O presente trabalho tem por objetivo desenvolver uma formulação numérica baseada em Análise Isogeométrica para o estudo de problemas de interação fluido-estrutura (IFE) em aplicações envolvendo corpos rígidos submersos, onde escoamentos incompressíveis de fluidos Newtonianos com superfície livre são considerados. Propõe-se o emprego da Análise Isogeométrica por permitir a unificação entre os procedimentos de pré-processamento e análise, melhorando assim as condições de continuidade das funções de base empregadas tanto na discretização espacial do problema como na aproximação das variáveis do sistema de equações. O sistema de equações fundamentais do escoamento é formado pelas equações de Navier-Stokes e pela equação da conservação de massa, descrita segundo a hipótese de pseudo-compressibilidade, em uma formulação cinemática ALE (Arbitrary Lagrangean- Eulerian). A consideração da superfície livre no escoamento se dá tratando o fluido como um meio bifásico, através do método Level Set. O corpo rígido apresenta não linearidade na rotação e restrições representadas por vínculos elásticos e amortecedores viscosos, sendo a equação de equilíbrio dinâmico resolvida através do método de Newmark. O esquema de acoplamento sólido-fluido adotado é o particionado convencional, que impõe condições de compatibilidade cinemáticas e de equilíbrio sobre a interface sólido-fluido, analisando ambos os meios de maneira sequencial. A discretização das equações governantes é realizada através do esquema explícito de dois passos de Taylor-Galerkin, aplicado no contexto da Análise Isogeométrica. Por fim, são analisados alguns problemas da Dinâmica de Fluidos Computacional, de onde se concluiu que os resultados obtidos são bastante consistentes com os fenômenos envolvidos, com as ferramentas exclusivas da Análise Isogeométrica, como o refinamento k, melhorando a convergência dos resultados. Para escoamentos bifásicos, verificou-se que o método Level Set obteve resultados bastante promissores apresentando, entretanto, uma dissipação numérica excessiva. Propõe-se, para estudos futuros, a elaboração de esquemas numéricos que conservem melhor o volume da fase líquida do escoamento. / The present work aims to development of a numerical formulation based on Isogeometric Analysis for the study of Fluid-Structure Interaction problems in applications involving rigid bodies submerged, considering incompressible Newtonian flows with free surface. The use of the Isogeometric Analysis allows unification between the preprocessing and analysis steps, improving then the continuity of the base functions employed, both in the spatial discretization and approximation of the variables in the system of equations. The fundamental flow equations are formed by the Navier-Stokes and the mass conservation, described by de pseudo-compressibility hypothesis, in an ALE (Arbitrary Lagrangean-Eulerian) kinematic formulation. The free surface consideration of the flow is handled treating the fluid like a two- phase medium, using the Level Set method. The rigid body considers nonlinearity in rotation, and restrictions represented by elastic springs and viscous dampers, with the dynamic equilibrium equation being resolved using the Newmark’s method. The solid-fluid coupling scheme is the conventional partitioned, which imposes kinematics and equilibrium compatibility conditions on the solid-fluid interface, analyzing both mediums in a sequential manner. The governing equations are discretized using the explicit two step Taylor-Galerkin method, applied in an Isogeometric Analisys context. Finally, some Computational Fluid Dinamics problems are analysed, from which it was concluded that the results obtained are quite consistent with phenomena involved, with the unique tools of Isogeometric Analysis, such as k-refinement, improving the convergence of the results. For biphasic flows, it was verified that the Level Set method obtained very promising results, presenting, however, an excessive numerical dissipation. For future studies, it is proposed the elaboration of numerical schemes that better preserve the volume of the liquid phase of the flow.

O presente trabalho tem por objetivo desenvolver uma formulação numérica baseada em Análise Isogeométrica para o estudo de problemas de interação fluido-estrutura (IFE) em aplicações envolvendo corpos rígidos submersos, onde escoamentos incompressíveis de fluidos Newtonianos com superfície livre são considerados. Propõe-se o emprego da Análise Isogeométrica por permitir a unificação entre os procedimentos de pré-processamento e análise, melhorando assim as condições de continuidade das funções de base empregadas tanto na discretização espacial do problema como na aproximação das variáveis do sistema de equações. O sistema de equações fundamentais do escoamento é formado pelas equações de Navier-Stokes e pela equação da conservação de massa, descrita segundo a hipótese de pseudo-compressibilidade, em uma formulação cinemática ALE (Arbitrary Lagrangean- Eulerian). A consideração da superfície livre no escoamento se dá tratando o fluido como um meio bifásico, através do método Level Set. O corpo rígido apresenta não linearidade na rotação e restrições representadas por vínculos elásticos e amortecedores viscosos, sendo a equação de equilíbrio dinâmico resolvida através do método de Newmark. O esquema de acoplamento sólido-fluido adotado é o particionado convencional, que impõe condições de compatibilidade cinemáticas e de equilíbrio sobre a interface sólido-fluido, analisando ambos os meios de maneira sequencial. A discretização das equações governantes é realizada através do esquema explícito de dois passos de Taylor-Galerkin, aplicado no contexto da Análise Isogeométrica. Por fim, são analisados alguns problemas da Dinâmica de Fluidos Computacional, de onde se concluiu que os resultados obtidos são bastante consistentes com os fenômenos envolvidos, com as ferramentas exclusivas da Análise Isogeométrica, como o refinamento k, melhorando a convergência dos resultados. Para escoamentos bifásicos, verificou-se que o método Level Set obteve resultados bastante promissores apresentando, entretanto, uma dissipação numérica excessiva. Propõe-se, para estudos futuros, a elaboração de esquemas numéricos que conservem melhor o volume da fase líquida do escoamento. / The present work aims to development of a numerical formulation based on Isogeometric Analysis for the study of Fluid-Structure Interaction problems in applications involving rigid bodies submerged, considering incompressible Newtonian flows with free surface. The use of the Isogeometric Analysis allows unification between the preprocessing and analysis steps, improving then the continuity of the base functions employed, both in the spatial discretization and approximation of the variables in the system of equations. The fundamental flow equations are formed by the Navier-Stokes and the mass conservation, described by de pseudo-compressibility hypothesis, in an ALE (Arbitrary Lagrangean-Eulerian) kinematic formulation. The free surface consideration of the flow is handled treating the fluid like a two- phase medium, using the Level Set method. The rigid body considers nonlinearity in rotation, and restrictions represented by elastic springs and viscous dampers, with the dynamic equilibrium equation being resolved using the Newmark’s method. The solid-fluid coupling scheme is the conventional partitioned, which imposes kinematics and equilibrium compatibility conditions on the solid-fluid interface, analyzing both mediums in a sequential manner. The governing equations are discretized using the explicit two step Taylor-Galerkin method, applied in an Isogeometric Analisys context. Finally, some Computational Fluid Dinamics problems are analysed, from which it was concluded that the results obtained are quite consistent with phenomena involved, with the unique tools of Isogeometric Analysis, such as k-refinement, improving the convergence of the results. For biphasic flows, it was verified that the Level Set method obtained very promising results, presenting, however, an excessive numerical dissipation. For future studies, it is proposed the elaboration of numerical schemes that better preserve the volume of the liquid phase of the flow.

O presente trabalho trata da formulação e implementação de modelos numéricos baseados no Método dos Elementos de Contorno (MEC). Inspirando-se em problemas de engenharia, uma abordagem multidisciplinar é proposta como meio de representação numérica mais realista. Há materiais de uso corrente na engenharia que possuem resposta dependente do tempo. Nesta tese os fenômenos dependentes do tempo são abordados por meio da Mecânica Viscoelástica Linear associada a modelos reológicos. Neste trabalho, se apresenta a dedução do modelo constitutivo de Maxwell para ser utilizado via MEC. As equações deduzidas são verificadas em problemas de referência. Os resultados mostram que a formulação deduzida pode ser utilizada para representar estruturas compostas, mesmo em casos envolvendo uma junção entre materiais viscoelásticos e não viscoelásticos. Adicionalmente as formulações apresentadas se mantém estáveis na presença de fissuras de domínio e bordo. Verifica-se que a formulação clássica dual pode ser utilizada para simular o comportamento de fissuras com resposta dependente do tempo. Essa constatação serve de base para maiores investigações no campo da Mecânica da Fratura de materiais viscoelásticos. Na sequência, mostra-se como o MEC pode ser aliado a conceitos probabilísticos para fazer estimativas de comportamentos a longo prazo. Estas estimativas incluem as incertezas inerentes nos processos de engenharia. As incertezas envolvem os parâmetros materiais, de carregamento e de geometria. Por meio do conceito de probabilidade de falha, os resultados mostram que as incertezas relacionadas às estimativas das cargas atuantes apresentam maior impacto no desempenho esperado a longo prazo. Esta constatação serve para realizar estudos que colaborem para a melhoria dos processos de concepção estrutural. Outro aspecto de interesse desta tese é a busca de formas otimizadas, por meio da Otimização Topológica. Neste trabalho, um algoritmo alternativo de otimização topológica é proposto. O algoritmo é baseado no acoplamento entre o Método Level Set (MLS) e o MEC. A diferença entre o algoritmo aqui proposto, e os demais presentes na literatura, é forma de obtenção do campo de velocidades. Nesta tese, os campos normais de velocidades são obtidos por meio da sensibilidade à forma. Esta mudança torna o algoritmo propício a ser tratado pelo MEC, pois as informações necessárias para o cálculo das sensibilidades residem exclusivamente no contorno. Verifica-se que o algoritmo necessita de uma extensão particular de velocidades para o domínio a fim de manter a estabilidade. Limitando-se a casos bidimensionais, o algoritmo é capaz de obter os conhecidos casos de referência reportados pela literatura. O último aspecto tratado nesta tese retrata a maneira pela qual as incertezas geométricas podem influenciar na determinação das estruturas otimizadas. Utilizando o MEC, propõe-se um critério probabilístico que permite embasar escolhas levando em consideração a sensibilidade geométrica. Os resultados mostram que os critérios deterministas, nem sempre, conduzem às escolhas mais adequadas sob o ponto de vista de engenharia. Assim, este trabalho contribui para a expansão e difusão das aplicações do MEC em problemas de engenharia de estruturas. / The present work deals with the formulation and implementation of numerical models based on the Boundary Element Method (BEM). Inspired by engineering problems, a multidisciplinary combination is proposed as a more realistic approach. There are common engineering materials that have time-dependent response. In this thesis, time-dependent phenomena are approached through the Linear Viscoelastic Mechanics associated with rheological models. In this work, the formulation of Maxwell\'s constitutive model is presented to be used via MEC. The resultant equations are checked on reference problems. The results show that the presented formulation can be used to represent composite structures, even in cases involving a junction between viscoelastic and non-viscoelastic materials. Additionally the formulations presented remain stable in the presence of cracks. It is found that the classical DUAL-BEM formulation can be used to simulate cracks with time-dependent behaviour. This result serves as the basis for further investigations in the field of Fracture Mechanics of viscoelastic materials. In the sequence, it is shown how the BEM can be associated with probabilistic concepts to make predictions of long-term behaviour. These predictions include the inherent uncertainties in engineering processes. The uncertainties involve the material, loading and geometry parameters. Using the concept of probability of failure, the results show that the uncertainties related to the estimations of loads have important impact on the long-term expected performance. This finding serves to carry out studies that collaborate for the improvement of structural design processes. Another aspect of interest of this thesis is the search for optimized forms through Topological Optimization. In this work, an alternative topological optimization algorithm is proposed. The algorithm is based on the coupling between the Level Set Method (LSM) and BEM. The difference between the algorithm proposed here, and the others present in the literature, is a way of obtaining the velocity field. In this thesis, the normal fields of velocities are obtained by means of shape sensitivity. This change makes the algorithm adequate to be treated by the BEM, since the information necessary for the calculation of the sensitivities resides exclusively in the contour. It is found that the algorithm requires a particular velocity extension in order to maintain stability. Limiting to two-dimensional cases, the algorithm is able to obtain the known benchmark cases reported in the literature. The last aspect addressed in this thesis involves the way in which geometric uncertainties can influence the determination of optimized structures. Using the BEM, it is proposed a probabilistic criterion that takes into consideration the geometric sensitivity. The results show that deterministic criteria do not always lead to the most appropriate choices from an engineering point of view. In summary, this work contributes to the expansion and diffusion of MEC applications in structural engineering problems.

Image segmentation is the problem of partitioning an image into meaningful parts, often consisting of an object and background. As an important part of many imaging applications, e.g. face recognition, tracking of moving cars and people etc, it is of general interest to design robust and fast segmentation algorithms. However, it is well accepted that there is no general method for solving all segmentation problems. Instead, the algorithms have to be highly adapted to the application in order to achieve good performance. In this thesis, we will study segmentation methods for blood vessels in medical images. The need for accurate segmentation tools in medical applications is driven by the increased capacity of the imaging devices. Common modalities such as CT and MRI generate images which simply cannot be examined manually, due to high resolutions and a large number of image slices. Furthermore, it is very difficult to visualize complex structures in three-dimensional image volumes without cutting away large portions of, perhaps important, data. Tools, such as segmentation, can aid the medical staff in browsing through such large images by highlighting objects of particular importance. In addition, segmentation in particular can output models of organs, tumors, and other structures for further analysis, quantification or simulation. We have divided the segmentation of blood vessels into two parts. First, we model the vessels as a collection of lines and edges (linear structures) and use filtering techniques to detect such structures in an image. Second, the output from this filtering is used as input for segmentation tools. Our contributions mainly lie in the design of a multi-scale filtering and integration scheme for de- tecting vessels of varying widths and the modification of optimization schemes for finding better segmentations than traditional methods do. We validate our ideas on synthetical images mimicking typical blood vessel structures, and show proof-of-concept results on real medical images.

L'objectif de cette thèse est de trouver la forme optimale d'une antenne planaire ou d'un réseau d'antennes planaires à partir de contraintes imposées (diagramme de rayonnement, gain ou directivité) ou de reconstruire la forme à partir de mesures expérimentales. L'algorithme d'optimisation développé est basé sur une méthode de type gradient et la reconstruction des contours par une méthode d'ensembles de niveaux (Level Sets) ou "contours actifs". Le problème direct est résolu en utilisant une formulation intégrale du problème électromagnétique et une méthode d'éléments finis pour la discrétisation. Le gradient de forme est calculé en utilisant deux méthodes différentes. Tout d'abord, une méthode par différences finies basée sur la dérivée à un nœud du maillage, pour une modification infinitésimale des éléments triangulaires du contour, suivant la direction de la normale extérieure. La deuxième méthode est basée sur le gradient topologique pour le calcul de la déformation des contours. Une méthode d'ensembles de niveaux avec bande étroite a été développée pour faire évoluer le contour des antennes utilisant la vitesse de déformation calculée à partir du gradient de forme. Différentes configurations d'antennes et réseaux d'antennes planaires ont été utilisées pour étudier les performances de l'algorithme d'optimisation. Des techniques de type saut de fréquence et multifréquence ont été utilisées pour optimiser la forme dans une bande de fréquence. L'optimisation de forme pour la miniaturisation d'antennes planaires concerne de nombreuses applications, en particulier, pour les réseaux réflecteurs / The objective of this thesis work is to find the optimal shape of planar antenna elements and arrays from imposed constraints (e.g. desired or imposed radiation patterns, gain or directivity) or to reconstruct the shape from experimental measurements. The optimization algorithm is based on the gradient-type method and an active contour reconstruction by means of the Level Set method. The forward problem is solved using an integral formulation of the EM problem with finite element discretization. The shape gradient is computed using two different methods: one is finite differential method based on nodal point mesh derivation with an infinitesimal modification of the triangular elements on the contour along the outward normal direction, another the topological shape gradient, which is computed based on a topological deformation on a contour. A narrow band level set method has been developed to evolve the contour of antennas and arrays using the deformation velocity computed from the shape gradient. Different configurations of antennas and antenna arrays are studied for investigating the performance of the optimization algorithm. Frequency hopping and multi-frequency techniques have been used for optimizing the shape within a frequency band. Shape optimization for planar antenna miniaturization has a large number of applications, particularly, for reflectarrays

Performing tasks with a robotic hand often requires a complete knowledge of the manipulated object, including its properties (shape, rigidity, surface texture) and its location in the environment, in order to ensure safe and efficient manipulation. While well-established procedures exist for the manipulation of rigid objects, as well as several approaches for the manipulation of linear or planar deformable objects such as ropes or fabric, research addressing the characterization of deformable objects occupying a volume remains relatively limited. The fundamental objectives of this research are to track the deformation of non-rigid objects under robotic hand manipulation using RGB-D data, and to automatically classify deformable objects as either rigid, elastic, plastic, or elasto-plastic, based on the material they are made of, and to support recognition of the category of such objects through a robotic probing process in order to enhance manipulation capabilities. The goal is not to attempt to formally model the material of the object, but rather employ a data-driven approach to make decisions based on the observed properties of the object, capture implicitly its deformation behavior, and support adaptive control of a robotic hand for other research in the future. The proposed approach advantageously combines color image and point cloud processing techniques, and proposes a novel combination of the fast level set method with a log-polar mapping of the visual data to robustly detect and track the contour of a deformable object in a RGB-D data stream. Dynamic time warping is employed to characterize the object properties independently from the varying length of the detected contour as the object deforms. The research results demonstrate that a recognition rate over all categories of material of up to 98.3% is achieved based on the detected contour. When integrated in the control loop of a robotic hand, it can contribute to ensure stable grasp, and safe manipulation capability that will preserve the physical integrity of the object.

Dans le cadre de la simulation du procédé de consolidation de pièces céramiques ou composites CerMet par frittage, cette thèse se propose de modéliser et de simuler deux aspects particuliers du frittage. Le premier consiste à prendre en compte l'effet d'éléments dopants sur l'évolution microstructurale d'un élément volumique représentatif d'un compact de poudre. Pour cela les chemins de diffusion tels que la diffusion volumique et de surface sont pris en compte. Le second aspect est en relation avec l'élaboration de matériaux composites à dispersoïdes et l'étude de l'évolution de leur microstructure par simulation numérique selon les caractéristiques des inclusions ne participant pas au processus de frittage. Ces simulations reposent sur le développement de la méthode Level-Set qui permet de suivre tous les changements de topologie qui interviennent au cours du frittage à l'échelle des grains.Des résultats concluants ont été obtenus à partir de la simulation de l'effet du dopage, dans le cas particulier de l'alumine dopée magnésie, puis généralisés au cas du codopage. Pour les multimatériaux, la première étape de la modélisation a consisté à considérer des inclusions ayant le même type de loi de comportement que la matrice céramique, à savoir élastique, linéaire et isotrope. Cependant, les propriétés des matériaux seront différentes. Du point de vue numérique, la complexité du problème a consisté à bien gérer les deux phases solides, et en particulier leur interface commune en vue de la résolution de l'équilibre mécanique par éléments finis, en utilisant plusieurs fonctions Level-Set. / In the framework of the numerical modelling of ceramic powder consolidation or CerMet composites by sintering, this work aims to model and to simulate two aspects of sintering. The first it is to study the doping effect on microstructural evolution of a powder compact, taking into account the main diffusion routes as volume and surface diffusion. The second aspect aims to simulate the evolution of a continue ceramic matrix phase containing a dispersoïde of inclusions that are inert to the diffusion phenomena. Interesting results are obtained in the simulation of the doping effect, and are generalized to the codoping case thanks to the Level-Set method adoped. It is important to recall that the Level-Set method is able to handle topological changes occuring during the simulation. Concerning the multimaterials, a first approach considers that both inclusions and the ceramic matrix have the same constituve elastic, linear and isotropic law but with different materials properties. Numerically, the complexity appears when managing the solid phases (matrix and inclusions), particulary their interface when the momentum conservation problem is solved by finite elements. The diffusion problem is then solved like in the case of the doping effect simulations. Numerical simulations of granular compacts are held to evaluate the dopant and the inclusions effect.

Since the inverse problem in Diffusive Optical Tomography (DOT) is nonlinear and severely ill-posed, only low resolution reconstructions are feasible when noise is added to the data nowadays. The purpose of this thesis is to improve image reconstruction in DOT of the main optical properties of tissues with some novel mathematical methods. We have used the Landweber (L) method, the Landweber-Kaczmarz (LK) method and its improved Loping-Landweber-Kaczmarz (L-LK) method combined with sparsity or with total variation regularizations for single and simultaneous image reconstructions of the absorption and scattering coefficients. The sparsity method assumes the existence of a sparse solution which has a simple description and is superposed onto a known background. The sparsity method is solved using a smooth gradient and a soft thresholding operator. Moreover, we have proposed an improved sparsity method. For the total variation reconstruction imaging, we have used the split Bregman method and the lagged diffusivity method. For the total variation method, we also have implemented a memory-efficient method to minimise the storage of large Hessian matrices. In addition, an individual and simultaneous contrast value reconstructions are presented using the level set (LS) method. Besides, the shape derivative of DOT based on the RTE is derived using shape sensitivity analysis, and some reconstructions for the absorption coefficient are presented using this shape derivative via the LS method.\\Whereas most of the approaches for solving the nonlinear problem of DOT make use of the diffusion approximation (DA) to the radiative transfer equation (RTE) to model the propagation of the light in tissue, the accuracy of the DA is not satisfactory in situations where the medium is not scattering dominant, in particular close to the light sources and to the boundary, as well as inside low-scattering or non-scattering regions. Therefore, we have solved the inverse problem in DOT by the more accurate time-dependant RTE in two dimensions.

La première préoccupation de cette thèse est le problème de deux fluides ou un fluide à deux phases, c’est-à-dire que nous nous sommes intéressés à la simulation d’écoulements impliquant deux ou plusieurs fluides visqueux incompressibles immiscibles de propriétés mécaniques et rhéologiques différentes. Dans ce contexte, nous avons considéré que l’interface mobile entre les deux fluides est représentée par la ligne de niveau zéro d’une fonction ligne de niveau et régie par l’équation d’advection, où le champ advectant est la solution des équations de Navier-Stokes. La plupart des méthodes de capture d’interface utilisent une grille cartésienne fixe au cours de la simulation. Contrairement à ces approches, la nôtre est fortement basée sur l’adaptation de maillage, notamment au voisinage de l’interface. Cette adaptation de maillage permet une représentation précise de l’interface, à l’aide de ses propriétés géométriques, avec un nombre de degrés de liberté minimal.La résolution d'un problème à deux fluides est résumée par les étapes suivantes:- Résoudre les équations de Navier-Stokes par la méthode de Lagrange-Galerkin d’ordre 1;- Traitement géométrique la tension de surface se basant sur la discrétisation explicite de l'interface dans le domaine de calcul;- Résoudre l'équation d’advection par la méthode des caractéristiques;- Les techniques de l'adaptation de maillage.On propose ici un schéma entre l’advection de l’interface, la résolution des équations de Navier-Stokes et l’adaptation de maillage. Certains résultats des exemples classiques pour les deux problèmes de monofluide et bifluide comme la cavité entrainée, la rémontée d’une bulle, la coalescence de deux bulles et les instabilités Rayleigh-Taylor sont étudiés en deux et trois dimensions.La deuxième partie de cette thèse est liée à l'optimisation des formes en mécanique des fluides. Nous construisons un schéma numérique en utilisant la méthode des lignes de niveau et l’adaptation de maillage dans le contexte des systèmes de Stokes. Le calcul de la sensibilité de la fonction objective est liée à la méthode de variation des limites d’Hadamard et les dérivées des formes sont calculées par la méthode de Céa. Un exemple numérique avec la fonction objective de la dissipation d'énergie est présenté pour évaluer l'efficacité et la fiabilité du schéma proposé. / The first concern of this thesis is the problem of two fluids flow or two-phase flow, i.e weare interested in the simulation of the evolution of an interface (or a free surface) between twoimmiscible viscous fluids or two phases of a fluid. We propose a general scheme for solving two fluids flow or two-phase flow which takes advantage of the flexibility of the level set method for capturing evolution of the interfaces, including topological changes. Unlike similar approaches that solve the flow problem and the transport equation related to the evolution of the interface on Cartesian grids, our approach relies on an adaptive unstructured mesh to carry out these computations and enjoys an exact and accurate description of the interface. The explicit representation of the manifold separating the two fluids will be extracted to compute approximately the surface tension as well as some algebraic quantities like the normal vector and the curvature at the interface.In a nutshell, the resolution of a two-fluid problem is summarized by the steps involves thefollowing ingredients:– solving incompressible Navier-Stokes equations by the first order Lagrange-Galerkin method;– geometrical treatment to evaluate the surface tension basing on the explicit discretisation of the interface;– solving the level set advection by method of characteristics; – the techniques of mesh adaptation.It is obvious that no numerical method is completely exact in solving the PDE problemat hand, hence, we need a discretized computational domain. However, the accuracy of numericalsolutions or the mass loss/gain can generally be improved with mesh refinement. The question thatarises is related to where and how to refine the mesh. At each time, our mesh adaptation producesthe adapted mesh based on the geometric properties of the interface and the physical properties ofthe fluid, simply speaking, only one adapted mesh at each time step to assume both the resolutionof Navier-Stokes and the advection equations. It answers to the need for an accurate representationof the interface and an accurate approximation of the velocity of fluids with a minimal number ofelements, then decreasing the amount of computational time. Some results of the classical examples for both problems of monofluid and bifluid flows as : lid-driven cavity, rising bubble, coalescence of two bubbles, and Rayleigh-Taylor instability are investigated in two and three dimensions.The second part of this thesis is related to shape optimization in fluid mechanics. We construct a numerical scheme using level set method and mesh adaptation in the context of Stokes systems. The computation of the sensitivity of objective function is related to the Hadamard’s boundary variation method and the shape derivatives is computed by Céa’s formal method. A numerical example with theobjective function of energy dissipation is presented to assess the efficiency and the reliability of theproposed scheme.

Cette thèse montre le développement d’un code de calcul pour les simulations numériques directes d’écoulements diphasiques compressibles avec évaporation. Un couplage entre les méthodes Level Set et VOF est réalisé pour le suivi d’interface. Afin de résoudre les équations de la mécanique des fluides, une méthode basée sur la pression est employée et, pour découpler la vitesse de la pression, une méthode de projection est effectuée. Cette méthode permet l’implicitation des termes liés à l’acoustique et donc de diminuer la contrainte sur le pas de temps. Le liquide et le gaz sont traités de manière compressible permettant des variations locales des masses volumiques grâce à l’utilisation d’équations d’état. L’évaporation est simulée de deux manières différentes ; une première, où un taux d’évaporation constant est employé et une seconde, où ce taux est calculé par la thermique. Parallèlement à ce sujet, une étude de la distribution des courbures dans une injection de liquide est réalisée. Cette étude permet d’étendre le concept de distribution des tailles de gouttes dans un spray et d’améliorer les informations disponibles dans le modèle ELSA. Enfin, une autre étude est effectuée sur la recherche d’un critère, basé sur les courbures à l’interface, pour estimer la qualité d’une simulation. / This PhD thesis shows the development of a numerical method for solving two-phase flows with vaporisation. A coupling between Level Set and VOF methods is realised for the interface capturing. In order to solve fluid mechanics equations, a pressure based method is employed and, to decouple velocity and pressure, a projection method is performed. This method allows the implicitation of the acoustic terms and the time step constraint reduction. Liquid and gas are considered as compressible allowing local density variations with equations of state. The vaporisation is computed in two different ways ; a first one where the vaporisation rate is constant and a second one, where this rate is calculated by thermodynamics. Along with this topic, a study on curvature distribution in a liquid injection configuration is realised. This study allows to extend the drop size distribution concept in a spray and to improve available informations on ELSA model. Finally, an other study is performed on thedevelopment of a criterion, based on interface curvatures, which estimates the quality of a simulation.