elementos Finitos um modelo tridimensional é gerado no Abaqus ®, a fim de identificar as pressões de contato, as tensões tangenciais e normais resultantes e os coeficientes de atrito decorrrentes do deslizamento entre uma superfície texturizada e lubrificada e um plano rígido (em analogia aos modelos de contato clássicos), cujos perfis de rugosidade são construídos a partir de informações da rugosidade média quadrática de superfícies dentárias. São avaliados também a sensibilidade de alguns parâmetros do lubrificante na determinação do coeficiente de atrito e são propostos modelos com condições de contorno distintas. Entretanto, para a verificação destes últimos busca-se reproduzir qualitativamente o resultado encontrado por Lorentz (2013) na investigação numérica de sistemas tribológicos no regime misto de lubrificação. A metodologia aqui proposta emerge como uma alternativa eficaz no campo da Tribologia, na predição do coeficiente de atrito e outras variáveis pertinentes a um fenômeno ainda pouco compreendido. Realiza-se uma análise de sensibilidade dos parâmetros de modelagem, a fim de identificar como os mesmos afetam consideravelmente o comportamento mecânico na interface de contato.<br>The knowledge of the topography of surfaces and an understanding of the interaction between them is essential for any study involving the phenomena of friction, wear and lubrication. The study of the relationship between friction and roughness parameters is a difficult problem of both industrial and academic interest and experimental and theoretical works have shown that a fluid film between two rough surfaces in relative motion prevents solid - solid contact and can provide very low friction and negligible wear. The mathematical modeling used in this paper is based on classical models, such as the Reynolds equation for the description of the hydrodynamic phenomena and the formulations of Hertz (1896) and Greenwood e Williamson (1966) of the contact between the asperities of rough surfaces. To address the complexity of the interactions between the fluid and the contacted solid pairs, the Lagrangian-Eulerian Arbitrary description is presented in this research. Through the Finite Element Method, a three-dimensional model is generated in Abaqus ®R to identify contact pressures, resulting tangential and normal stresses, and friction coefficients resulting from sliding between a textured and lubricated surface and a rigid plane (in analogy to classic contact models), whose roughness profiles are constructed from information on the quadratic roughness of dental surfaces. The sensitivity of some lubricant parameters in the determination of the coefficient of friction is also evaluated and models with different boundary conditions are proposed. However, for the vefrification of the latter, it is sought to qualitatively reproduce the result found by Lorentz (2013) in the numerical investigation of tribological systems without mixed lubrication regime. A methodology proposed here emerges as an effective alternative in the field of Tribology, in the prediction of the coefficient of friction and other relevant variables to a phenomenon still little understood. A sensitivity analysis of the modeling parameters is performed, in order to identify how they considerably affect the mechanical behavior at the contact interface.

Thesis (Master of Engineering in Ocean Engineering)--University of California at Berkeley, 2004.<br>"January 2005." Description based on title screen as viewed on May 25, 2010. DTIC Descriptor(s): Fluid Dynamics, Lagrangian Functions, Equations Of Motion, Acceleration, Formulations, Grids, Continuum Mechanics, Gaussian Quadrature, Derivatives (Mathematics), Compact Disks, Boundary Value Problems, Polynomials, Interpolation, Pressure, Operators (Mathematics). DTIC Identifier(s): Multimedia (CD-Rom), Moving Grids, Meshless Discretization, Lifs (Lagrange Implicit Fraction Step), Lagrangian Dynamics, Meshless Operators, Mlip (Multidimensional Lagrange Interpolating Polynomials), Flux Boundary Conditions, Radial Basis Functions Includes bibliographical references (58-59).

Although ships have been used for thousands of years, modeling the dynamics of marine craft has historically been restricted by the complex nature of the hydrodynamics. The principal challenge is that the vehicle motion is coupled to the ambient fluid motion, effectively requiring one to solve an infinite dimensional set of equations to predict the hydrodynamic forces and moments acting on a marine vehicle. Additional challenges arise in parametric modeling, where one approximates the fluid behavior using reduced-order ordinary differential equations. Parametric models are typically required for model-based state estimation and feedback control design, while also supporting other applications including vehicle design and submarine operator training. In this dissertation, Lagrangian mechanics is used to derive nonlinear, parametric motion models for marine craft operating in the presence of a free surface. In Lagrangian mechanics, one constructs the equations of motion for a dynamic system using a system Lagrangian, a scalar energy-like function canonically defined as the system kinetic energy minus the system potential energies. The Lagrangian functions are identified under ideal flow assumptions and are used to derive two sets of equations. The first set of equations neglects hydrodynamic forces due to exogenous fluid motions and may be interpreted as a nonlinear calm water maneuvering model. The second set of equations incorporates effects due to exogenous fluid motion, and may be interpreted as a nonlinear, unified maneuvering and seakeeping model. Having identified the state- and time-dependent model parameters, one may use these models to rapidly simulate surface-affected marine craft maneuvers, enabling model-based control design and state estimation algorithms.<br>Ph. D.

Métodos de Lagrangianos aumentados são muito utilizados para resolver problemas de minimização de funções sujeitas a restrições gerais. Em particular, estudamos um método de Lagrangianos aumentados que utiliza a função PHR, implementado em ALGENCAN, e observamos seu comportamento quando o aplicamos na resolução de um problema encontrado na área de Computação Gráfica. O problema estudado é um problema encontrado na geração de malhas de superfícies, na etapa de pós-processamento, para o qual propomos uma técnica de otimização visando a melhoria dos elementos da malha. Quando se trata de geração de malhas de superfícies em \'R POT. 3\', parametrizações de malhas triângulares que representam superfícies são usadas em muitas aplicações de processamento de malhas para vários fins. Muitas vezes é necessário preservar a métrica da superfície e, assim, minimizar a deformação do ângulo e da área. A técnica que propomos de otimização visa melhorar as distorções de ângulos e áreas impostas por uma parametrização. Para verificar o comportamento da técnica proposta, implementamo-na em C++ e utilizamos algumas malhas de modelos clássicos da literatura para realizar os experimentos numéricos. Os resultados obtidos foram promissores<br>Augmented Lagrangian methods are frequently used to solve minimization problems subject to general constraints. In particular, we study an augmented Lagrangian method that uses the PHR function, implemented in ALGENCAN, and observe its behavior when applied to solve a problem found in the field of Computer Graphics. The problem we will study and solve is found in the post-processing stage of the surface mesh generation, for which we propose an optimization technique to improve the mesh elements. When it comes to meshing surfaces in \'R POT..3\', triangular meshes parametrizations are widely used in applications of mesh processing. It is often necessary to preserve the surface metric and, thus, minimize the angle and area deformation. The optimization technique we propose aims to improve the distortions imposed by a parametrization onto angles and areas. To assert the efectiveness of the proposed technique, we implemented it in C++ language and used some classic mesh models from the literature to performe numerical experiments. The results were promising

La circulation atmosphérique en Afrique de l'Ouest est caractérisée par des vents de sud-ouest (mousson) pendant la saison humide et par des vents de nord-est (harmattan) pendant la saison sèche. Cette alternance des saisons est due aux variations de pression liée à l'état des surfaces (rugosité, albédo, végétation) en réaction au forçage solaire. Ces mêmes états de surface génèrent une variabilité de flux turbulents de surface et des circulations secondaires qui rendent complexes les analyses des mesures effectuées sur place en vue de documenter les interactions surface-atmosphère. La modélisation fine échelle (LES) couramment utilisée dans l'étude de la couche limite atmosphérique est requise pour pouvoir palier à ces difficultés en raison de sa capacité à prendre en compte les flux turbulents en 3D et sur topographie complexe. Notre site d'étude est le bassin versant d'ARA située au Nord du Bénin dans un contexte Soudanien avec des propriétés de surface variables. Une analyse climatique est effectuée sur la base des observations de radiosondage, de radar UHF et de stations au sol afin d'extraire des données composites représentatives des saisons sèche et humide. Ces données composites ont servi par la suite à forcer le modèle Méso-NH dans sa version LES. Pour pouvoir caractériser les échelles de longueur des flux turbulents de surface relatives aux saisons sèche et humide, les données standard de forçage de surface de Méso-NH que sont le relief GTOPO30 (1km de résolution) et la végétation ECOCLIMAP (1km de résolution) ont été respectivement remplacer par le SRTM (90m de résolution) et les données de SPOT/HRV (20m de résolution) reéchantillonné à 90m de résolution. A l'aide d'outils statistiques comme la variographie 2D et le suivi Lagrangien, il ressort que la variabilité spatiale de la chaleur sensible H est gouvernée par le couple vent-relief tandis que celle de la chaleur latente E est difficile à mettre en lien sur végétation hétérogène (SPOT/HRV) en saison sèche. En saison humide, la variabilité spatiale du champ H dépend du vent tandis que celle du champ E dépend de la végétation. Cette étude révèle dans tous les cas que les échelles caractéristiques de ces deux champs diffèrent dans les mêmes conditions de forçage de surface et atmosphérique<br>West Africa atmosphere circulation is characterized by south-westerly wind (monsoon regime) during the wet season and north-easterly wind (harmattan regime) during the dry season. This alternation of wind regime is due to surface pressure variability linked to surface heterogeneities. Surface heterogeneities generate surface flux variability, secondary circulation and make complex analysis when trying to document surface-atmosphere feedbacks. LES modelling usually used for boundary-layer studies due to its potential to take into account 3D turbulence over complex topography, is used here to overcome these difficulties. Our site of interest is located in north of Benin characterized by Soudanian climate and heterogeneous surface properties. Climate analysis are first performed with radiosoundings, UHF radar, and EC station data in order to extract composite profile representing dry and wet season.. These composite profiles are then used to force atmosphere part of the Méso-NH LES model. To characterize turbulent fluxes length scales relative to dry and wet season, standard surface forcing data with Méso-NH like GTOPO30 orography (1km ) and ECOCLIMAP vegetation (1km) are respectively replaced by SRTM (90m) and SPOT/HRV vegetation data (20m) resampled to 90m. Along with statistical tools like 2D variography and Lagrangian, we notice that during dry season on heterogeneous vegetation, sensible heat flux H is more driven by wind and orography while we not able to discuss the latent heat flux E case. During wet season with the same surface forcing, it appears that H is driven by wind while E is more dependent to vegetation variability. Our study concludes in all case that H and E are not characterized by the same length scale

This work presents a study of the mesoscale surface processes occurring in the Southwestern Atlantic Ocean. Two regions in this ocean, the Brazil-Malvinas (Falkland) Confluence (BMC) Zone and the South Brazilian Continental Shelf (SBCS) are studied by means of a 14 year long series of low-resolution Multi-Channel Sea Surface Temperature (MCSST) images of the Advanced Very High Resolution Radiometer (AVHRR) together with high-resolution data from the same sensor and Lagrangian (buoy) data for the period between March 1993 and July 1994. The AVHRR and buoy data were available from the project COROAS (Oceanic Circulation in the Western Region of the South Atlantic), the Brazilian contribution to the World Ocean Circulation Experiment (WOCE). The variability of the sea surface temperature (SST) fields in the South Atlantic is investigated for the period between January 1982 and December 1995 utilising Principal Component analysis techniques on the MCSST data set. The distribution and oscillation of the SST fields of the South Atlantic are compared to those present in the BMC and SBCS regions, as described by the high-resolution AVHRR and buoy data. The oceanographic surface frontal systems observed in the AVHRR images and buoy trajectories are also studied for the BMC and SBCS regions during 1993 and 1994. Direct measurements of currents taken by the buoys are utilised to describe the characteristics of the Brazil Current (BC), the South Atlantic Current (SAC) and the Brazilian Coastal Current (BCC). These currents are described by their mean surface velocities, kinetic energies, temperature statistics and oscillations. The BCC is a newly described current, very poorly understood in the past and very important for fisheries and, possibly, for the weather of the southern region of Brazil. The surface component of the BCC is described in this thesis as a coastal, northeasterly current flowing in opposition to the BC main flow and with a seasonal behaviour off the South American coast. The eddy field present in the BMC and SBCS regions during 1993 and 1994 is investigated in this work as well. Distinct behaviour and driving mechanisms are reported for the eddies present in these two areas of the Southwestern Atlantic. For the first time in the known literature, small scale and shelfbreak eddies are described for the SBCS region. The nature of these small scale eddies is discussed in relation to that of the mesoscale, geostrophically balanced BMC eddies already known to occur in the study area. The importance of the shear instabilities in the oceanographic front between the BC and the BCC for the eddy generation and mixture processes is emphasised here. Comparing AVHRR and buoy data, empirical relationships are obtained for linking eddy sizes to their rotational periods and tangential velocities. The relationships are useful for monitoring the effects of the eddies in the ocean by remote sensing techniques when in situ data are lacking. The question of whether the high-resolution satellite images utilised in this work are truly representing the SST of the ocean is also addressed here. Moreover, with the support of extra satellite data from the Along-Track Scanning Radiometer (ATSR) and in situ data from ships of opportunity, we investigate the nature of the temperature differences (deltaT) between 'skin' and 'bulk' SSTs in the study area. 'Match-ups' between satellite and in situ SSTs demonstrated the presence of a bias in the satellite estimates of SST. DeltaT images also indicated that, owing to the highly dynamic nature of the BMC and BC/BCC fronts, large errors can arise when matching-up buoy with satellite data in these areas.

Thesis: Sc. D., Joint Program in Applied Ocean Science and Engineering (Massachusetts Institute of Technology, Department of Earth, Atmospheric, and Planetary Sciences; and the Woods Hole Oceanographic Institution), 2019<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 207-218).<br>Ocean surface transport is at the core of many environmental disasters, including the spread of marine plastic pollution, the Deepwater Horizon oil spill and the Fukushima nuclear contamination. Understanding and predicting flow transport, however, remains a scientific challenge, because it operates on multiple length- and time-scales that are set by the underlying dynamics. Building on the recent emergence of Lagrangian methods, this thesis investigates the present-day abilities to describe and understand the organization of flow transport at the ocean surface, including the abilities to detect the underlying key structures, the regions of stirring and regions of coherence within the flow. Over the past four years, the field of dynamical system theory has adapted several algorithms from unsupervised machine learning for the detection of Lagrangian Coherent Structures (LCS). The robustness and applicability of these tools is yet to be proven, especially for geophysical flows.<br>An updated, parameter-free spectral clustering approach is developed and a noise-based cluster coherence metric is proposed to evaluate the resulting clusters. The method is tested against benchmarks flows of dynamical system theory: the quasi-periodic Bickley jet, the Duffing oscillator and a modified, asymmetric Duffing oscillator. The applicability of this newly developed spectral clustering method, along with several common LCS approaches, such as the Finite-Time Lyapunov Exponent, is tested in several field studies. The focus is on the ability to predict these LCS in submesoscale ocean surface flows, given all the uncertainties of the modeled and observed velocity fields, as well as the sparsity of Lagrangian data. This includes the design and execution of field experiments targeting LCS from predictive models and their subsequent Lagrangian analysis.<br>These experiments took place in Scott Reef, an atoll system in Western Australia, and off the coast of Martha's Vineyard, Massachusetts, two case studies with tidally-driven channel flows. The FTLE and spectral clustering analyses were particularly helpful in describing key transient flow features and how they were impacted by tidal forcing and vertical velocities. This could not have been identified from the Eulerian perspective, showing the utility of the Lagrangian approach in understanding the organization of transport.<br>by Margaux Filippi.<br>Sc. D.<br>Sc.D. Joint Program in Applied Ocean Science and Engineering (Massachusetts Institute of Technology, Department of Earth, Atmospheric, and Planetary Sciences; and the Woods Hole Oceanographic Institution)

Notre thèse est divisée en 2 chapitres indépendants correspondant chacun à un article. Dans le premier chapitre, nous définissons une notion de surfaces isotropes dans les octonions, i.e. sur lesquelles certaines formes symplectiques canoniques s'annulent. En utilisant le produit vectoriel dans O, nous définissons une application rho de la grassmanienne des plans de O dans la sphère de dimension 6. Cela nous permet d'associer à chaque surface Sigma de O une fonction rho_Sigma de la surface sur la sphère. Alors, nous montrons que les surfaces isotropes de O telles que cette fonction est harmonique sont solutions d'un système complètement intégrable. En utilisant les groupes de lacets, nous construisons une représentation de type Weierstrass de ces surfaces. Par restriction au corps des quaternions, nous retrouvons comme cas particulier les surfaces lagrangiennes hamiltoniennes stationnaires de R^4. Par restriction à Im(H), nous retrouvons les surfaces CMC de R^3. Dans le second chapitre, nous étudions les applications supersymétriques harmoniques définies sur R^{2|2} et à valeurs dans un espace symétrique, du point de vue des systèmes intégrables. Il est bien connu que les applications harmoniques de R^2 à valeurs dans un espace symétrique sont solutions d'un système intégrable. Nous montrons que les applications superharmoniques de R^{2|2} dans un espace symétrique sont solutions d'un système intégrable, et que l'on a une représentation de type Weierstrass en termes de potentiels holomorphes (ainsi qu'en termes de potentiels méromorphes). Nous montrons également que les applications supersymétriques primitives de R^{2|2} dans un espace 4-symétrique donnent lieu, par restriction à R^2, à des solutions du système elliptique du second ordre associé à l'espace 4-symétrique considéré (au sens de C.L. Terng).Ceci nous permet d'obtenir, de manière conceptuelle, une sorte d'interprétation supersymétrique de tous les systèmes elliptiques du second ordre associés à un espace 4-symétrique, en particulier du système intégrable construit au chapitre 1 (et plus particulièrement des surfaces lagrangiennes hamiltoniennes stationnaires dans un espace symétrique).

It is well known that in civil engineering structures are designed so that they remain,whenever possible, in an elastic regime and with their mechanical properties intact. The truth isthat in reality there are uncertainties either in the execution of the work (geometric errors ormaterial quality) or during its subsequent use (loads not contemplated or its value has beenestimated incorrectly) that can lead to the collapse of the structure. This is why the study of thefailure of structures is inherently interesting and, once is known, its design can be improvedto be the less catastrophic as possible or to dissipate the maximum energy before collapsing.Another area of application of fracture mechanics is that of processes of which interest liesin the breakage or cracking of a medium. Within the mining engineering we can enumerateseveral processes of this nature, namely: hydraulic fracture processes orfracking, blasting fortunnels, explosion of slopes in open pit mines, among others. Equally relevant is the analysis ofstructural failures due to natural disasters, such as large avenues or even tsunamis impactingprotection structures such as walls or dikes. In this work numerous implementations and studieshave been made in relation to the mentioned processes.That said, the objective of this thesis is to develop an advanced numerical method capableof simulating multi-fracture processes in materials and structures. The general approach ofthe proposed method can be seen in various publications made by the author and directorsof this thesis. This methodology is meant to cover the maximum spectrum of engineeringapplications possible. For this purpose, a coupled formulation of theFinite Element Method(FEM) and theDiscrete Element Method(DEM) is used, which employs an isotropic damageconstitutive model to simulate the initial degradation of the material and, once the strength ofthe material has been completely exhausted, thoseFinite Element(FE) are removed from theFEMmesh and a set ofDiscrete Element(DE) are generated at its nodes. In addition to ensurethe conservation of the mass of the system, theseDEprevent the indentation between thefissure planes thanks to the frictional repulsive forces calculated by theDEM, if any.Additionally, in this thesis it has been studied how the proposed coupled method namedFEM-DEMtogether with the smoothing of stresses based on thesuper-convergent patchisable to obtain reasonably mesh-independent results but, as one can imagine, the crack width isdirectly related to the size of the elements that have been removed. This favours the inclusionof an adaptive remeshing technique that will refine the mesh where it is required (according tothe Hessian of a nodal indicator of interest) thus improving the discretization quality of the crackobtained and thereby optimizing the simulation cost. In this sense, the procedures for mappingnodal and internal variables as well as the calculation of the nodal variable of interest will bediscussed.As far as the studies of natural disasters are concerned, especially those related to free-surface water flows such as tsunamis, one more level of coupling between the aforementionedmethodFEM-DEMand oneComputational Fluid Dynamics(CFD) formulation commonlyreferred to asParticle Finite Element Method(PFEM) has been implemented. With this strongcoupled formulation, many cases of wave impacts and fluid flows have been simulated agains solid structures such as walls and dikes, among others.<br>Es bien sabido que en ingeniería civil las estructuras se diseñan para que permanezcan, siempre que sea posible, en régimen elástico y con sus propiedades mecánicas intactas. Lo cierto es que en realidad existen incertidumbres tanto en la ejecución de la obra (errores geométricos o de calidad de los materiales) como en su posterior utilización (cargas no contempladas o cuyo valor y/o punto de aplicación se ha estimado incorrectamente) que pueden conllevar al colapso de la estructura. Por ello, el estudio del fallo de las estructuras es inherentemente interesante y, una vez conocido, se puede mejorar el diseño de la misma para que sea lo menos catastrófico posible o para que disipe la máxima energía antes del colapso y aumentar así su ductilidad y seguridad. Otra área de aplicación de la mecánica de la fractura es la de los procesos cuyo interés radica en la rotura o la fisuración de un medio. Dentro de la ingeniería de minas podemos enumerar varios procesos de esta naturaleza, a saber: procesos de fractura hidráulica o fracking, voladuras para excavación de túneles, explosión de taludes en minas a cielo abierto, entre otros. Igualmente relevante es el análisis de los fallos estructurales debidos a desastres naturales, como grandes avenidas o incluso tsunamis que impactan en estructuras de protección como muros o diques. En este ámbito se han realizado numerosas implementaciones y estudios en relación con los procesos mencionados. Dicho esto, el objetivo de esta tesis es desarrollar un método numérico avanzado, cuyo enfoque general puede verse en diversas publicaciones realizadas por el autor y los directores de esta tesis, capaz de simular procesos de multifractura en materiales y estructuras cubriendo así el máximo espectro de aplicaciones de ingeniería posible. Para ello se emplea una formulación acoplada del Método de los Elementos Finitos (FEM) y del Método de los Elementos Discretos (DEM), que internamente incluye un modelo constitutivo de daño isótropo para simular la degradación irrecuperable del material. Una vez agotada la energía de deformación disponible de algunos elementos finitos (FE), se eliminan de la malla FEM y se genera un conjunto de elementos discretos (DE) en los nodos del mismo. Los DE generados, además de asegurar la conservación de la masa del sistema, evitan la indentación entre los planos de la fisura gracias a las fuerzas friccionales de repulsión calculadas por el DEM, si las hubiere. En esta tesis se ha estudiado cómo el método acoplado propuesto denominado FEM-DEM junto con el suavizado de tensiones basado en el super-convergent patch es capaz de obtener resultados razonablemente independientes de la malla pero, como se puede imaginar, el ancho de la fisura está directamente relacionado con el tamaño de los elementos finitos que se han eliminado. Esto propicia la inclusión de una técnica de remallado adaptativo que refinará la malla donde se requiera (según la matriz Hessiana de un indicador nodal) mejorando así la calidad de discretización de la fisura obtenida y optimizando el coste computacional de la simulación. En este sentido, se discutirán los procedimientos de mapeo de las variables nodales e internas, así como el cálculo de la variable nodal de interés. En lo que respecta al estudio de los desastres naturales, especialmente los relacionados con flujos de agua de superficie libre como los tsunamis, se ha implementado un nivel más de acoplamiento entre el mencionado método FEM-DEM y una formulación de Dinámica de Fluidos Computacional (CFD) comúnmente conocida como Método de Elementos Finitos y Partículas (PFEM). Con esta formulación fuertemente acoplada, se han simulado diversos casos de impactos de olas contra estructuras sólidas como muros y diques, entre otros.

In this dissertation, an approach for determining parameters for a nonlinear Lagrangian mechanical system model of a submerged vessel maneuvering near waves is presented. The nonlinear model with determined parameters is capable of capturing nonlinear effects neglected by other linear models, and therefore can be applied to improve maneuvering performance and expand the operating envelope for submerged vessels operating in elevated sea states. To begin, a first principles Lagrangian nonlinear maneuvering (LNM) model for a surface-affected submerged vessel derived by using Lagrangian mechanics cite{BattistaPhD2018} is reformulated to allow the application of data from a medium fidelity potential flow code. In the reformulation process, the order of integration and differentiation in the integro-differential parameters are switched and partial derivatives of the Lagrangian function are computed with readily available data from the panel code solution. As a result, all model parameters can be computed individually using the panel code, wherein the need for additional numerical discretization is circumvented in the computation process through use of solutions already performed by the basic panel code, enabling higher accuracy and lower computational cost. Furthermore, incident wave effects are incorporated into the reformulated LNM model to yield a Lagrangian nonlinear maneuvering and seakeeping (LNMS) model. The LNMS model is numerically validated by confirming the proposed methods and by comparing steady and unsteady hydrodynamic force calculations from the LNMS model against panel code computations for various vessel motions in calm water and in plane progressive waves. Finally, methods for computing physically intuitive components of the model parameters, as well as methods for making approximations of the terms accounting for memory effects are presented, leading to a model formulation amenable to control design. By applying the methods proposed in this dissertation, each and every parameter of the Lagrangian mechanical system model of a submerged vessel maneuvering in waves can be obtained accurately and with computational efficiency by using a potential flow panel code. The resulting nonlinear motion model provides higher model fidelity than existing unified maneuvering and seakeeping models, especially in applications such as nonlinear control design and simulation.<br>Doctor of Philosophy<br>A unified maneuvering and seakeeping model for a submerged vessel maneuvering near waves describes mathematically the relationship between input values to the dynamical system, such as thrust from the propulsors, and output values from the system, such as the position and orientation of the vessel. This unified model has a wide range of applications, ranging from vessel hull form optimization in the early design phase to motion controller tuning after the vessel has been constructed. In order for a unified model to make accurate predictions, for instance, for a submerged vessel making a rapid turn near large waves, nonlinear effects have to be included in the model formulation. To that end, a nonlinear motion model for a marine craft affected by a free surface has been developed using Lagrangian mechanics. This dissertation describes an approach for determining the parameters of the nonlinear motion model using a potential flow panel code, which is originally designed to determine flow velocity of the fluid and pressure distribution over marine vessels. The nonlinear motion model is reformulated and the software implementation is modified to support parameter computations. In addition, the methods are numerically validated by comparing computations using the model against solutions output by the panel code. Compared to traditional parameter estimation approaches, the proposed methods allow for a more accurate and efficient determination of parameters of the nonlinear potential flow model for a submerged vessel operating near waves. The resulting Lagrangian nonlinear maneuvering and seakeeping (LNMS) model with determined parameters is able to capture critical nonlinear effects and has applications such as nonlinear control design, rapid design optimization and training simulator development.

Le travail présenté ici avait pour but le développement d'un schéma de type Galerkin discontinu (GD) d'ordre élevé pour la résolution des équations de la dynamique des gaz écrites dans un formalisme Lagrangien total, sur des maillages bi-dimensionnels totalement déstructurés. À cette fin, une méthode progressive a été utilisée afin d'étudier étape par étape les difficultés numériques inhérentes à la discrétisation Galerkin discontinue ainsi qu'aux équations de la dynamique des gaz Lagrangienne. Par conséquent, nous avons développé dans un premier temps des schémas de type Galerkin discontinu jusqu'à l'ordre trois pour la résolution des lois de conservation scalaires mono-dimensionnelles et bi-dimensionnelles sur des maillages déstructurés. La particularité principale de la discrétisation GD présentée est l'utilisation des bases polynomiales de Taylor. Ces dernières permettent, dans le cadre de maillages bi-dimensionnels déstructurés, une prise en compte globale et unifiée des différentes géométries. Une procédure de limitation hiérarchique, basée aux noeuds et préservant les extrema réguliers a été mise en place, ainsi qu'une forme générale des flux numériques assurant une stabilité globale L_2 de la solution. Ensuite, nous avons tâché d'appliquer la discrétisation Galerkin discontinue développée aux systèmes mono-dimensionnels de lois de conservation comme celui de l'acoustique, de Saint-Venant et de la dynamique des gaz Lagrangienne. Nous avons noté au cours de cette étude que l'application directe de la limitation mise en place dans le cadre des lois de conservation scalaires, aux variables physiques des systèmes mono-dimensionnels étudiés provoquait l'apparition d'oscillations parasites. En conséquence, une procédure de limitation basée sur les variables caractéristiques a été développée. Dans le cas de la dynamique des gaz, les flux numériques ont été construits afin que le système satisfasse une inégalité entropique globale. Fort de l'expérience acquise, nous avons appliqué la discrétisation GD mise en place aux équations bi-dimensionnelles de la dynamique des gaz, écrites dans un formalisme Lagrangien total. Dans ce cadre, le domaine de référence est fixe. Cependant, il est nécessaire de suivre l'évolution temporelle de la matrice jacobienne associée à la transformation Lagrange-Euler de l'écoulement, à savoir le tenseur gradient de déformation. Dans le travail présent, la transformation résultant de l'écoulement est discrétisée de manière continue à l'aide d'une base Éléments Finis. Cela permet une approximation du tenseur gradient de déformation vérifiant l'identité essentielle de Piola. La discrétisation des lois de conservation physiques sur le volume spécifique, le moment et l'énergie totale repose sur une méthode Galerkin discontinu. Le schéma est construit de sorte à satisfaire de manière exacte la loi de conservation géométrique (GCL). Dans le cas du schéma d'ordre trois, le champ de vitesse étant quadratique, la géométrie doit pouvoir se courber. Pour ce faire, des courbes de Bézier sont utilisées pour la paramétrisation des bords des cellules du maillage. Nous illustrons la robustesse et la précision des schémas mis en place à l'aide d'un grand nombre de cas tests pertinents, ainsi que par une étude de taux de convergence<br>The intent of the present work was the development of a high-order discontinuous Galerkin scheme for solving the gas dynamics equations written under total Lagrangian form on two-dimensional unstructured grids. To achieve this goal, a progressive approach has been used to study the inherent numerical difficulties step by step. Thus, discontinuous Galerkin schemes up to the third order of accuracy have firstly been implemented for the one-dimensional and two-dimensional scalar conservation laws on unstructured grids. The main feature of the presented DG scheme lies on the use of a polynomial Taylor basis. This particular choice allows in the two-dimensional case to take into general unstructured grids account in a unified framework. In this frame, a vertex-based hierarchical limitation which preserves smooth extrema has been implemented. A generic form of numerical fluxes ensuring the global stability of our semi-discrete discretization in the $L_2$ norm has also been designed. Then, this DG discretization has been applied to the one-dimensional system ofconservation laws such as the acoustic system, the shallow-water one and the gas dynamics equations system written in the Lagrangian form. Noticing that the application of the limiting procedure, developed for scalar equations, to the physical variables leads to spurious oscillations, we have described a limiting procedure based on the characteristic variables. In the case of the one-dimensional gas dynamics case, numerical fluxes have been designed so that our semi-discrete DG scheme satisfies a global entropy inequality. Finally, we have applied all the knowledge gathered to the case of the two-dimensional gas dynamics equation written under total Lagrangian form. In this framework, the computational grid is fixed, however one has to follow the time evolution of the Jacobian matrix associated to the Lagrange-Euler flow map, namely the gradient deformation tensor. In the present work, the flow map is discretized by means of continuous mapping, using a finite element basis. This provides an approximation of the deformation gradient tensor which satisfies the important Piola identity. The discretization of the physical conservation laws for specific volume, momentum and total energy relies on a discontinuous Galerkin method. The scheme is built to satisfying exactly the Geometric Conservation Law (GCL). In the case of the third-order scheme, the velocity field being quadratic we allow the geometry to curve. To do so, a Bezier representation is employed to define the mesh edges. We illustrate the robustness and the accuracy of the implemented schemes using several relevant test cases and performing rate convergences analysis

O fenômeno de molhamento, estudo de como um líquido se deposita em um sólido, apresenta problemas ainda em aberto, dos pontos de vista da modelagem física e da simulação numérica. O maior interesse acadêmico neste tipo de escoamento é a linha tríplice (ou linha de contato) formada da interação sólido-líquido-gás. A condição de contorno clássica de não escorregamento na interface líquido-sólido leva a uma singularidade no tensor de tensões nesta linha. Além disso, ainda não está estabelecido qual o melhor modelo para descrever o ângulo de contato formado entre a superfície livre e o substrato (o sólido). Neste trabalho, são discutidos métodos numéricos para a simulação de linhas de contato dinâmicas. Os efeitos da tensão superficial são estudados com a abordagem do princípio do trabalho virtual, o qual leva o problema à equações na formulação variacional, linguagem natural para o tratamento numérico com o método dos elementos finitos (FEM). O domínio é discretizado por uma malha não-estruturada de forma que as interfaces separadoras são explicitamente representadas pela malha. As derivadas temporais são tratadas em uma abordagem Lagrangeana-Euleriana arbitrária (ALE). Finalmente, são apresentados os resultados numéricos obtidos com o método ALE-FEM, discutindo alguns aspectos da sua convergência temporal e espacial.<br>Wetting phenomena, study of how of a liquid spreads out on a solid substrate, presents challenges both in physical modeling and in numerical simulation. The triple line (or contact line) formed by the solid-liquid-gas interaction has increasingly attracted the attention of the fluid dynamic community. The classical no-slip boundary condition on the liquid-solid interface leads to a singularity in the stress tensor at contact lines. Furthermore, there is no consensus on what the best model to describe the dynamics of the contact angle formed by the solid substrate and free surface. In this work, numerical methods for simulating dynamic contact lines are considered. The capillarity effects are studied in the approach of the virtual-work principle, which describes the problem in the variational formulation, natural language for numerical treatment with the finite element method (FEM). The domain is discretized by a dynamic unstructured mesh, where the separating interfaces are explicit represented by the mesh. Time derivatives present in the governing equations are treated with the arbitrary Lagrangian-Eulerian (ALE) framework. Finally, we discuss some temporal and spatial convergence issues ofthe ALE-FEM method.

Cette étude concerne la mise en œuvre de méthodes d'optimisation de type contrôle optimal sur les équations de Maxwell, dans le but de résoudre un grand nombre de problèmes liés à la furtivité électromagnétique. Il s'agit ainsi de créer des outils performants d'aide à la conception d'objets discrets. Nous nous sommes limités dans cette thèse à l'étude des problèmes 2D (représentant une configuration 3D cylindrique) pour lesquels nous avons choisi une représentation équations intégrales. De cette formulation, nous avons extrait deux types de paramètres d'optimisation: la forme de la section plane du cylindre, ainsi que la répartition d'impédance le long de cette section. Les deux problèmes ainsi engendrés ont été résolus, de manière indépendante, par une approche lagrangienne. Cette dernière permet, par l'intermédiaire d'un système adjoint, le calcul du gradient de la fonctionnelle que l'on cherche à minimiser, en l'occurrence ici la LER du cylindre. C'est cette grandeur physique qui caractérise, en dimension 2, la signature radar de la cible. Numériquement, le fait que l'on puisse évaluer rapidement le gradient de la fonction coût, autorise l'utilisation de méthodes itératives classiques de type algorithme de descente

Dans cette thèse, nous nous intéressons à la résolution numérique des équations tridimensionnelles de Navier–Stokes à surface libre, écrites sous formalisme ALE, par la méthode des éléments finis. Ces équations permettent la représentation d’écoulements environnementaux. L’objectif initial et principal porte sur une analyse précise des limitations existantes des méthodes numériques et de possibles voies d’amélioration, mathématiquement justifiées, afin de réviser et d’améliorer le cœur numérique du code hydrodynamique Telemac-3D, développé par le Laboratoire National d’Hydraulique et Environnement d’EDF R&amp;D. Nous décrivons ainsi précisément l’algorithme de ce dernier et nous l’évaluons à l’aune des publications les plus récentes. Ainsi, au sein de ce logiciel,les équations de Navier–Stokes à surface libre dans lesquelles la pression a été décomposée en une partie hydrostatique et une partie non-hydrostatique sont résolues. Une des limitations majeures concerne le fait que la vitesse calculée ne satisfait pas l’équation de continuité. De plus, nous avons relevé l’existence d’une restriction sur le pas de temps.Des voies alternatives sont explorées, et un algorithme très différent est analysé et programmé à des fins de comparaison. La stratégie numérique consiste à convecter la surface libre, à mettre à jour le domaine et à résoudre ensuite les équations de Navier–Stokes.Considérant cette approche, nous analysons un schéma éléments finis explicite d’ordre 1 en temps avec un terme de stabilisation symétrique pour l’équation cinématique de surface libre. Nous montrons que ce schéma permet de satisfaire deux propriétés importantes: la conservation globale de la masse d’eau et la divergence nulle faible. De plus, nous démontrons la stabilité conditionnelle de l’algorithme et nous proposons une nouvelle formulation variationnelle associée aux équations de Navier–Stokes permettant d’aboutir à un schéma éléments finis semi-implicite en temps, qui est stable indépendamment de la vitesse du domaine et d’une vitesse de convection à divergence nulle exacte.Finalement, certains modèles simplifiés utilisés dans d’autres logiciels développés par EDF R&amp;D, notamment le modèle asymptotique en fréquence de Berkhoff utilisé au sein du logiciel Artemis [51], sont également étudiés afin d’acquérir une vue d’ensemble du domaine.L’équation de Berkhoff est dérivée asymptotiquement des équations de la houle linéaire.Une étude systématique de la dérivation de différents modèles simplifiés (Berkhoff, Shallowwater linéaire, Helmholtz) à partir des équations de la houle linéaire est effectuée.Le calcul d’une solution approchée des équations de Berkhoff utilisant des résultats de l’optique géométrique complète ce chapitre<br>In this thesis, we are interested by Finite Elements methods for the three-dimensional free surface Navier–Stokes equations under the ALE formulation. They enable to simulate geophysical flows. The initial and main goal is to analyse the existing limitations of these numerical methods and to provide perspectives of improvement, justified mathematically.This purpose helps us to present a review and improvement way for Telemac-3D, which is a hydrodynamics industrial software developed by the Laboratoire National d’Hydraulique et Environnement of EDF R&amp;D. Therefore, we analyse precisely and we evaluate this algorithm, with respect to the recent scientific publications. This software solves the free surface Navier–Stokes equations with the decomposition of the pressure through a hydrostatic part and a dynamic part. A major limitation is that the velocity field of the fluid is not divergence-free. Furthermore, we highlight a time restriction on the time step. Moreover, alternative approaches are studied and compared. In particular, we focus on a numerical strategy which consists in advecting the free surface, in updating the domain and in solving the Navier–Stokes equations. Based on this strategy, we analyze a first order explicit scheme in time with a Finite Elements stabilization term. The numerical method allows to ensure important properties : the mass conservation of the water quantity and the weak free divergence condition. We demonstrate that this scheme is conditionally stable in time. Besides, we propose a new variational formulation allowing to obtain a semi-implicit scheme in time combined with the Finite Elements method,which is stable independently from the velocity of the mesh and without an exact free divergence velocity.Finally, in order to expand the hydrodynamic knowledges, some simplified models used in other software developed by EDF R&amp;D are studied. In particular, we focus on the mild-slope equation solved in the software Artemis [51]. It is an asymptotic model derived from the linear water wave equation. As a consequence, we study the hypothesis and the validity of the derivation. An approximate analytical solution is additionally derived for this purpose. Moreover, comparisons with other asymptotic models, such as the linear shallow water equation or the Helmholtz equation, are presented

O método numérico para fluidos incompressíveis desenvolvido no presente estudo é o Moving Particle Semi-Implicit Method (MPS) que enxerga o domínio discretizado em partículas, é baseado em representação lagrangeana e não tem a necessidade de utilização de malhas. O método MPS tem como equações governantes uma forma particular da equação de Navier-Stokes e a equação da continuidade para fluidos incompressíveis e não viscosos. Os métodos de simulação de fluidos mais comumente utilizados são baseados em representação euleriana e utilizam malhas para descrever a geometria do domínio a ser simulado. Devido a essas diferenças, uma das grandes virtudes do método de partículas é a facilidade de investigação de fenômenos altamente não-lineares como o de superfície livre com quebra de ondas, de líquidos no interior de uma embarcação em movimento, de ondas batendo na parte externa do casco de um navio, etc. Em artigos já publicados, resultados de experimentos físicos mostraram boa aderência aos resultados numéricos de simulações realizadas com o método MPS. No presente trabalho, resultados das forças de excitação das simulações com ondas regulares foram comparados com os resultados do programa Wave Analysis MIT (WAMIT) que é um programa consagrado no meio científico. Houve uma boa concordância de resultados entre os dois programas. A otimização do cálculo de vizinhança forneceu uma grande economia de tempo computacional. A maior contribuição deste estudo foi a otimização da função que resolve o sistema linear implementando no código desenvolvido um código paralelizado de uso público existente chamado Portable, Extensible Toolkit for Scientific Computation (PETSc) que proporcionou um bom ganho de desempenho.<br>A numerical method called Moving Particle Semi-implicit (MPS) method was developed in this study to analyze incompressible fluids. It is a particle method using a lagrangean representation without any grid. The governing equations are the Navier-Stokes equation and continuity equation for incompressible and non-viscous flow. Most of the computational fluid dynamics (CFD) methods are based on eulerian representation and use grids to describe the geometry of the simulated domain. These differences make the MPS method easier to analyze highly nonlinear phenomena as free surface with wave breaking, sloshing, slamming, etc. In previously published articles, results of physical experiments had shown good agreement with the numerical results obtained with MPS method. In the present work, results of exciting forces were compared with the results obtained with a validated program called Wave Analysis MIT (WAMIT). It had a good agreement of results between these two programs. The optimization of the neighborhood calculation function got a good economy of computational time. The greatest contribution of this study was the optimization of the linear system solver. It was made implementing in the developed code a parallelized public code called Portable, Extensible Toolkit for Scientific Computation (PETSc) that provided a good performance profit.

The potential flow initial-boundary value problem describing fluid-structure interaction with fully nonlinear free surface boundary conditions has been studied using a mixed Lagrangian-Eulerian formulation. The boundary-value problem has been solved in the physical domain by means of a Bubnov-Galerkin formulation of the Laplace equation. The initialvalue problem related to the behavior of some of the moving boundaries has been discretized using various numerical techniques. Among these is a series of predictor-corrector methods. These methodologies proved to require considerable numerical smoothing to maintain stability of the numerical scheme. In turn, dissipation led to inaccuracies in the solution of the problem. In order to avoid this negative effect, a semi-implicit semi-Lagrangian two-time level iterative scheme that is almost free from smoothing has been developed. A Bubnov-Galerkin formulation of an elliptic system for the generation of boundary fitted curvilinear coordinates has been used. When solved iteratively, this method provides orthogonal meshes of very good characteristics for both symmetric and non-symmetric domains. Previous publications concluded that the present system was inadequate for non-symmetric regions leading to lack of convergence in the iterative process. Solutions described in this work show that this limitation has been overcome. Fluid responses to periodic excitation of surface-piercing and submerged bodies have been calculated. Both linear and nonlinear cases show agreement with published results. Very low total energy/work error has been obtained which demonstrates accuracy, good stability and convergence characteristics of the numerical scheme. The impulsive response of tanks of various shapes has also been simulated. Resulting natural frequencies show good agreement with available data. A slender body representation of the flow around a hull advancing with forward speed in otherwise calm water has also been simulated. Numerical calculations of a number of quantities of engineering interest are presented for different length Froude numbers. Results compare favorably with experimental data.<br>Applied Science, Faculty of<br>Mechanical Engineering, Department of<br>Graduate

Atualmente diversos produtos são fabricados por meio de injeção de polímeros, num processo denominado moldagem por injeção: material fundido é injetado em um molde no qual resfria e endurece. Contudo, ao contrário de outros processos de produção, a qualidade da peça criada por meio de moldagem por injeção não depende apenas do material e da sua forma geométrica, mas também da maneira na qual o material é processado durante a moldagem. Por esse motivo, o uso de modelagem matemática e simulações numéricas tem aumentado consideravelmente como maneira de auxiliar o processo de produção e tem-se tornado uma ferramenta indispensável. Desta forma, este projeto tem o propósito de simular o escoamento de fluidos durante a fase de preenchimento do processo de moldagem por injeção, utilizando o modelo 21/2-dimensional, composto por uma equação bidimensional para a pressão, conhecida como equação de Hele-Shaw, e uma equação tridimensional para a temperatura do fluido. Um modelo bidimensional para a temperatura é também desenvolvido e apresentado. Este projeto de doutorado propõe duas estratégias numéricas para a solução da equação de Hele-Shaw. A primeira delas é baseada em uma formulação euleriana do método Smoothed Particle Hydrodynamics, onde os pontos utilizados na discretização não se movem, e não há utilização de malhas. A segunda estratégia é baseada na criação de malhas dinamicamente construídas na região do molde que já encontra-se parcialmente cheio de fluido e subseqüente aplicação do método Control Volume Finite Element Method. Uma estratégia dinâmica do método semi lagrangeano é apresentada e aplicada à solução da equação bidimensional da temperatura. O projeto também pretende investigar três novas abordagens para o tratamento da superfície livre. Duas delas são baseadas na técnica Volume of Fluid e uma delas é uma adaptação meshless do método Front-Tracking. O comportamento não newtoniano do fluido é caracterizado por uma família de modelos de viscosidade. Testes numéricos indicando a confiabilidade das metodologias propostas são conduzidos<br>Currently, several plastic products are manufactured by polymer injection, in a process named injection molding: molten material is injected into a thin mold where it cools and solidifies. However, unlike other manufacturing processes, the quality of injection-molded parts depends not only on the material and shape of the part, but also on how the material is processed throughout the molding. For this reason, the use of mathematical modelling and numerical simulations has been increasing in order to assist in the manufacturing process, and it has become an essential tool. Therefore, this Sc.D. project has the purpose of simulating the fluid flow during the filling stage of the injection molding process, using the 21/2-dimensional model, compounded by a two-dimensional equation for the pressure field (also known as Hele-Shaw equation) and a three-dimensional equation for the temperature of the fluid. A simpler two-dimensional model for the temperature field is also derived and presented. This project proposes two novel numerical strategies for the solution of Hele-Shaw equation. The first one is based on an Eulerian formulation of the Smoothed Particle Hydrodynamics method, where the particles used in the discretization do not move along as the simulation evolves, thereby avoing the use of meshes. In the second strategy, local active dual patches are constructed on-the-fly for each active point to form a dynamic virtual mesh of active elements that evolves with the moving interface, then the Control Volume Finite Element Method is applied for the pressure field approximation. A dynamic approach of the semi-Lagrangian scheme is applied to the solution of the two-dimensional temperature equation. The project also assesses three new approaches for the treatment of the free surface of the fluid flow. Two of them are based on the Volume of Fluid technique and one of them is a meshless adaptation of the Front-Tracking method. The non-Newtonian behavior is characterized by a family of generalized viscosity models. Supporting numerical tests and performance studies, which assess the accuracy and the reliability of the proposed methodologies, are conducted

Pollutants follow various subsurface and surface water pathways from sources within a catchment to its outlet and may cause detrimental effects on downstream water quality and ecosystems. Along their different transport pathways through a catchment, pollutants may be attenuated subject to different physical and biogeochemical processes. In this thesis, physical process effects on such catchment-scale pollutant transport and attenuation, resulting coastal pollutant loading and its efficient abatement are investigated. For this purpose, pollutant transport-attenuation is modeled both generically using a Lagrangian Stochastic Advective-Reactive (LaSAR) approach and site specifically for the Swedish Norrström basin using the GIS-based dynamic nitrogen transport-attenuation model POLFLOW. Furthermore, the role of such modeling for catchment-scale pollutant abatement is also investigated by use of economic optimization modeling. Results indicate that appropriate characterization of catchment-scale solute transport and attenuation processes requires accurate quantification of the specific solute pathways from different sources in a catchment, through the subsurface and surface water systems of the catchment, to the catchment outlet. The various physical processes that act on solute transported along these pathways may be quantified appropriately by use of relevant solute travel time distributions for each water subsystem that the pathways cross through the catchment. Such distributions capture the physical solute travel time variability from source to catchment outlet and its effects on reactive pollutant transport. Results of this thesis show specifically that neglect of such physical solute travel time variability in large-scale models of nitrogen transport and attenuation in catchments may yield misleading model estimates of nitrogen attenuation rates. Results for nitrogen abatement optimization in catchments further indicate that inefficient solutions for coastal nitrogen load reduction may result from simplifying physical transport assumptions made in different catchment-scale nitrogen transport-attenuation models. Modeling of possible future nitrogen management scenarios show also that slow nitrogen transport and reversible mass transfer processes in the subsurface water systems of catchments may greatly delay and temporally redistribute coastal nitrogen load effects of inland nitrogen source abatement over decades or much longer. Achievement of the national Swedish environmental objective to reduce the anthropogenic coastal nitrogen loading by 30% may therefore require up to a 40% reduction of both point sources, for achieving a fast coastal load response, and diffuse sources, for maintaining the coastal load reduction also in the long term.<br>QC 20100908

La circulation atmosphérique en Afrique de l'Ouest est caractérisée par des vents de sud-ouest (mousson) pendant la saison humide et par des vents de nord-est (harmattan) pendant la saison sèche. Cette alternance des saisons est due aux variations de pression liée à l'état des surfaces (rugosité, albédo, végétation) en réaction au forçage solaire. Ces mêmes états de surface génèrent une variabilité de flux turbulents de surface et des circulations secondaires qui rendent complexes les analyses des mesures effectuées sur place en vue de documenter les interactions surface-atmosphère. La modélisation fine échelle (LES) couramment utilisée dans l'étude de la couche limite atmosphérique est requise pour pouvoir palier à ces difficultés en raison de sa capacité à prendre en compte les flux turbulents en 3D et sur topographie complexe. Notre site d'étude est le bassin versant d'ARA située au Nord du Bénin dans un contexte Soudanien avec des propriétés de surface variables. Une analyse climatique est effectuée sur la base des observations de radiosondage, de radar UHF et de stations au sol afin d'extraire des données composites représentatives des saisons sèche et humide. Ces données composites ont servi par la suite à forcer le modèle Méso-NH dans sa version LES. Pour pouvoir caractériser les échelles de longueur des flux turbulents de surface relatives aux saisons sèche et humide, les données standard de forçage de surface de Méso-NH que sont le relief GTOPO30 (1km de résolution) et la végétation ECOCLIMAP (1km de résolution) ont été respectivement remplacer par le SRTM (90m de résolution) et les données de SPOT/HRV (20m de résolution) reéchantillonné à 90m de résolution. A l'aide d'outils statistiques comme la variographie 2D et le suivi Lagrangien, il ressort que la variabilité spatiale de la chaleur sensible H est gouvernée par le couple vent-relief tandis que celle de la chaleur latente E est difficile à mettre en lien sur végétation hétérogène (SPOT/HRV) en saison sèche. En saison humide, la variabilité spatiale du champ H dépend du vent tandis que celle du champ E dépend de la végétation. Cette étude révèle dans tous les cas que les échelles caractéristiques de ces deux champs diffèrent dans les mêmes conditions de forçage de surface et atmosphérique.

La 3D s'impose comme un nouveau média dont l'adoption généralisée passe par la conception d'outils, accessibles au grand public, de création et de manipulation de formes tridimensionnelles quelconques. Les outils actuels reposent fortement sur la modélisation sous-jacente des formes, généralement surfacique, et sont alors peu intuitifs ou limitatifs dans l'expressivité offerte à l'utilisateur.Nous souhaitons, dans ces travaux, définir une approche ne présentant pas ces défauts et permettant à l'utilisateur de se concentrer sur le processus créatif. En nous inspirant de l'utilisation séculaire de l'argile, nous proposons une approche modélisant la matière sous forme lagrangienne.Une forme est ainsi décrite par un système de particules, où chaque particule représente un petit volume du volume global.Dans ce cadre lagrangien, la méthode Smoothed Particle Hydrodynamics (SPH) permet l'approximation de grandeurs physiques en tout point de l'espace. Nous proposons alors une modélisation de matériaux à deux couches, l'une décrivant la topologie et l'autre décrivant la géométrie du système global.La méthode SPH permet, entre autres, d'évaluer la densité de matière. Ceci nous permet de définir une surface implicite basée sur les propriétés physiques du système de particules pour redonner un aspect continu à la matière.Ces matériaux peuvent alors être manipulés au moyen d'interactions locales reproduisant le maniement de la pâte à modeler, et de déformations globales. L'intérêt de notre approche est démontrée par plusieurs prototypes fonctionnant sur des stations de travail standard ou dans des environnements immersifs<br>3D is emerging as a new media. Its widespread adoption requires the implementation of userfriendly tools to create and manipulate three-dimensional shapes. Current softwares heavily rely on underlying shape modeling, usually a surfacic one, and are then often counter-intuitive orlimiting. Our objective is the design of an approach alleviating those limitations and allowing the user to only focus on the process of creating forms. Drawing inspiration from the ancient use of clay,we propose to model a material in a lagrangian description. A shape is described by a particles system, where each particle represents a small fraction of the total volume of the shape. In this framework, the Smoothed Particle Hydrodynamics method enables to approximate physical values anywhere in space. Relying on this method, we propose a modeling of material with two levels, one level representing the topology and the other one describing local geometry of the shape.The SPH method especially enables to evaluate a density of matter. We use this property todefine an implicit surface based on the physical properties of the particles system to reproduce the continuous aspect of matter. Those virtual materials can then be manipulated locally through interactions reproducing the handling of dough in the real world or through global shape deformation. Our approach is demonstrated by several prototypes running either on typical desktop workstation or in immersive environment system

Je présente dans cette thèse des travaux concernant la simulation d'interactions entre un fluide et des membranes déformables. Ce sujet ne manque pas d'applications puisque l'interaction d'un fluide avec des feuilles, des tissus ou même des nageoires de poisson est un scénario courant. Pourtant, peu de travaux en synthèse d'images se sont intéressés à reproduire ce phénomène. Pour ce faire, je propose un algorithme de réaction de contacts entre un fluide Lagrangien et une membrane déformable qui est indépendant du pas d'intégration temporelle. Afin de pallier les artefacts visuels dus à des triangles, issus du processus d'extraction de surface du fluide, qui passent au travers de la membrane lors d'interactions, je présente une technique qui projette la portion de volume erronée le long de la membrane. De plus, une paramétrisation intuitive de coefficients hétérogènes de friction sur une surface est exposée. Je présente également deux modèles d'optimisation. Le premier modèle propose de filtrer les vitesses de particules calculées par une méthode explicite afin de réduire la forte contrainte sur le pas d'intégration temporelle. Des analyses fréquentielles permettent de quantifier cette réduction. Le deuxième modèle est une structure de subdivision spatiale dynamique qui détermine efficacement le voisinage d'un point et d'un triangle. Cette structure a pour but de réduire les temps de calculs des processus de détermination du voisinage pour les fluides Lagrangiens, mais aussi ceux de la détection de collisions et enfin ceux de l'extraction de surface<br>The presented works' main focus is the interaction of liquids and thin shells, such as sheets of paper, fish fins and even clothes. Even though such interactions is an every day scenario, few research work in the computer graphics community have investigated this phenomenon. Thereby, I propose an algorithm which resolves contacts between Lagrangian fluids and deformable thin shells. Visual artefacts may appear during the surface extraction procedure due to the proximity of the fluids and the shells. Thus, to avoid such artefacts, I propose a visibility algorithm which projects the undesired overlapping volume of liquid onto the thin shells' surface. In addition, an intuitive parametrisation model for the definition of heterogeneous friction coefficients on a surface is presented. I also propose two optimisation methods. The first one reduces the well-known dependency of numerical stability and the timestep when using explicit schemes by filtering particles' velocities. This reduction is quantified with the use of frequency analysis. The second optimisation method is a unified dynamic spatial acceleration model, composed of a hierarchical hash table data structure, that speeds up the particle neighbourhood query and the collision broad phase. The proposed unified model is besides used to efficiently prune unnecessary computations during the surface extraction procedure

<p align='justify'>L’adaptation des surfaces pour des fonctions prédéterminées par le choix des matériaux métalliques ou des couches minces ayant des propriétés mécaniques avancées peut potentiellement permettre de réaliser des nouvelles applications à petites échelles. Concevoir de telles applications utilisant des nouveaux matériaux nécessite en premier lieu la connaissance des propriétés mécaniques des matériaux ciblés à l’échelle microscopique et nanoscopique. Une méthode souvent appliquée pour caractériser les matériaux à petites échelles est la nanoindentation, qui peut être vue comme une mesure de dureté à l’échelle nanoscopique.</p><p><p align='justify'>Ce travail présente une contribution relative à l'interprétation des résultats de la nanoindentation, qui fait intervenir un grand nombre de phénomènes physiques couplés à l'aide de simulations numériques. A cette fin une approche interdisciplinaire, adaptée aux phénomènes apparaissant à petites échelles, et située à l’intersection entre la physique, la mécanique et la science des matériaux a été utilisée. Des modèles numériques de la nanoindentation ont été conçus à l'échelle atomique (modèle discret) et à l'échelle des milieux continus (méthode des éléments finis), pour étudier le comportement du nickel pur. Ce matériau a été choisi pour ses propriétés mécaniques avancées, sa résistance à l'usure et sa bio-compatibilité, qui peuvent permettre des applications futures intéressantes à l'échelle nanoscopique, particulièrement dans le domaine biomédical. Des méthodes avancées de mécanique du solide ont été utilisées pour prendre en compte les grandes déformations locales du matériau (par la formulation corotationelle), et pour décrire les conditions de contact qui évoluent au cours de l'analyse dans le modèle à l'échelle des milieux continus (traitement des conditions de contact unilatérales et tangentielles par une forme de Lagrangien augmenté).</p><p><p align='justify'>L’application des modèles numériques a permis de contribuer à l’identification des phénomènes qui gouvernent la nanoindentation du nickel pur. Le comportement viscoplastique du nickel pur pendant nanoindentation a été identifié dans une étude expérimentale-numérique couplée, et l'effet cumulatif de la rugosité et du frottement sur la dispersion des résultats de la nanoindentation a été montré par une étude numérique (dont les résultats sont en accord avec des tendances expérimentales).</p> <p><p align='justify'>Par ailleurs, l’utilisation de l’outil numérique pour une autre application à petites échelles, la manipulation des objets par contact, a contribué à la compréhension de la variation de l’adhésion électrostatique pendant micromanipulation. La déformation plastique des aspérités de surface sur le bras de manipulateur (en nickel pur) a été identifiée comme une source potentielle d’augmentation importante de l'adhésion pendant la micromanipulation, qui peut potentiellement causer des problèmes de relâche et de précision de positionnement, observés expérimentalement.</p><p><p align='justify'>Les résultats présentés dans cette thèse montrent que des simulations numériques basées sur la physique du problème traité peuvent expliquer des tendances expérimentales et contribuer à la compréhension et l'interprétation d'essais couramment utilisé pour la caractérisation aux petites échelles. Le travail réalisé dans cette thèse s’inscrit dans un projet de recherche appelé "mini-micro-nano" (mµn), financé par la Communauté Française de Belgique dans le cadre de "l'Action de Recherche Concertée", convention 04/09-310.</p><br>Doctorat en Sciences de l'ingénieur<br>info:eu-repo/semantics/nonPublished

Dans cette thèse, nous implémentons les équations de Saint Venant (SV), ou de Shallow Water, sur des grilles non structurées afin de simuler des écoulements de surface libre sur des bathymétries irrégulières, incluant inondation et d'autres phénomènes complexes qui se produisent généralement dans des applications hydrodynamiques. En particulier, nous voudrions simuler avec précision les tsunamis, la propagation d'onde à grande échelle jusqu'à l'inondation très localisé. À cette fin, nous utilisons deux méthodes qui sont comparées en profondeur le long du manuscrit: la méthode des volumes finis, très populaire dans la communauté hydrodynamique et hydraulique et une technique plus récente appelée Distribution du Résidu appartenant à la classe des schémas upwind multidimensionnels. Pour améliorer la résolution de certaines caractéristiques de l'écoulement telles que le développement du déferlement et les inondations à petite échelle, nous utilisons une adaptation de maillage dynamique basée sur une redistribution des noeuds de maillage, aussi appelé adaptation de type r (r signifiant "relocalisation"). La combinaison appropriée de cette méthode avec le solveur SV est généralement appelée Méthode de Maillage Mobile. Parmi les nombreux algorithmes de maillage mobile disponibles, nous proposons une forme Arbitrary Lagrangian Eulerian (ALE) des équation SV qui permettent de faire évoluer les variables de flux d'une maille à l'autre de manière élégante. Dans ce contexte, nous soulignons les principales contributions de la thèse: Nous montrons l'importance de conserver toutes les propriétés standards d'un solveur Eulérien SWE tel que la préservation du lac au repos et la conservation de la masse également sur des maillages en mouvement. Notre couplage ALE est comparé à l'approche de rezoning, avec une légère augmentation de la performance globale de l'algorithme en termes de précision et de temps CPU. Nous étendons l'approche ALE sur la sphère afin d'inclure l'effet de la courbure terrestre dans la dynamique de propagation des ondes à grande échelle du tsunami. La simulation du tsunami 2011 de Tohoku-Honsu devrait prouver que la méthode de maillage mobile étudiée dans la thèse, bien que simple, pourrait être un bon candidat pour réduire le coût de calcul des simulations de tsunami<br>In this thesis we implement the Shallow Water equations (SWEs) on unstructured grids in order to simulate free surface flow over irregular bathymetries, wetting/drying and other complex phenomena that typically occurs in hydrodynamic applications. In particular we would to accurately simulate tsunami events, from large scale wave propagation up to localized runup. To this aim we use two methods that are extensively compared along the manuscript: the Finite Volume method, which is very popular in the hydrodynamics and hydraulic community and a more recent technique called Residual Distribution which belongs to the class of multidimensional upwind schemes. To enhance the resolution of important flow feature such as bore development or small scale flooding, we use a dynamic mesh adaptation based on a redistribution of mesh nodes or r-adaptation (r stands for "relocation"). The proper combination of this method with the flow solver is usually referred to as Moving Mesh Method. Among the many different moving mesh algorithms available we propose an Arbitrary Lagrangian Eulerian (ALE) form of the SWEs which elegantly permit to evolve the flow variables from one mesh to the updated one

La fatigue de surface est aujourd'hui la principale cause de défaillances des roulements. Ce type de fatigue peut se développer du simple fait de la rugosité des surfaces mais est exacerbée par la présence de défauts de surface tels que les indents. La gestion de la pollution des lubrifiants, à l'origine de l'indentation des surfaces, est très coûteuse et ne peut être parfaite puisque la pollution est à la fois présente dans les huiles neuves, générée de manière continue par les systèmes lubrifiés et introduite lors des opérations sur le système. En conséquence, les huiles charrient systématiquement des particules d'origines variées qui sont amenées dans les contacts par les systèmes de lubrification. Au passage entre les surfaces, les particules sont écrasées et indentent les surfaces, créant ainsi des défauts qui seront les sites privilégiés d'amorçage de fatigue au cours des cycles de fonctionnement suivants. Ne pouvant se prémunir de l'indentation des surfaces, une bonne compréhension des mécanismes d'indentation et de fatigue sur indent est nécessaire pour garantir la fiabilité des roulements ainsi que pour réduire les coûts liés à leur maintenance. Au cours de cette thèse, un modèle éléments finis « couplé Euler-Lagrange » est développé pour reproduire le processus d’indentation réel des roulements et en étudier les effets. Dans un second temps, la fatigue des surfaces est étudiée par l’emploi de critères de fatigue issus de la littérature dans le cadre d’un contact sec. Enfin, l’effet du lubrifiant est ajouté par la mise en place d’un solveur multigrilles permettant la résolution du problème EHD transitoire<br>Surface fatigue is currently the main cause of rolling element bearings failures. This type of fatigue can appear due to the presence of surface asperities but is exacerbated by the presence of surface defects such as dents. Handling the contamination of the lubricants that causes the denting of the surfaces is expensive and imperfect since the particles are not only already present in brand new oil but also generated during the operation of the system. Consequently, the lubricant carts particles of various nature into the contact. As they pass through the contact, the particles are crushed and dent the bearing surfaces, creating surface defects that will turn into initiation site for fatigue phenomena. As it is impossible to avoid debris denting, a better understanding of the denting and fatigue mechanisms is required to guarantee the reliability of the components and reduce their maintenance costs. During this PhD, a “coupled Euler-Lagrange” finite element model has been developed to reproduce the realistic debris denting process and study its effects. Then, the surface fatigue of dented surfaces was investigated using fatigue criteria in dry contact conditions. Finally, the effect of the lubricant on the dented surface was introduced using a multigrid solver for the transient EHL problem

Thesis (Ph.D.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2008.<br>Committee Chair: Allen R. Tannenbaum; Committee Member: Anthony J. Yezzi; Committee Member: Gregory Turk; Committee Member: Joel R. Jackson; Committee Member: Patricio A. Vela

Cette thèse concerne le développement, l'extension et l'application d'une formulation stochastique des équations de la mécanique des fluides introduite par Mémin (2014). La vitesse petite échelle, non-résolue, est modélisée au moyen d'un champ aléatoire décorrélé en temps. Cela modifie l'expression de la dérivée particulaire et donc les équations de la mécanique des fluides. Les modèles qui en découlent sont dénommés modèles sous incertitude de position. La thèse s'articulent autour de l'étude successive de modèles réduits, de versions stochastiques du transport et de l'advection à temps long d'un champ de traceur par une vitesse mal résolue. La POD est une méthode de réduction de dimension, pour EDP, rendue possible par l'utilisation d'observations. L'EDP régissant l'évolution de la vitesse du fluide est remplacée par un nombre fini d'EDOs couplées. Grâce à la modélisation sous incertitude de position et à de nouveaux estimateurs statistiques, nous avons dérivé et simulé des versions réduites, déterministe et aléatoire, de l'équation de Navier-Stokes. Après avoir obtenu des versions aléatoires de plusieurs modèles océaniques, nous avons montré numériquement que ces modèles permettaient de mieux prendre en compte les petites échelles des écoulements, tout en donnant accès à des estimés de bonne qualité des erreurs du modèle. Ils permettent par ailleurs de mieux rendre compte des évènements extrêmes, des bifurcations ainsi que des phénomènes physiques réalistes absents de certains modèles déterministes équivalents. Nous avons expliqué, démontré et quantifié mathématiquement l'apparition de petites échelles de traceur, lors de l'advection par une vitesse mal résolu. Cette quantification permet de fixer proprement des paramètres de la méthode d'advection Lagrangienne, de mieux le comprendre le phénomène de mélange et d'aider au paramétrage des simulations grande échelle en mécanique des fluides<br>This thesis develops, analyzes and demonstrates several valuable applications of randomized fluid dynamics models referred to as under location uncertainty. The velocity is decomposed between large-scale components and random time-uncorrelated small-scale components. This assumption leads to a modification of the material derivative and hence of every fluid dynamics models. Through the thesis, the mixing induced by deterministic low-resolution flows is also investigated. We first applied that decomposition to reduced order models (ROM). The fluid velocity is expressed on a finite-dimensional basis and its evolution law is projected onto each of these modes. We derive two types of ROMs of Navier-Stokes equations. A deterministic LES-like model is able to stabilize ROMs and to better analyze the influence of the residual velocity on the resolved component. The random one additionally maintains the variability of stable modes and quantifies the model errors. We derive random versions of several geophysical models. We numerically study the transport under location uncertainty through a simplified one. A single realization of our model better retrieves the small-scale tracer structures than a deterministic simulation. Furthermore, a small ensemble of simulations accurately predicts and describes the extreme events, the bifurcations as well as the amplitude and the position of the ensemble errors. Another of our derived simplified model quantifies the frontolysis and the frontogenesis in the upper ocean. This thesis also studied the mixing of tracers generated by smooth fluid flows, after a finite time. We propose a simple model to describe the stretching as well as the spatial and spectral structures of advected tracers. With a toy flow but also with satellite images, we apply our model to locally and globally describe the mixing, specify the advection time and the filter width of the Lagrangian advection method, as well as the turbulent diffusivity in numerical simulations

Ma, Man Shun.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.<br>Includes bibliographical references (leaves 75-76).<br>Abstracts in English and Chinese.<br>Chapter 1 --- Introduction --- p.6<br>Chapter 2 --- Basic notions in Riemannian geometry --- p.10<br>Chapter 2.1 --- Basic manifold theory --- p.11<br>Chapter 2.2 --- "Connection, curvature" --- p.19<br>Chapter 2.3 --- Submanifold theory --- p.29<br>Chapter 3 --- Basic facts in symplectic and complex geometry --- p.33<br>Chapter 3.1 --- "Symplectic manifolds, Lagrangian submanifolds" --- p.34<br>Chapter 3.2 --- Kahler and Calabi-Yau manifolds --- p.39<br>Chapter 3.3 --- Calibration --- p.49<br>Chapter 4 --- Mean curvature flow --- p.52<br>Chapter 4.1 --- Basic equations in Lagrangian immersions --- p.53<br>Chapter 4.2 --- Evolution equation for --- p.57<br>Chapter 4.3 --- Evolution equations for H and θ --- p.62<br>Chapter 5 --- Lagrangian angle of a foliation --- p.67<br>Chapter 5.1 --- "Proof of equation (5.1), (5.2)" --- p.68<br>Chapter 5.2 --- Main theorem --- p.70<br>Chapter 5.3 --- Examples of invariant solution --- p.73<br>Bibliography --- p.75

<p>In this thesis, we focus on Lagrangian investigations of isotropic turbulence, wall-bounded turbulence and vortex dynamics. In particular, the evolutionary multi-scale geometry of Lagrangian structures is quantified and analyzed. Additionally, we also study the dynamics of vortex-surface fields for some simple viscous flows with both Taylor--Green and Kida--Pelz initial conditions.</p> <p>First, we study the non-local geometry of finite-sized Lagrangian structures in both stationary, evolving homogenous isotropic turbulence and also with a frozen turbulent velocity field. The multi-scale geometric analysis is applied on the evolution of Lagrangian fields, obtained by a particle-backward-tracking method, to extract Lagrangian structures at different length scales and to characterize their non-local geometry in a space of reduced geometrical parameters. Next, we report a geometric study of both evolving Lagrangian, and also instantaneous Eulerian structures in turbulent channel flow at low and moderate Reynolds numbers. A multi-scale and multi-directional analysis, based on the mirror-extended curvelet transform, is developed to quantify flow structure geometry including the averaged inclination and sweep angles of both classes of turbulent structures at multiple scales ranging from the half-height of the channel to several viscous length scales. Results for turbulent channel flow include the geometry of candidate quasi-streamwise vortices in the near-wall region, the structural evolution of near-wall vortices, and evidence for the existence and geometry of structure packets based on statistical inter-scale correlations.</p> <p>In order to explore the connection and corresponding representations between Lagrangian kinematics and vortex dynamics, we develop a theoretical formulation and numerical methods for computation of the evolution of a vortex-surface field. Iso-surfaces of the vortex-surface field define vortex surfaces. A systematic methodology is developed for constructing smooth vortex-surface fields for initial Taylor--Green and Kida--Pelz velocity fields by using an optimization approach. Equations describing the evolution of vortex-surface fields are then obtained for both inviscid and viscous incompressible flows. Numerical results on the evolution of vortex-surface fields clarify the continuous vortex dynamics in viscous Taylor--Green and Kida--Pelz flows including the vortex reconnection, rolling-up of vortex tubes, vorticity intensification between anti-parallel vortex tubes, and vortex stretching and twisting. This suggests a possible scenario for explaining the transition from a smooth laminar flow to turbulent flow in terms of topology and geometry of vortex surfaces.</p>

碩士<br>國立中山大學<br>海洋環境及工程學系研究所<br>88<br>The main purpose of this paper is to analyze the surface progressive gravity waves propagating on a gentle sloping beach in two dimension. Instead of using the method of Eulerian system by the previous investigators, we introduce the governing equations completely in the Lagrangian system directly. All the characteristics of the wave system is expressed by a suitable perturbation expansion in the bottom slope under linearizing the problem in wave amplitude, then all the governing equations are systematically expanded to order. The solution of the wave system is to be solved to second order , even to high order could also be obtained. Based on the obtained results, the velocity potential, pressure and motion of the fluid particle in the wave system in time and space is therefore presented, and we can see that the bottom slope is a main factor to screw the wave field to deform to break. Finally, the experimental result is cited to compare and verify.

博士<br>國立中山大學<br>海洋環境及工程學系研究所<br>101<br>The purpose of this thesis is applying Lagrangian approach to analyze shoreward progressive waves over a gently sloping bottom. A series of laboratorial experiments were executed to validate the analytical results. Then, the theory is extended to the prediction of wave breaking and the resulting breaking criteria are shown to be more accurate than regression formula in the literature. In the analysis, a two-parameter perturbation were used that employs both bottom slope α and wave steepness ε , and the solution is expanded up to the order. Based on this analytical solution, water particle trajectory, waveform and wave velocity in the shoaling process are calculated and their counterparts in the laboratorial experiment are recorded for comparison. Then, the analytical solution is used to derive the wave height, the water depth, and the wave velocity for a breaking wave where the Kinematic Stability Parameter (K.S.P.) u/Cw equaling one is adopted as the breaking criteria. In deriving the O( ε^3α^0) solution, the following conditions are satisfied at each order: (a) The pressure on the free surface is constant, and (b) the mass flux is conserved at each vertical cross section. This solution can accurately describe the waveform, the water particle trajectory and the wave velocity all the way from the deep water to the breaking point, as is shown by the comparison with the laboratorial experiments. The perturbation with respect to the bottom slope α is included and the flow at the bottom is consistent with the sloping bottom condition. Consequently, the present analytical solution can provide better breaking criteria than previous regression formula, especially in the case of large sloping angles.

碩士<br>國立中山大學<br>海洋生物科技暨資源學系研究所<br>95<br>The surface circulation of the northern South China Sea (NSCS) for the period of 1986-2006 is studied using the data of more than 505 satellite-tracked drifters from NOAA/AOML database and the data from ten drifters which were released by our lab in the Penghu channel and in the Luzon Strait in 2006. In this study, the spatial structure and the temporal variability of the surface currents, at mesoscale to seasonal cycle, are described in terms of Eulerian and Lagrangian statistics from the drifter velocities that have been processed. Maps of mean currents, velocity variance ellipses and mean kinetic energies were produced in domain of 0.5°×0.5°. The mean flow map confirms that during the winter monsoon, there is a global cyclonic circulation in the NSCS and the southwestward current which passes Dongsha Island and is called the “Dongsha Current”. Its continuation is the southward coastal jet off Vietnam which is called the “Vietnam Current”. Maximum velocities in the Vietnam Current can exceed 100 cm/s. During the summer monsoon, the Dongsha Current became very weak and the drifters looped near Dongsha Island. The drifter data shows that part of Kuroshio water intrudes into South China Sea through Luzon Strait, Dongsha Current and Vietnam Current were coherent flows. Values of 5.12×107 cm2/s, 2.56 days and 64.43 km were obtained for the diffusivity, Lagrangian time scale and spatial scale in the meridional direction in the NSCS, respectively. In the zonal direction, the statistics are half of the above values which show that the characteristic time and space scale are anisotropic. The mean velocity in the Dongsha Current is 0.33 m/s. The domain of Dongsha Current is subdivided into ten boxes of size 2°× 2° in order to analyze the spatial structure of Lagrangian statistics. The result shows that the eddy kinetic energy is considerably higher than the mean kinetic energy in the region 113-121°E, indicating that the mesoscale motions are particularly frequent. The eddy kinetic energy gradually decreases toward the west and has a maximum value near the Luzon Strait. The drifters that flow southward along the east coast of Vietnam shows that the width of the Vietnam Current varies between 80 and 100 km and has a mean core speed of 60-150 cm/s. In winter, Maximum southward velocities could reach 130 cm/s at 38 km off the coast. In spring, a weaker maximum speed (around 100 cm/s) exists at about 18 km off the Vietnam coast. There were not enough drifter data in summer and fall.

Tese de doutoramento em Engenharia Mecânica, na especialidade de Tecnologias de Produção, apresentada ao Departamento de Engenharia Mecânica da Faculdade de Ciências e Tecnologia da Universidade de Coimbra<br>All movements in the world involve contact and friction, from walking to car driving. The contact mechanics has application in many engineering problems, including the connection of structural members by bolts or screws, design of gears and bearings, sheet metal or bulk forming, rolling contact of car tyres, crash analysis of structures, as well as prosthetics in biomedical engineering. Due to the nonlinear and non-smooth nature of contact mechanics (contact area is not known a priori), such problems are currently solved using the finite element method within the field of computational contact mechanics. However, most of the commercial finite element software packages presently available are not entirely capable to solve frictional contact problems, demanding for efficient and robust methods. Therefore, the main objective of this study is the development of algorithms and numerical methods to apply in the numerical simulation of 3D frictional contact problems between bodies undergoing large deformations. The presented original developments are implemented in the in-house finite element code DD3IMP. The formulation of quasi-static frictional contact problems between bodies undergoing large deformations is firstly presented in the framework of the continuum mechanics, following the classical scheme used in solid mechanics. The kinematic description of the deformable bodies is presented adopting an updated Lagrangian formulation. The mechanical behaviour of the bodies is described by an elastoplastic constitutive law in conjunction with an associated flow rule, allowing to model a wide variety of contact problems arising in industrial applications. The frictional contact between the bodies is established by means of two conditions: the principle of impenetrability and the Coulomb’s friction law, both imposed to the contact interface. The augmented Lagrangian method is applied for solving the constrained minimization incremental problem resulting from the frictional contact inequalities, yielding a mixed functional involving both displacements and contact forces. The spatial discretization of the bodies is performed with isoparametric solid finite elements, while the discretization of the contact interface is carried out using the classical Node-to-Segment technique, preventing the slave nodes from penetrating on the master surface. The geometrical part of the contact elements, defined by a slave node and the closest master segment, is created by the contact search algorithm based on the selection of the closest point on the master surface, defined by the normal projection of the slave node. In the particular case of contact between a deformable body and a rigid obstacle, the master rigid surface can be described by smooth parameterizations typically used in CAD models. However, in the general case of contact between deformable bodies, the spatial discretization of both bodies with low order finite elements yields a piecewise bilinear representation of the master surface. This is the central source of problems in solving contact problems involving large sliding, since it leads to the discontinuity of the surface normal vector field. Thus, a surface smoothing procedure based on the Nagata patch interpolation is proposed to describe the master contact surfaces, which led to the development of the Node-to-Nagata contact element. The accuracy of the surface smoothing method using Nagata patches is evaluated by means of simple geometries. The nodal normal vectors required for the Nagata interpolation are evaluated from the CAD geometry in case of rigid master surfaces, while in case of deformable bodies they are approximated using the weighted average of the normal vectors of the neighbouring facets. The residual vectors and tangent matrices of the contact elements are derived coherently with the surface smoothing approach, allowing to obtain quadratic convergence rate in the generalized Newton method used for solving the nonlinear system of equations. The developed surface smoothing method and corresponding contact elements are validated through standard numerical examples with known analytical or semi-analytical solutions. More advanced frictional contact problems are studied, covering the contact of a deformable body with rigid obstacles and the contact between deformable bodies, including self-contact phenomena. The smoothing of the master surface improves the robustness of the computational methods and reduces strongly the non-physical oscillations in the contact force introduced by the traditional faceted description of the contact surface. The presented results are compared with numerical solutions obtained by other authors and experimental results, demonstrating the accuracy and performance of the implemented algorithms for highly nonlinear problems.<br>Todos os movimentos no mundo envolvem contato e atrito, desde andar até conduzir um carro. A mecânica do contacto tem aplicação em muitos problemas de engenharia, incluindo a ligação de elementos estruturais com parafusos, projeto de engrenagens e rolamentos, estampagem ou forjamento, contato entre os pneus e a estrada, colisão de estruturas, bem como o desenvolvimento de próteses em engenharia biomédica. Devido à natureza não-linear e não-suave da mecânica do contato (área de contato desconhecida a priori), tais problemas são atualmente resolvidos usando o método dos elementos finitos no domínio da mecânica do contato computacional. No entanto, a maioria dos programas comerciais de elementos finitos atualmente disponíveis não é totalmente capaz de resolver problemas de contato com atrito, exigindo métodos numéricos mais eficientes e robustos. Portanto, o principal objetivo deste estudo é o desenvolvimento de algoritmos e métodos numéricos para aplicar na simulação numérica de problemas de contato com atrito entre corpos envolvendo grandes deformações. Os desenvolvimentos apresentados são implementados no programa de elementos finitos DD3IMP. A formulação quasi-estática de problemas de contato com atrito entre corpos deformáveis envolvendo grandes deformações é primeiramente apresentada no âmbito da mecânica dos meios contínuos, seguindo o método clássico usado em mecânica dos sólidos. A descrição cinemática dos corpos deformáveis é apresentada adotando uma formulação Lagrangeana reatualizada. O comportamento mecânico dos corpos é descrito por uma lei constitutiva elastoplástica em conjunto com uma lei de plasticidade associada, permitindo modelar uma grande variedade de problemas de contacto envolvidos em aplicações industriais. O contacto com atrito entre os corpos é definido por duas condições: o princípio da impenetrabilidade e a lei de atrito de Coulomb, ambas impostas na interface de contato. O método do Lagrangeano aumentado é aplicado na resolução do problema de minimização com restrições resultantes das condições de contato e atrito, produzindo uma formulação mista envolvendo deslocamentos e forças de contato. A discretização espacial dos corpos é realizada com elementos finitos sólidos isoparamétricos, enquanto a discretização da interface de contacto é realizado utilizando a técnica Node-to-Segment, impedindo os nós slave de penetrar na superfície master. A parte geométrica do elemento de contacto, definida por um nó slave e o segmento master mais próximo, é criada pelo algoritmo de deteção de contacto com base na seleção do ponto mais próximo na superfície master, obtido pela projeção normal do nó slave. No caso particular de contato entre um corpo deformável e um obstáculo rígido, a superfície rígida master pode ser descrita por parametrizações normalmente utilizadas em modelos CAD. No entanto, no caso geral de contato entre corpos deformáveis, a discretização espacial dos corpos com elementos finitos lineares origina uma representação da superfície master por facetas. Esta é a principal fonte de problemas na resolução de problemas de contato envolvendo grandes escorregamentos, uma vez que a distribuição dos vetor normais à superfície é descontínua. Assim, é proposto um método de suavização para descrever as superfícies de contacto master baseado na interpolação Nagata, que conduziu ao desenvolvimento do elemento de contacto Node-to-Nagata. A precisão do método de suavização das superfícies é avaliada através de geometrias simples. Os vetores normais nodais necessários para a interpolação Nagata são avaliados a partir da geometria CAD no caso de superfícies rígidas, enquanto no caso de corpos deformáveis são aproximados utilizando a média ponderada dos vetores normais das facetas vizinhas. Tanto os vetores de segundo membro como as matrizes residuais tangentes dos elementos de contacto são obtidas de forma coerente com o método de suavização da superfície, permitindo obter convergência quadrática no método de Newton generalizado, o qual é utilizado para resolver o sistema de equações não lineares. O método de suavização das superfícies e os elementos de contacto desenvolvidos são validados através de exemplos com soluções analíticas ou semi-analíticas conhecidas. Também são estudados outros problemas de contato mais complexos, incluindo o contato de um corpo deformável com obstáculos rígidos e o contato entre corpos deformáveis, contemplando fenómenos de auto-contato. A suavização da superfície master melhora a robustez dos métodos computacionais e reduz fortemente as oscilações na força de contato, associadas à descrição facetada da superfície de contato. Os resultados são comparados com soluções numéricas de outros autores e com resultados experimentais, demonstrando a precisão e o desempenho dos algoritmos implementados para problemas fortemente não-lineares.<br>Fundação para a Ciência e Tecnologia - SFRH/BD/69140/2010

A surface reconstruction and image enhancement non-linear finite element technique based on minimization of L1 norm of the total variation of the gradient is introduced. Since minimization in the L1 norm is computationally expensive, we seek to improve the performance of this algorithm in two fronts: first, local L1- minimization, which allows parallel implementation; second, application of the Augmented Lagrangian method to solve the minimization problem. We show that local solution of the minimization problem is feasible. Furthermore, the Augmented Lagrangian method can successfully be used to solve the L1 minimization problem. This result is expected to be useful for improving algorithms computing digital elevation maps for natural and urban terrain, fitting surfaces to point-cloud data, and image super-resolution.

Die künstliche Grundwasserabsenkung stellt eine wichtige Maßnahme für die Entwässerung von Baugruben und bergbaulich genutzten Flächen dar. Eine erfolgreiche und zielgerichtete Absenkung des Grundwasserspiegels setzt ein zweckmäßiges Design und die richtige Auswahl der genutzten Absenkungstechniken voraus. Dabei sind insbesondere die Dimension des abzusenkenden Bereichs, die Untergrundbeschaffenheit sowie zu erfüllende umweltschutzrechtliche Regelungen zu berücksichtigen. Zur Grundwasserabsenkung kommen üblicherweise verschiedene Ausführungen und Anordnungen von Pumpbrunnen zum Einsatz. Konventionelle Pumpbrunnen, welche für Absenkungsmaßnahmen eingesetzt werden, entnehmen Grundwasser aus dem Aquifer. Durch das fortwährende Abpumpen von in der Regel erheblichen Wassermengen können jedoch Umweltprobleme entstehen, und es ist mit zusätzlichen Entsorgungskosten für die Ableitung des geförderten Wassers zu rechnen. Im Gegensatz hierzu stellen vertikale Zirkulationsbrunnen (VCW) einen innovativen Ansatz dar, der eine lokale Grundwasserabsenkung ohne Nettowasserentnahme aus dem Aquifer erlaubt. Ein VCW kann als ein Einbohrlochsystem aufgefasst werden, bei dem im oberen Bereich eines Brunnens Wasser entnommen und dieses in einem separaten, weiter unten installierten Brunnenbereich wieder injiziert wird. Die erfolgreiche Anwendung dieser neuen Grundwasserabsenkungstechnik erfordert die genaue Kenntnis der Faktoren, welche für die Grundwasserströmungsverhältnisse relevant sind und somit die Absenkung bestimmen. Traditionelle Berechnungsansätze vernachlässigen oft vertikale Grundwasserbewegungen und sind deshalb für die Beschreibung der komplexen Strömungsverhältnisse in unmittelbarer Nähe eines VCW nicht geeignet. Aus diesem Grund steht die systematische Untersuchung der Grundwasserströmung unter Berücksichtigung vertikaler Strömungskomponenten im Hauptfokus dieser Arbeit. Die Untersuchungen beschäftigen sich in erster Linie mit der Entwicklung einer geeigneten Simulationsmethode, mit der Evaluierung des Einflusses relevanter hydrogeologischer Parameter sowie mit der Durchführung und Auswertung von Pumpversuchen an einem Feldstandort. Die hier vorgestellte neue Simulationsmethode koppelt den sogenannten Arbitrary‐Lagrangian‐Eulerian‐(ALE)‐Algorithmus mit der Grundwasserströmungsgleichung. Die Simulationsergebnisse werden mit mehreren analytischen Lösungen verglichen und verifiziert. Das entwickelte numerische Modell berücksichtigt auch Vertikalströmungen und eignet sich somit zur Simulation der Grundwasserströmung in der Nähe von VCW. Folglich kann nun die Lage des Grundwasserspiegels, vor allem für ungespannte Grundwasserleiter, präzise berechnet werden. Nach erfolgter Kalibrierung des numerischen Modells anhand von Felddaten wurde eine Sensitivitätsanalyse relevanter Parameter im Hinblick auf die erzielte Absenkung und deren Auswirkungen auf die Grundwasserströmungssituation durchgeführt. Die dabei erhaltenen Ergebnisse zeigen, dass die Grundwasserabsenkung proportional zur Pumprate, indirekt proportional zur hydraulischen Leitfähigkeit und fast unabhängig von der Anisotropie des Grundwasserleiters um den VCW ist. Des Weiteren zeigte sich, dass die Lage des oberen Entnahmepunktes einen größeren Einfluss auf die Absenkung als die Lage des darunter liegenden Injektionspunktes hat. Die Größe des von der Grundwasserzirkulation beeinflussten Bereiches hängt dagegen neben dem Abstand dieser beiden Punkte hauptsächlich auch von der Anisotropie des Aquifermaterials ab. Um den Einfluss der Hydrostratigraphie auf die Grundwasserströmung zu untersuchen, wurden die Eigenschaften der einzelnen Schichten genau charakterisiert. Hierfür wurden Direct‐Push‐, Pump‐, Injektions‐ sowie Zirkulationsversuche an einem Feldstandort durchgeführt. Zudem wurden Bohrkerne entnommen und mithilfe von Siebanalysen vertikale Korngrößenverteilungsprofile im Labor bestimmt. Die eingesetzten experimentellen Methoden stellen in Kombination mit numerischen Simulationsrechnungen eine gute Basis dar, um die Rolle der Schichtstruktur im Aquifer besser beurteilen zu können. Die Untersuchungen leisten somit einen wichtigen Beitrag für das zukünftige Design und den Betrieb von VCW für Grundwasserabsenkungszwecke in ungespannten Grundwasserleitern. Zudem zeigt die hier vorliegende Arbeit das große Potential dieser neuen Grundwasserabsenkungstechnik als vielversprechende Alternative zu konventionellen Absenkungsverfahren auf.

L’objectif de ce mémoire est d’introduire une nouvelle méthode smoothed particle hydrodynamics (SPH) implicite purement lagrangienne, pour la résolution des équations de Navier- Stokes incompressibles bidimensionnelles en présence d’une surface libre. Notre schéma de discrétisation est basé sur celui de Kéou Noutcheuwa et Owens [19]. Nous avons traité la surface libre en combinant la méthode multiple boundary tangent (MBT) de Yildiz et al. [43] et les conditions aux limites sur les champs auxiliaires de Yang et Prosperetti [42]. Ce faisant, nous obtenons un schéma de discrétisation d’ordre $\mathcal{O}(\Delta t ^2)$ et $\mathcal{O}(\Delta x ^2)$, selon certaines contraintes sur la longueur de lissage $h$. Dans un premier temps, nous avons testé notre schéma avec un écoulement de Poiseuille bidimensionnel à l’aide duquel nous analysons l’erreur de discrétisation de la méthode SPH. Ensuite, nous avons tenté de simuler un problème d’extrusion newtonien bidimensionnel. Malheureusement, bien que le comportement de la surface libre soit satisfaisant, nous avons rencontré des problèmes numériques sur la singularité à la sortie du moule.<br>The objective of this thesis is to introduce a new implicit purely lagrangian smoothed particle hydrodynamics (SPH) method, for the resolution of the two-dimensional incompressible Navier-Stokes equations in the presence of a free surface. Our discretization scheme is based on that of Kéou Noutcheuwa et Owens [19]. We have treated the free surface by combining Yildiz et al. [43] multiple boundary tangent (MBT) method and boundary conditions on the auxiliary fields of Yang et Prosperetti [42]. In this way, we obtain a discretization scheme of order $\mathcal{O}(\Delta t ^2)$ and $\mathcal{O}(\Delta x ^2)$, according to certain constraints on the smoothing length $h$. First, we tested our scheme with a two-dimensional Poiseuille flow by means of which we analyze the discretization error of the SPH method. Then, we tried to simulate a two-dimensional Newtonian extrusion problem. Unfortunately, although the behavior of the free surface is satisfactory, we have encountered numerical problems on the singularity at the output of the die.