Dans cette thèse, nous proposons de nouvelles méthodes permettant de résoudre numériquement des problèmes de diffraction harmoniques et tridimensionnels, aussi bien acoustiques qu'électromagnétiques, pour lesquels l'objet diffractant est pénétrable et inhomogène. La résolution de tels problèmes est centrale pour des calculs de surfaces équivalentes sonar et radar (SES et SER). Elle est toutefois connue pour être difficile car elle requiert de discrétiser des équations aux dérivées partielles posées dans un domaine extérieur. Étant infini, ce domaine ne peut pas être maillé en vue d'une résolution par la méthode des éléments finis volumiques. Deux approches classiques permettent de contourner cette difficulté. La première consiste à tronquer le domaine extérieur et rend alors possible une résolution par la méthode des éléments finis volumiques. Étant donné qu'elles approximent les problèmes de diffraction au niveau continu, les méthodes de troncature de domaine peuvent toutefois manquer de précision pour des calculs de SES et de SER. Les problèmes de diffraction harmoniques, pénétrables et inhomogènes peuvent également être résolus en couplant une formulation variationnelle volumique associée à l'objet diffractant et des équations intégrales surfaciques rattachées au domaine extérieur. Nous parlons de couplages FEM-BEM (Finite Element Method-Boundary Element Method). L'intérêt de cette approche réside dans le fait qu'elle est exacte au niveau continu. Les couplages FEM-BEM classiques sont dits forts car ils couplent la formulation variationnelle volumique et les équations intégrales surfaciques au sein d'une même formulation. Ils ne sont toutefois pas adaptés à la résolution de problèmes à haute fréquence. Pour pallier cette limitation, d'autres couplages FEM-BEM, dits faibles, ont été proposés. Ils correspondent concrètement à des algorithmes de décomposition de domaine itérant entre l'objet diffractant et le domaine extérieur. Dans cette thèse, nous introduisons de nouveaux couplages faibles FEM-BEM acoustiques et électromagnétiques basés sur des approximations de Padé récemment développées pour les opérateurs Dirichlet-to-Neumann et Magnetic-to-Electric. Le nombre d'itérations nécessaires à la résolution de ces couplages ne dépend que faiblement de la fréquence et du raffinement du maillage. Les couplages faibles FEM-BEM que nous proposons sont donc adaptés pour des calculs précis de SES et de SER à haute fréquence / In this doctoral dissertation, we propose new methods for solving acoustic and electromagnetic three-dimensional harmonic scattering problems for which the scatterer is penetrable and inhomogeneous. The resolution of such problems is key in the computation of sonar and radar cross sections (SCS and RCS). However, this task is known to be difficult because it requires discretizing partial differential equations set in an exterior domain. Being unbounded, this domain cannot be meshed thus hindering a volume finite element resolution. There are two standard approaches to overcome this difficulty. The first one consists in truncating the exterior domain and renders possible a volume finite element resolution. Given that they approximate the scattering problems at the continuous level, truncation methods may however not be accurate enough for SCS and RCS computations. Inhomogeneous penetrable harmonic scattering problems can also be solved by coupling a volume variational formulation associated with the scatterer and surface integral equations related to the exterior domain. This approach is known as FEM-BEM coupling (Finite Element Method-Boundary Element Method). It is of great interest because it is exact at the continuous level. Classical FEM-BEM couplings are qualified as strong because they couple the volume variational formulation and the surface integral equations within one unique formulation. They are however not suited for solving high-frequency problems. To remedy this drawback, other FEM-BEM couplings, said to be weak, have been proposed. These couplings are actually domain decomposition algorithms iterating between the scatterer and the exterior domain. In this thesis, we introduce new acoustic and electromagnetic weak FEM-BEM couplings based on recently developed Padé approximations of Dirichlet-to-Neumann and Magnetic-to-Electric operators. The number of iterations required to solve these couplings is only slightly dependent on the frequency and the mesh refinement. The weak FEM-BEM couplings that we propose are therefore suited to accurate SCS and RCS computations at high frequencies

Made available in DSpace on 2016-12-08T17:19:36Z (GMT). No. of bitstreams: 1 Gerson Filippini.pdf: 3306780 bytes, checksum: e9e94632db2e1724ef9cf694d93a5724 (MD5) Previous issue date: 2004-11-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The Finite Elements Method (MEF) has been traditionally applied to stress analysis in solid mechanics, whereas the Finite Volume Method (MVF) has its main application in heat transfer and fluid flow analyses. In the last years, use of Finite Elements in fluid dynamics problems has shown a substantial increase due, not only to its well-known facility to handle complex geometries, but to the development of new element stabilization techniques. On the other hand, the development of new models based on unstructured meshes has open new possibilities for application of the Finite Volume method. The present work addresses some aspects associated to the application of the MVF to plane elasticity, in which a discretisation procedure for Cartesian meshes is presented and comparisons between FEM and FVM for test problems are discussed. Emphasis is given to stress computation for Finite Volumes and comparisons to those obtained via recovery techniques for Finite Elements. The discretisation strategy and solution of the linear equation system have been approached under the classical FVM perspective, aiming at integration in existing Finite Volume codes. The analyses have been performed for a doubly-clamped beam with prescribed displacements in both ends, in which special attention is given to the shear stresses. It has been observed that the stresses evaluated using the MVF yields smaller differences when compared to the global smoothing method associated to the FEM. Furthermore, Finite Volumes has shown less susceptibility to poor aspect ratio then Finite Elements using linear shape functions. A qualitative analysis of the compression of a cylindrical billet has also shown no hourglass for Finite Volumes solutions. / O Método de Elementos Finitos (MEF) tem sido Tradicionalmente aplicado a problemas mecânicos de análise de tensões, enquanto o Método de Volumes Finitos (MVF) tem sua aplicação principal em transferência de calor e mecânica dos fluidos. Nos últimos anos, o uso de Elementos Finitos em problemas de dinâmica dos fluidos tem mostrado um aumento substancial. Isso se deve não somente a sua conhecida facilidade de tratar geometrias complexas, mas também ao desenvolvimento de novas técnicas de estabilização de elementos. Por outro lado, o desenvolvimento de novas estratégias baseadas em malhas não estruturadas tem renovado o incentivo na aplicação do método de Volumes Finitos. O presente trabalho discute diversos aspectos relativos à aplicação do MVF a problemas de elasticidade plana com malhas estruturadas e cartesianas, com ênfase nas comparações entre as distribuições de tensões obtidas pelo MVF e aquelas calculadas pelo MEF a partir de diferentes esquemas de suavização. As análises são feitas para uma viga engastada em ambos lados com deslocamentos prescritos nas extremidades visando avaliar principalmente as tensões cisalhantes. Observou-se que o campo de tensões calculado pelo MVF apresenta menor diferença quando comparado com aquele obtido pelo MEF utilizando-se o esquema de suavização global. Ressalta-se que o problema é abordado pelo prisma de Volumes Finitos (discretização das equações de governo e métodos de solução) visando futura implementação em códigos já existentes para problemas de termofluidos, com vistas à aplicação a problemas de interação fluidoestrutura. Fez-se também uma verificação inicial da existência de modos espúrios em um problema compressivo e a influência da variação da razão de aspecto dos elementos sobre os resultados.

L’objectif de ce travail est de contribuer à la modélisation du couplage hydromécanique, existant entre la déformation de la préforme fibreuse et l’écoulement de la résine, et par la suite à la simulation des procédés d’infusion. La méthode de résolution numérique déployée dans ce cadre est de type éléments finis avec volumes de contrôles (CVFEM) formulée en 2D½. Une nouvelle approche de modélisation de procédé d’infusion est proposée. Dans cette méthode, nous avons introduit des éléments 1D qui traduisent l’écoulement transverse. Cette approche permet de surmonter la difficulté numérique relative à l’usage des éléments finis volumiques pour un calcul 3D, notamment pour simuler la mise en œuvre des pièces industrielles de grandes dimensions. Le modèle fait appel à des lois de comportements caractérisées expérimentalement et qui permettent de tenir compte de l’évolution de la perméabilité et la compressibilité du milieu fibreux au cours de l’infusion. Diverses confrontations entre le modèle numérique proposé, des méthodes analytiques et expérimentales ont été menées. Une application du modèle dans la simulation de l’infusion d’un démonstrateur industriel de géométrie complexe est également réalisée. Les résultats obtenus sont très encourageants et révèlent l’efficacité de l’outil développé dans la simulation du procédé d’infusion / The aim of this work is to model the hydromechanical coupling that exists between the preform compressibility and the resin flow in order to simulate the infusion processes. The numerical method used in this study is based on the Control Volume Finite Elements Method (CVFEM) in 2D½. A new modelling approach of the infusion process is proposed. In this method, we introduced 1D elements to include through-the-thickness flow. This approach allows to reduce the computational time in comparison with full 3D modelling, especially in the simulation of industrial part infusion with large dimensions. The developed model is alimented by behavior laws that we characterized experimentally. These laws allow to take into account the evolution of the permeability and the compressibility of the fibrous medium during the infusion. We validated our model by comparing its results with analytical and experimental data. Additionally, an application of this simulation approach has been carried out to simulate the infusion of an industrial demonstrator with complex geometry. These comparisons show a good agreement between numerical and experimental results and reveal the efficiency of the developed tool in the infusion process simulation.