This thesis presents a two-phase liquid-solid numerical model using Smoothed Particle Hydrodynamics (SPH). The scheme is developed for multi-phase flows in industrial tanks containing sediment used in the nuclear industry for decommissioning. These two-phase liquid-sediments flows feature a changing interfacial profile, large deformations and fragmentation of the interface with internal jets generating resuspension of the solid phase. SPH is a meshless Lagrangian discretization scheme whose major advantage is the absence of a mesh making the method ideal for interfacial and highly non-linear flows with fragmentation and resuspension. Emphasis has been given to the yield profile and rheological characteristics of the sediment solid phase using a yielding, shear and suspension layer which is needed to predict accurately the erosion phenomena. The numerical SPH scheme is based on the explicit treatment of both phases using Newtonian and non-Newtonian Bingham-type constitutive models. This is supplemented by a yield criterion to predict the onset of yielding of the sediment surface and a suspension model at low volumetric concentrations of sediment solid. The multi-phase model has been compared with experimental and 2-D reference numerical models for scour following a dry-bed dam break yielding satisfactory results and improvements over well-known SPH multi-phase models. A 3-D case using more than 4 million particles, that is to the author’s best knowledge one of the largest liquid-sediment SPH simulations, is presented for the first time. The numerical model is accelerated with the use of Graphic Processing Units (GPUs), with massively parallel capabilities. With the adoption of a multi-phase model the computational requirements increase due to extra arithmetic operations required to resolve both phases and the additional memory requirements for storing a second phase in the device memory. The open source weakly compressible SPH solver DualSPHysics was chosen as the platform for both CPU and GPU implementations. The implementation and optimisation of the multi-phase GPU code achieved a speed up of over 50 compared to a single thread serial code. Prior to this thesis, large resolution liquid-solid simulations were prohibitive and 3-D simulations with millions of particles were unfeasible unless variable particle resolution was employed. Finally, the thesis addresses the challenging problem of enforcing wall boundary conditions in SPH with a novel extension of an existing Modified Virtual Boundary Particle (MVBP) technique. In contrast to the MVBP method, the extended MVBP (eMVBP) boundary condition guarantees that arbitrarily complex domains can be readily discretized ensuring approximate zeroth and first order consistency for all particles whose smoothing kernel support overlaps the boundary. The 2-D eMVBP method has also been extended to 3-D using boundary surfaces discretized into sets of triangular planes to represent the solid wall. Boundary particles are then obtained by translating a full uniform stencil according to the fluid particle position and applying an efficient ray casting algorithm to select particles inside the fluid domain. No special treatment for corners and low computational cost make the method ideal for GPU parallelization. The models are validated for a number of 2-D and 3-D cases, where significantly improved behaviour is obtained in comparison with the conventional boundary techniques. Finally the capability of the numerical scheme to simulate a dam break simulation is also shown in 2-D and 3-D.

Le titre de ma thèse de doctorat est "Equations de Stokes et de Navier-Stokes avec la con- dition de Navier", où j’ai considéré l’écoulement d’un fluide newtonien visqueux, incompressible dans un domaine borné de R3. L’écoulement du fluide est décrit par les équations bien connues de Navier-Stokes, données par le système suivant ∂t − ∆u + (u • ∇)u + ∇π = 0, div u = 0 dans Ω × (0, T )u • n = 0, 2[(Du)n]τ + αuτ = 0 sur Γ × (0, T )u(0) = u0 dans Ω (0.1) dans un domaine borné Ω ⊂ R3 de frontière Γ, éventuellement non simplement connexe, de classe C1,1. La vitesse initiale u0 et le coefficient de friction α, scalaire, sont des fonctions don- nées. Les vecteurs unitaires normal extérieur et tangents à Γ sont notés n et τ respectivement et Du = 1 (∇u + ∇uT ) est le tenseur des déformations. Les fonctions u et π décrivent respective- ment les champs de vitesses et de pression du fluide dans Ω satisfaisant la condition aux limites (0.1.2).Cette condition aux limites, proposée par H. Navier en 1823, a été abondamment étudiée ces dernières années, qui pour de nombreuses raisons convient parfois mieux que la condition aux limites de Dirichlet sans glissement : elle offre plus de liberté et est susceptible de fournir une solution physiquement acceptable au moins pour certains des phénomènes paradoxaux résultant de la condition de non-glissement, comme par exemple le paradoxe de D’Alembert ou le paradoxe de non-collision.Ma thèse comporte trois parties. Dans la première, je cherche à savoir si le problème (0.1) est bien posé en théorie Lp, en particulier l’existence, l’unicité de solutions faibles, fortes dans W 1,p(Ω) et W 2,p(Ω) pour tout p ∈ (1, ∞), en considérant la régularité minimale du coefficient de friction α. Ici α est une fonction, pas simplement une constante qui reflète les diverses propriétés du fluide et/ou de la frontière, ce qui nous permet d’analyser le comportement de la solution par rapport au coefficient de frottement.Utilisant le fait que les solutions sont bornées indépendamment de α, on montre que la solution des équations de Navier-Stokes avec la condition de Navier converge fortement vers une solution des équations de Navier-Stokes avec la condition de Dirichlet, correspondant à la même donnée initiale dans l’espace d’énergie lorsque α → ∞. Des résultats similaires ont été obtenus pour le cas stationnaire.Le dernier chapitre concerne les estimations pour le problème de Robin pour le laplacien : l’opérateur elliptique de second ordre suivant, sous forme divergentielle dans un domaine bornéΩ ⊂ Rn de classe C1, avec la condition aux limites de Robin a été considéré div(A∇)u = divf + F dans Ω, ∂u+ αu = f n + g sur Γ.∂n (0.2) Les coefficients de la matrice symétrique A sont supposés appartenir à l’espace V MO(R3). Aussi α est une fonction appartenant à un certain espace Lq . En plus de prouver l’existence, l’unicité de solutions faibles et fortes, nous obtenons une borne sur u, uniforme par rapport à α pour α suffisamment large, en norme Lp. Pour plus de clarté, nous avons étudié séparément les deux cas: l’estimation intérieure et l’estimation au bord. / My PhD thesis title is "Navier-Stokes equations with Navier boundary condition" where I have considered the motion of an incompressible, viscous, Newtonian fluid in a bounded do- main in R3. The fluid flow is described by the well-known Navier-Stokes equations, given by thefollowing system 1 )t − L1u + (u ⋅ ∇)u + ∇n = 0, div u = 01u ⋅ n = 0, 2[(IDu)n]r + aur = 0 in Q × (0, T )on Γ × (0, T ) (0.1) 11lu(0) = u0 in Qin a bounded domain Q ⊂ R3 with boundary Γ, possibly not connected, of class C1,1. The initialvelocity u0 and the (scalar) friction coefficient a are given functions. The unit outward normal and tangent vectors on Γ are denoted by n and r respectively and IDu = 1 (∇u + ∇uT ) is the rate of strain tensor. The functions u and n describe respectively the velocity2 and the pressure of a fluid in Q satisfying the boundary condition (0.1.2).This boundary condition, first proposed by H. Navier in 1823, has been studied extensively in recent years, among many reasons due to its contrast with the no-slip Dirichlet boundary condition: it offers more freedom and are likely to provide a physically acceptable solution at least to some of the paradoxical phenomenons, resulting from the no-slip condition, for example, D’Alembert’s paradox or no-collision paradox.My PhD work consists of three parts. primarily I have discussed the Lp -theory of well-posedness of the problem (0.1), in particular existence, uniqueness of weak and strong solutions in W 1,p (Q) and W 2,p (Q) for all p ∈ (1, ∞) considering minimal regularity on the friction coefficienta. Here a is a function, not merely a constant which reflects various properties of the fluid and/or of the boundary. Moreover, I have deduced estimates showing explicitly the dependence of u on a which enables us to analyze the behavior of the solution with respect to the friction coefficient.Using this fact that the solutions are bounded with respect to a, we have shown the solution of the Navier-Stokes equations with Navier boundary condition converges strongly to a solution of the Navier-Stokes equations with Dirichlet boundary condition corresponding to the sameinitial data in the energy space as a → ∞. The similar results have also been deduced for thestationary case.The last chapter is concerned with estimates for a Laplace-Robin problem: the following second order elliptic operator in divergence form in a bounded domain Q ⊂ Rn of class C1, withthe Robin boundary condition has been considered1div(A∇)u = divf + F in Q, 11 )u + u = f ⋅ n + g on Γ. (0.2) 2The coefficient matrix A is symmetric and belongs to V MO(R3). Also a is a function belonging to some Lq -space. Apart from proving existence, uniqueness of weak and strong solutions, we obtain the bound on u, uniform in a for a sufficiently large, in the Lp -norm. We have separately studied the two cases: the interior estimate and the boundary estimate to make the main idea clear in the simple set up.

Les systèmes de combustion sont sujets aux instabilités de combustion (IC). Elles résultent d'un couplage constructif entre le taux de dégagement de chaleur instationnaire et des modes acoustiques du système. Les IC peuvent mettre en danger la performance et l'intégrité des systèmes de combustion. Même si ces phénomènes sont connus depuis plus d'un siècle, éviter quelles aient lieux dans les chambres de combustions industrielles reste difficile. Les objectifs de cette thèse sont les suivants : (1) étudier la dynamique des modes acoustiques, (2) analyser la réponse de flamme d'un moteur de fusée à propergol liquide H2/O2 (appelé "BKD"), sujet aux IC, à l'aide de la Simulation aux Grandes Echelles (SGE) et (3) dériver, utiliser et étudier des conditions limites permettant d'imposer des impédances acoustiques complexes en SGE. / Combustion devices are prone to combustion instabilities. They arise from a constructive coupling between the unsteady heat release rate of the flame and the resonant acoustic modes of the entire system. The occurence of such instabilities can pose a threat to both performance and integrity of combustion systems. Although these phenomena have been known for more than a century, avoiding their appearance in industrial engines is still challenging. The objective of this thesis is threefold: (1) study the dynamics of the resonant acoustic modes, (2) investigate the flame response of a liquid rocket engine under unstable conditions using Large Eddy Simulation(LES) and (3) derive, use and study Time Domain Impedance Boundary Conditions (TDIBCs), i.e. boundary conditions modeling complex acoustic impedances.

Orientador: Marcelo Cristianini / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia de Alimentos / Made available in DSpace on 2018-08-13T10:42:20Z (GMT). No. of bitstreams: 1 Augusto_PedroEstevesDuarte_M.pdf: 2374617 bytes, checksum: 51b7576f4277bc0fdae47e5122fc60fd (MD5) Previous issue date: 2009 / Resumo: A crescente busca por alimentos mais seguros e de melhor qualidade nutricional e sensorial cria a necessidade de melhor entendimento dos processos envolvidos na produção dos mesmos. O tratamento térmico é um dos métodos mais utilizados na conservação de alimentos, sendo o processamento dentro da embalagem um dos mais seguros. A utilização de modelamento matemático da transferência de calor na avaliação de tratamentos térmicos vem se mostrando uma poderosa ferramenta na garantia da segurança sem comprometimento da qualidade nutricional e sensorial dos alimentos. A fluidodinâmica computacional (CFD) vem sendo utilizada em diversos trabalhos para melhor entendimento de processos térmicos de alimentos líquidos. Entretanto, a falta de consistência e uniformidade nas modelagens, aliadas as raras avaliações experimentais das simulações, criam a necessidade de avaliações entre metodologias utilizadas e validações criteriosas. O presente trabalho estudou a transferência de calor durante tratamentos térmicos de alimentos líquidos embalados em garrafas comerciais através de modelagem matemática por CFD. Determinou-se o coeficiente convectivo de transferência de calor (h) para duas garrafas comerciais em um sistema de aquecimento e um de resfriamento em imersão em água. Observou-se que mesmo pequenas diferenças entre geometrias de embalagens resultaram em considerável diferença nos valores de h entre embalagens e sistemas, reforçando a necessidade de avaliação dessa propriedade para cada processo real estudado. Avaliou-se quatro metodologias utilizadas nos trabalhos de CFD para determinação das condições de contorno das simulações, observando-se que as que consideram perfis de temperatura superestimam o fluxo de calor trocado com o produto, podendo comprometer a segurança e conservação do mesmo. A metodologia que considera o fluxo de calor decorrente das condições de contorno h e perfil térmico do meio de aquecimento apresentaram boa concordância com os perfis térmicos experimentais, mostrando-se adequados à modelagem de processos térmicos de alimentos. Caracterizou-se reologicamente um alimento líquido modelo, podendo ser utilizado para simulação de sucos de frutas, assim como a inativação térmica de um microrganismo modelo em processos de pasteurização (Lactobacillus plantarum). Analisou-se as características do tratamento térmico de alimentos líquidos em duas embalagens comerciais, através de perfis de temperatura, velocidade, característica da região de aquecimento mais lento (RAML) e inativação microbiana. Os perfis de temperatura e velocidade obtidos nas simulações de CFD do processo térmico do alimento modelo utilizado se mostraram semelhantes aos reportados na literatura, sendo descritas as características do processo. A análise dos perfis de temperatura obtidos experimentalmente e através do modelo indicaram boa correlação das simulações de CFD, sugerindo a possibilidade de utilização dessa ferramenta para avaliação de perfis térmicos em processos térmicos de alimentos embalados. Entretanto, a análise de validação microbiológica indicou grande desvio entre os valores experimentais e obtidos pelo modelo, atribuído a baixa resistência térmica do microrganismo alvo utilizado nas condições de processo. Nesse caso, mesmo pequenos desvios entre as temperaturas experimentais e obtidas por CFD podem resultar em grande desvio na inativação microbiana final, sugerindo que a utilização de CFD na avaliação de tratamentos térmicos deve ser vista com cautela. Os resultados obtidos comprovam a necessidade de validação dos modelos obtidos através de avaliação de perfil térmico e inativação microbiológica / Abstract: The growing demand for safer and high-quality food products creates the need for better knowledge of the processes involved in food production. Thermal process is one of the safest and most frequently used methods for food preservation, in special when performed in the package. The mathematical modelling of heat transfer is a useful tool for designing safety process while minimizing nutritional and sensory drops. The computational fluid dynamics (CFD) have been widely used for better understand of liquid food thermal process. However, no consistency in the mathematical models built is observed, and just a very few works compare the CFD data with experimental ones. There is a need for the evaluation of the use of CFD for thermal process design. The present work has evaluated the heat transfer in in-package liquid food during thermal process, using mathematical modelling by CFD. The convective heat transfer coefficient (h) among two commercial bottles and a heat and a cooling system were determinated. It was observed that even small differences among packages and heat transfer system result in distinct coefficient and that it must be measured for the exact heat transfer system. Four methodologies were evaluated for the boundary conditions definition of the CFD simulations, based on the previous CFD works. The models that considered the temperature profiles as boundary condition, showed faster heating. By over-estimating the product heating rate, those models are not appropriated for the mathematical modelling of heat process, as it compromises the safety and preservation of food products. The model that considered the measured value of h and temperature profile of the water bath as boundary condition showed good agreement with experimental values, being appropriated for thermal process modelling. The rheological characteristics of a model liquid food was determinated, and the thermal resistance of Lactobacillus plantarum, a target microorganism in pasteurization processes, was evaluated in this model, which can be used as a fruit juice simulator. The thermal process of liquid foods was evaluated in two commercial bottles, using temperature, velocity, slowest heating zone (SHZ) and microbiological inactivation profiles. The temperature and velocity profiles were compatible with those described in CFD works. The thermal profile obtained by CFD shown good correlation with experimental values, suggesting that CFD can be used in thermal process temperature profiles evaluation. Although, the microbiological validation shown large deviation between the experimental values and obtained by the model, probably due the low thermal resistance of the studied microorganism. These results indicate that the CFD utilization in thermal process evaluation might be carefully seen, in especial when the microorganism thermal resistance is low in process conditions. In these situations, even small differences between CFD and experimental temperatures results in considerable microbial inactivation divergence. The results obtained in this work show the need for CFD models evaluation by thermal profile and microbiological inactivation / Mestrado / Mestre em Tecnologia de Alimentos

A model for stress and strain accumulation in strike slip earthquake faults is presented in which a finite width cuboidal fault region is embedded between two cuboidal tectonic plates. Elasto-plastic continuum constitutive equations model the gouge in the fault and the tectonic plates are linear elastic solids obeying the generalised Hooke's law. The model predicts a velocity field which is comparable to surface deformations. The plastic behaviour of the fault material allows the velocities in the tectonic plate to increase to values which are independent of the distance from the fault. Both of the non-trivial stress and strain components accumulate most significantly in the vicinity of the fault. The release of these strains during a dynamic earthquake event would produce the most severe deformations at the fault which is consistent with observations and the notion of an epicenter. The accumulations in the model, however, are at depths larger than would be expected. Plastic strains build up most significantly at the base of the fault which is in yield for the longest length of time but additionally is subject to larger temperatures which makes the material more ductile. The speed of propagation of the elasto-plastic boundary is calculated and its acceleration towards the surface of the fault may be indicative of a dynamic earthquake type event.

En se basant sur un niveau océanique constant, les études des nappes côtières ne considèrent généralement pas l'impact des forçages océaniques. Notre approche combine le suivi à long terme de la « Nappe des Sables » de l'Ermitage (en arrière d'un récif frangeant, La Réunion) avec la réalisation de modèles numériques dans le but de tester l'influence des de ces forçages sur l'évolution de la piézométrie, du front dispersif et des flux transitant le long de la limite océanique. En mettant en parallèle le comportement de la nappe et du domaine océanique (récif), ces travaux présentent l'étude comparative la plus complète d'un système côtier, basée sur un enregistrement en continu d'environ 600 jours. Il apparaît que la géométrie du modèle et les paramètres hydrodynamiques choisis, associés à différents types de forçages océaniques, ont des conséquences variables sur la piézométrie, le front dispersif et les flux. Ainsi, les différentes définitions de limite océanique testées sur des simulations reproduisant la période de suivi montrent que la prise en compte d'une limite océanique complexe en régime transitoire sur cette période génère une meilleure reproductibilité des signaux enregistrés (piézométriques et salinité) que lorsque l'on utilise un niveau océanique moyen constant dans les modèles. Ces résultats mettent en évidence qu'une bonne compréhension des mécanismes hydrodynamiques au sein des nappes côtières implique la mise en place d'un suivi à long terme des phénomènes de forçage océanique qui agissent directement sur la nappe. La caractérisation des différents forçages océaniques nécessite de décomposer le signal global, dont l'analyse en harmonique permet d'identifier les contributions respectives des oscillations périodiques et homogènes de marée et des oscillations brusques et ponctuelles liées à la houle. La modélisation met ici en évidence qu'il est indispensable que la complexité du système naturel soit reproduite de manière réaliste dans les futures études des nappes côtières. Dans cette optique, la combinaison des données hydrogéologiques et océanographiques dans des environnements côtiers où ces approches n'ont, jusqu'à présent, jamais été couplées, permettra de quantifier l'impact des forçages océaniques sur ces milieux. / Studies of coastal aquifers based on a constant mean sea level generally not consider the impact of oceanic oscillations. Our approach combines a long-term recording of “La Nappe des Sables” (adjacent to the fringing reef system of l'Ermitage, La Reunion) with numerical models in order to investigate the influence of these oceanic seasonal oscillations on groundwater hydrodynamics, seawater intrusions and submarine groundwater discharges. Analyzing both the behavior of the aquifer and the oceanic domain (reef), this study integrates a continuous recording of 600 days. It shows that the geometry and the hydrodynamic parameters chosen in the model, correlated to three types of oceanic oscillations, have variable consequences on the hydraulic head, the dispersive front and submarine groundwater discharges. Moreover, taking into account different complex oceanic boundaries in transient simulations over this 600 days period generates a better reproducibility of recorded signals (hydraulic head and salinity). These results underline that a long-term recording of oceanic oscillations is necessary for a good understanding of hydrodynamic mechanisms within coastal aquifers. The global signal must be decomposed with a harmonic analysis in order to identify the respective contributions of wave set up and tidal pumping to this signal. Our models reveal that the complexity of the natural system must be accounted for realistically in future numerical studies. The combination of hydrogeological and oceanographical data will allow the quantification of the impact of oceanic seasonal oscillations on such environments.

As ever more challenging designs are required in present-day industries, the traditional trial-and-error procedure frequently used for designing mechanical parts slows down the design process and yields suboptimal designs, so that new approaches are needed to obtain a competitive advantage. With the ascent of the Finite Element Method (FEM) in the engineering community in the 1970s, structural shape optimization arose as a promising area of application. However, due to the iterative nature of shape optimization processes, the handling of large quantities of numerical models along with the approximated character of numerical methods may even dissuade the use of these techniques (or fail to exploit their full potential) because the development time of new products is becoming ever shorter. This Thesis is concerned with the formulation of a 3D methodology based on the Cartesian-grid Finite Element Method (cgFEM) as a tool for efficient and robust numerical analysis. This methodology belongs to the category of embedded (or fictitious) domain discretization techniques in which the key concept is to extend the structural analysis problem to an easy-to-mesh approximation domain that encloses the physical domain boundary. The use of Cartesian grids provides a natural platform for structural shape optimization because the numerical domain is separated from a physical model, which can easily be changed during the optimization procedure without altering the background discretization. Another advantage is the fact that mesh generation becomes a trivial task since the discretization of the numerical domain and its manipulation, in combination with an efficient hierarchical data structure, can be exploited to save computational effort. However, these advantages are challenged by several numerical issues. Basically, the computational effort has moved from the use of expensive meshing algorithms towards the use of, for example, elaborate numerical integration schemes designed to capture the mismatch between the geometrical domain boundary and the embedding finite element mesh. To do this we used a stabilized formulation to impose boundary conditions and developed novel techniques to be able to capture the exact boundary representation of the models. To complete the implementation of a structural shape optimization method an adjunct formulation is used for the differentiation of the design sensitivities required for gradient-based algorithms. The derivatives are not only the variables required for the process, but also compose a powerful tool for projecting information between different designs, or even projecting the information to create h-adapted meshes without going through a full h-adaptive refinement process. The proposed improvements are reflected in the numerical examples included in this Thesis. These analyses clearly show the improved behavior of the cgFEM technology as regards numerical accuracy and computational efficiency, and consequently the suitability of the cgFEM approach for shape optimization or contact problems. / La competitividad en la industria actual impone la necesidad de generar nuevos y mejores diseños. El tradicional procedimiento de prueba y error, usado a menudo para el diseño de componentes mecánicos, ralentiza el proceso de diseño y produce diseños subóptimos, por lo que se necesitan nuevos enfoques para obtener una ventaja competitiva. Con el desarrollo del Método de los Elementos Finitos (MEF) en el campo de la ingeniería en la década de 1970, la optimización de forma estructural surgió como un área de aplicación prometedora. El entorno industrial cada vez más exigente implica ciclos cada vez más cortos de desarrollo de nuevos productos. Por tanto, la naturaleza iterativa de los procesos de optimización de forma, que supone el análisis de gran cantidad de geometrías (para las se han de usar modelos numéricos de gran tamaño a fin de limitar el efecto de los errores intrínsecamente asociados a las técnicas numéricas), puede incluso disuadir del uso de estas técnicas. Esta Tesis se centra en la formulación de una metodología 3D basada en el Cartesian-grid Finite Element Method (cgFEM) como herramienta para un análisis numérico eficiente y robusto. Esta metodología pertenece a la categoría de técnicas de discretización Immersed Boundary donde el concepto clave es extender el problema de análisis estructural a un dominio de aproximación, que contiene la frontera del dominio físico, cuya discretización (mallado) resulte sencilla. El uso de mallados cartesianos proporciona una plataforma natural para la optimización de forma estructural porque el dominio numérico está separado del modelo físico, que podrá cambiar libremente durante el procedimiento de optimización sin alterar la discretización subyacente. Otro argumento positivo reside en el hecho de que la generación de malla se convierte en una tarea trivial. La discretización del dominio numérico y su manipulación, en coalición con la eficiencia de una estructura jerárquica de datos, pueden ser explotados para ahorrar coste computacional. Sin embargo, estas ventajas pueden ser cuestionadas por varios problemas numéricos. Básicamente, el esfuerzo computacional se ha desplazado. Del uso de costosos algoritmos de mallado nos movemos hacia el uso de, por ejemplo, esquemas de integración numérica elaborados para poder capturar la discrepancia entre la frontera del dominio geométrico y la malla de elementos finitos que lo embebe. Para ello, utilizamos, por un lado, una formulación de estabilización para imponer condiciones de contorno y, por otro lado, hemos desarrollado nuevas técnicas para poder captar la representación exacta de los modelos geométricos. Para completar la implementación de un método de optimización de forma estructural se usa una formulación adjunta para derivar las sensibilidades de diseño requeridas por los algoritmos basados en gradiente. Las derivadas no son sólo variables requeridas para el proceso, sino una poderosa herramienta para poder proyectar información entre diferentes diseños o, incluso, proyectar la información para crear mallas h-adaptadas sin pasar por un proceso completo de refinamiento h-adaptativo. Las mejoras propuestas se reflejan en los ejemplos numéricos presentados en esta Tesis. Estos análisis muestran claramente el comportamiento superior de la tecnología cgFEM en cuanto a precisión numérica y eficiencia computacional. En consecuencia, el enfoque cgFEM se postula como una herramienta adecuada para la optimización de forma. / Actualment, amb la competència existent en la industria, s'imposa la necessitat de generar nous i millors dissenys . El tradicional procediment de prova i error, que amb freqüència es fa servir pel disseny de components mecànics, endarrereix el procés de disseny i produeix dissenys subòptims, pel que es necessiten nous enfocaments per obtindre avantatge competitiu. Amb el desenvolupament del Mètode dels Elements Finits (MEF) en el camp de l'enginyeria en la dècada de 1970, l'optimització de forma estructural va sorgir com un àrea d'aplicació prometedora. No obstant això, a causa de la natura iterativa dels processos d'optimització de forma, la manipulació dels models numèrics en grans quantitats, junt amb l'error de discretització dels mètodes numèrics, pot fins i tot dissuadir de l'ús d'aquestes tècniques (o d'explotar tot el seu potencial), perquè al mateix temps els cicles de desenvolupament de nous productes s'estan acurtant. Esta Tesi se centra en la formulació d'una metodologia 3D basada en el Cartesian-grid Finite Element Method (cgFEM) com a ferramenta per una anàlisi numèrica eficient i sòlida. Esta metodologia pertany a la categoria de tècniques de discretització Immersed Boundary on el concepte clau és expandir el problema d'anàlisi estructural a un domini d'aproximació fàcil de mallar que conté la frontera del domini físic. L'utilització de mallats cartesians proporciona una plataforma natural per l'optimització de forma estructural perquè el domini numèric està separat del model físic, que podria canviar lliurement durant el procediment d'optimització sense alterar la discretització subjacent. A més, un altre argument positiu el trobem en què la generació de malla es converteix en una tasca trivial, ja que la discretització del domini numèric i la seua manipulació, en coalició amb l'eficiència d'una estructura jeràrquica de dades, poden ser explotats per estalviar cost computacional. Tot i això, estos avantatges poden ser qüestionats per diversos problemes numèrics. Bàsicament, l'esforç computacional s'ha desplaçat. De l'ús de costosos algoritmes de mallat ens movem cap a l'ús de, per exemple, esquemes d'integració numèrica elaborats per poder capturar la discrepància entre la frontera del domini geomètric i la malla d'elements finits que ho embeu. Per això, fem ús, d'una banda, d'una formulació d'estabilització per imposar condicions de contorn i, d'un altra, desevolupem noves tècniques per poder captar la representació exacta dels models geomètrics Per completar la implementació d'un mètode d'optimització de forma estructural es fa ús d'una formulació adjunta per derivar les sensibilitats de disseny requerides pels algoritmes basats en gradient. Les derivades no són únicament variables requerides pel procés, sinó una poderosa ferramenta per poder projectar informació entre diferents dissenys o, fins i tot, projectar la informació per crear malles h-adaptades sense passar per un procés complet de refinament h-adaptatiu. Les millores proposades s'evidencien en els exemples numèrics presentats en esta Tesi. Estes anàlisis mostren clarament el comportament superior de la tecnologia cgFEM en tant a precisió numèrica i eficiència computacional. Així, l'enfocament cgFEM es postula com una ferramenta adient per l'optimització de forma. / Marco Alacid, O. (2017). Structural Shape Optimization Based On The Use Of Cartesian Grids [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/86195 / TESIS

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Cette thèse est consacrée à l'étude des équations du Darcy Brinkman Forchheimer (DBF) avec des conditions aux limites non standards. Nous montrons d'abord l'existence de différents type de solutions (faible, forte) correspondant au problème DBF stationnaire dans un domaine simplement connexe avec des conditions portants sur la composante normale du champ de vitesse et la composante tangentielle du tourbillon. Ensuite, nous considérons le système Brinkman Forchheimer (BF) avec des conditions sur la pression dans un domaine non simplement connexe. Nous prouvons que ce problème est bien posé ainsi que l'existence de la solution forte. Nous établissons la régularité de la solution dans les espaces L^p pour p >= 2.L'étude et l'approximation du problème DBF non stationnaire est basée sur une approche pseudo-compressibilité. Une estimation d'erreur d'ordre deux est établie dans le cas o\`u les conditions aux limites sont de types Dirichlet ou Navier.Enfin, une méthode d'éléments finis Galerkin Discontinue est proposée et la convergence établie concernant le problème DBF linéarisé et le système DBF non linéaire avec des conditions aux limites non standard. / This thesis is devoted to Darcy Brinkman Forchheimer (DBF) equations with a non standard boundary conditions. We prove first the existence of different type of solutions (weak, strong) of the stationary DBF problem in a simply connected domain with boundary conditions on the normal component of the velocity field and the tangential component of the vorticity. Next, we consider Brinkman Forchheimer (BF) system with boundary conditions on the pressure in a non simply connected domain. We prove the well-posedness and the existence of a strong solution of this problem. We establish the regularity of the solution in the L^p spaces, for p >= 2.The approximation of the non stationary DBF problem is based on the pseudo-compressibility approach. The second order's error estimate is established in the case where the boundary conditions are of type Dirichlet or Navier. Finally, the finite elements Galerkin Discontinuous method is proposed and the convergence is settled concerning the linearized DBF problem and the non linear DBF system with a non standard boundary conditions.

Establishing dynamic characteristics of structures is a challenging area of research. The dynamic characteristics of structures, such as natural frequencies, modeshapes, response levels and damping characteristics play an important role in identifying the condition of the structures. The assumed modes method is a particular analytical method used to estimate the dynamic characteristics of a structure. However, the eigenfunctions used in the assumed mode method often led to ill-conditioning due to the presence of hyperbolic functions. Furthermore, a change in the boundary conditions of the system usually necessitates a change in the choice of assumed mode. In this thesis, a set of Alternative Admissible Functions (AAF), along with penalty functions, are used to obtain closed form solutions for an Euler-Bernoulli beam with various boundary conditions. A key advantage of the proposed approach is that the choice of AAF does not depend on the boundary conditions since the boundary conditions are modelled via penalty functions. The mathematical formulation is validated with different boundary conditions, Clamped-Free (CF), Simply-Supported (SS), and Clamped-Clamped (CC). A specific relation between the penalty function and the system parameters are established for CF, SS and CC boundary conditions to obtain appropriate values of penalties. Validation of results with the reported literature indicates excellent agreement when compared with closed-form Euler-Bernoulli beam values. The AAF approach with penalties is extended to a beam with a shallow crack to estimate the dynamic characteristics. The crack is modelled as a penalty function via a massless rotational spring. This model has the advantage of simplifying parametric studies, because of its discrete nature, allowing easy modification in the crack position and depth of the crack. Therefore, once the model is established, various practical applications may be performed without reformulation of the problem. Validation of results with the reported literature on beams with shallow cracks indicates the suitability of the proposed approach.