Turbulent flows present structures with a wide range of scales. The computation of the complete physics of a turbulent flow (termed DNS) is very expensive and is, for the time being, limited to low and medium Reynolds number flows. As a way to capture high Reynolds number flows, a part of the physics complexity has to be modeled. Large eddy simulation (LES) is a simulation strategy where the large turbulent eddies present on a given mesh are captured and the influence of the non-resolved scales onto the resolved ones is modeled. The present thesis reports on the development and validation of a methodology in order to apply LES for complex wall-bounded flows. Discretization methods and LES models, termed subgrid scale models (SGS), compatible with such a geometrical complexity are discussed. It is proved that discrete a kinetic energy conserving discretization of the convective term is an attractive solution to perform stable simulations without the use of an artificial dissipation, as upwinding. The dissipative effect of the SGS model is thus unaffected by any additional dissipation process. The methodology is first applied to a developed parallel fourth-order incompressible flow solver for cartesian non-uniform meshes. In order to solve the resulting Poisson equation, an efficient multigrid solver is also developed. The code is first validated using DNS (Taylor-Green vortex, channel flow, four-vortex system) and LES (channel flow), and finally applied to the investigation of an aircraft two-vortex system in ground effect. The methodology is then applied to improve a RANS-based industrial unstructured compressible flow solver, developed at CENAERO, to perform well for LES applications. The proposed modifications are tested successfully on the unsteady flow past a sphere at Reynolds of 300 and 10000, corresponding to the subcritical regime.

Turbulent flows present structures with a wide range of scales. The computation of the complete physics of a turbulent flow (termed DNS) is very expensive and is, for the time being, limited to low and medium Reynolds number flows. As a way to capture high Reynolds number flows, a part of the physics complexity has to be modeled. Large eddy simulation (LES) is a simulation strategy where the large turbulent eddies present on a given mesh are captured and the influence of the non-resolved scales onto the resolved ones is modeled. The present thesis reports on the development and validation of a methodology in order to apply LES for complex wall-bounded flows. Discretization methods and LES models, termed subgrid scale models (SGS), compatible with such a geometrical complexity are discussed. It is proved that discrete a kinetic energy conserving discretization of the convective term is an attractive solution to perform stable simulations without the use of an artificial dissipation, as upwinding. The dissipative effect of the SGS model is thus unaffected by any additional dissipation process. The methodology is first applied to a developed parallel fourth-order incompressible flow solver for cartesian non-uniform meshes. In order to solve the resulting Poisson equation, an efficient multigrid solver is also developed. The code is first validated using DNS (Taylor-Green vortex, channel flow, four-vortex system) and LES (channel flow), and finally applied to the investigation of an aircraft two-vortex system in ground effect. The methodology is then applied to improve a RANS-based industrial unstructured compressible flow solver, developed at CENAERO, to perform well for LES applications. The proposed modifications are tested successfully on the unsteady flow past a sphere at Reynolds of 300 and 10000, corresponding to the subcritical regime.

The plant leaf is one of the most challenging natural objects to be realistically depicted by computer graphics due to its complex morphological and optical characteristics. Although many studies have been done on plant modeling, previous research on leaf modeling required for close-up realistic plant images is very rare. In this thesis, a novel method for modeling of the leaf shape based on the leaf venation is presented. As the first step of the method, the leaf domain is defined by the enclosure of the leaf boundary. Second, the leaf venation is interactively modeled as a hierarchical skeleton based on the actual leaf image. Third, the leaf domain is triangulated with the skeleton as constraints. The skeleton is articulated with nodes on the skeleton. Fourth, the skeleton is interactively transformed to a specific shape. A user can manipulate the skeleton using two methods which are complementary to each other: one controls individual joints on the skeleton while the other controls the skeleton through an intermediate spline curve. Finally, the leaf blade shape is deformed to conform to the skeleton by interpolation. An interactive modeler was developed to help a user to model a leaf shape interactively and several leaves were modeled by the interactive modeler. The ray-traced rendering images demonstrate that the proposed method is effective in the leaf shape modeling.

The plant leaf is one of the most challenging natural objects to be realistically depicted by computer graphics due to its complex morphological and optical characteristics. Although many studies have been done on plant modeling, previous research on leaf modeling required for close-up realistic plant images is very rare. In this thesis, a novel method for modeling of the leaf shape based on the leaf venation is presented. As the first step of the method, the leaf domain is defined by the enclosure of the leaf boundary. Second, the leaf venation is interactively modeled as a hierarchical skeleton based on the actual leaf image. Third, the leaf domain is triangulated with the skeleton as constraints. The skeleton is articulated with nodes on the skeleton. Fourth, the skeleton is interactively transformed to a specific shape. A user can manipulate the skeleton using two methods which are complementary to each other: one controls individual joints on the skeleton while the other controls the skeleton through an intermediate spline curve. Finally, the leaf blade shape is deformed to conform to the skeleton by interpolation. An interactive modeler was developed to help a user to model a leaf shape interactively and several leaves were modeled by the interactive modeler. The ray-traced rendering images demonstrate that the proposed method is effective in the leaf shape modeling.

L'imagerie électrique est un outil de plus en plus important pour un large domaine d'applications relatives à la caractérisation de la subsurface proche. D'importants développements ont été réalisés au cours des vingt dernières années pour l'amélioration des systèmes d'acquisitions et des algorithmes d'inversions. L'acquisition et le traitement de gros jeux de données reste toutefois une tâche délicate, en particulier en présence de topographie. Afin d'améliorer la gestion de la topographie, nous avons développé un nouvel algorithme d'inversion électrique 2.5D et 3D. Nous avons proposé deux nouvelles formulations pour supprimer la singularité à la source. Le problème direct est résolu en utilisant la méthode des Différences Finies Généralisées et des maillages non structurés, permettant une représentation précise de la topographie. Le code d'inversion utilise la méthode de l'état adjoint pour calculer le gradient de la fonction objective de manière économique. Cette approche a donné de bons résultats avec des données synthétiques. Les premiers résultats sur des données réelles ont permis de retrouver les principales structures de la subsurface, ainsi que plusieurs zones de faibles résistivités pouvant correspondre à des zones fracturées. / DC resistivity imaging plays an important role for a wide range of applications related to the characterization of the shallow subsurface. Major developments have been made over the last two decades to improve acquisition systems as well as resistivity inversion. Nevertheless, large-scale data sets still represent a challenging task, in particular with arbitrary topography. In order to better take into account topography, we have developed a new 2.5D/3D tomographic inversion code. Two new formulations for the singularity removal have been proposed. The direct problem is solved in the framework of the Generalized Finite Differences Method, that allows the use of unstructured meshes yielding a fine represention of topography. The inversion code uses the adjoint state method to compute the gradient of the misfit function in a numerically efficient way, giving goodresults on synthetic data. First results on real data have shown the main subsurface structures, as well as several low resistivity zones possibly corresponding to fractured areas.

[pt] Técnicas de visualização científica criam imagens na tentativa de revelar estruturas e fenômenos complexos. Técnicas ilustrativas têm sido incorporadas aos sistemas de visualizacão científica para melhorar a expressividade de tais imagens. A visualização de linhas caracteríticas é uma técnica importante para transmitir uma melhor informacão sobre a forma das superfícies. Neste trabalho, propomos combinar visualização volumétrica de malhas não estruturadas com isosuperfícies ilustradas. Isto é feito estendendo um algoritmo de traçado de raio em GPU para incorporar ilustração com linhas de variação extrema da iluminação(photic extremum lines), um tipo de linha característica que captura mudanças bruscas de luminância, revelando formas de um jeito perceptualmente correto. / [en] Scientic visualization techniques create images attempting to reveal complex structures and phenomena. Illustrative techniques have been incorporated to scientic visualization systems in order to improve the expressiveness of such images. The rendering of feature lines is an important technique for better depicting surface shapes and features. In this thesis, we propose to combine volume visualization of unstructured meshes with illustrative isosurfaces. This is accomplished by extending a GPU-based ray-casting algorithm to incorporate illustration with photic extremum lines, a type of feature lines able to capture sudden changes of luminance, conveying shapes in a perceptually correct way.

This work examines the feasibility of a novel high-order numerical method, which has been termed Flux Correction. It has been given this name because it "corrects" the flux terms of an established numerical method, cancelling various error terms in the fluxes and making the method higher-order. In this work, this change is made to a traditionally second-order finite volume Galerkin method. To accomplish this, higher-order gradients of solution variables, as well as gradients of the fluxes are introduced to the method. Gradients are computed using lagrange interpolations in a fashion reminiscent of Finite Element techniques. For the Euler Equations, Flux Correction is compared against Flux Reconstruction, a derivative of the high-order Discontinuous Galerkin and Spectral Difference methods, both of which are currently popular areas of research in high-order numerical methods. Flux Correction is found to compare favorably in terms of accuracy, and exceeds expectations for convergence rates. For the full Navier-Stokes Equations, the effect of curved elements on Flux Correction are examined. Flux Correction is found to react negatively to curved elements due to the gradient procedure's poor handling of high-aspect ratio elements.

Cílem mé disertační práce je analyzovat a vyvinout parametrizační metodu pro 2D a 3D tvarové optimalizace v kontextu průmyslového aerodynamického návrhu letounu založeném na CFD simulacích. Aerodynamická tvarová optimalizace je efektivní nástroj, který si klade za cíl snížení nákladů na návrh letounů. Nástroj založený na automatickém hledání optimálního tvaru. Klíčovou částí úspěšného optimalizačního procesu je použití vhodné parametrizační metody, metody schopné garantovat možnost dosažení optimálního tvaru. Parametrizační metody obecně používané v oblasti aerodynamické tvarové optimalizace momentálně nejsou připravený na komplikované průmyslové aplikace vyskytující se u moderních dopravních letounů, které mají šípová zalomená křídla s winglety a motorovými gondolami, přechodové prvky spojující např. trup s křídlem atd.. Existuje tedy potřeba nalezení obecné parametrizační metody, která bude aplikovatelná na širokou škálu různých geometrických tvarů. Free-Form Deformation (FFD[1]) parametrizace může, vzhledem ke svým schopnostem při zacházení s geometrií, být odpovědí na tuto potřebu. Adaptivní parametrizace by se měla být schopna automaticky přizpůsobit danému tvaru tak, aby byly její kontrolní body vhodně rozmístěny. Což umožní dostatečnou kontrolu deformací objektu, která zaručí možnost vytvoření optimálního tvaru objektu a splnění geometrických omezení. Primární aplikací takové parametrizační metody je deformace tvaru objektu. Dalším navrhovaným cílem je modifikace FFD parametrizační metody pro současné deformace tvaru objektu a CFD výpočetní sítě, umožnující velké deformace objektu při zachování kvality výpočetní sítě.

[pt] Na visualização de campos escalares de dados volumétricos, o uso de seções de corte é uma técnica eficaz para se inspecionar a variação do campo no interior do domínio. A técnica de visualização consiste em mapear sobre a superfície da seção de corte um mapa de cores, o qual representa a variação do campo escalar na interseção da superfície com o volume. Este trabalho propõe um método eficiente para o mapeamento de campos escalares de malhas não estruturadas em seções de corte arbitrárias. Trata-se de um método de renderização direta (a interseção da superfície com o modelo não é extraída) que usa a GPU para garantir bom desempenho. A idéia básica do método proposto é utilizar o rasterizador da placa gráfica para gerar os fragmentos da superfície de corte e calcular a interseção de cada fragmento com o modelo em GPU. Para isso, é necessário testar a localização de cada fragmento na malha não estruturada de maneira eficiente. Como estrutura de aceleração, foram testadas três variações de grades regulares para armazenar os elementos (células) da malha, e cada elemento é representado pela lista de planos de suas faces, facilitando o teste de pertinência fragmento-elemento. Uma vez determinado o elemento que contém o fragmento, são aplicados procedimentos para interpolar o campo escalar e para identificar se o fragmento está próximo à fronteira do elemento, a fim de representar o aramado (wireframe) da malha na superfície de corte. Resultados obtidos demonstram a eficácia e a eficiência do método proposto. / [en] For the visualization of scalar fields in volume data, the use of cross sections is an effective technique to inspect the field variation inside the domain. The technique consists in mapping, on the cross section surfaces, a colormap that represents the scalar field on the surfasse-volume intersection. In this work, we propose an efficient method for mapping scalar fields of unstructured meshes on arbitrary cross sections. It is a direct-rendering method (the intersection of the surface and the model is not extracted) that uses GPU to ensure efficiency. The basic idea is to use the graphics rasterizer to generate the fragments of the cross-section surface and to compute the intersection of each fragment with the model. For this, it is necessary to test the location of each fragment with respect to the unstructured mesh in an efficient way. As acceleration data structure, we tested three variations of regular grids to store the elements (cells) of the mesh, and each elemento is represented by the list of face planes, easing the in-out test between fragments and elements. Once the element that contains the fragment is determined, it is applied procedures to interpolate the scalar field and to check if the fragment is close to the element boundary, to reveal the mesh wireframe on the surface. Achieved results demonstrate the effectiveness and the efficiency of the proposed method.

The first ocean general circulation models developed in the late sixties were based on finite differences schemes on structured grids. Many improvements in the fields of engineering have been achieved since three decades with the developments of new numerical methods based on unstructured meshes. Some components of the first models may now seem out of date and new second generation models are therefore under study, with the aim of taking advantage of the potential of modern numerical techniques such as finite elements. In particular, unstructured meshes are believed to be more efficient to resolve the large range of time and space scales present in the ocean. Besides the classical continuous finite element or finite volume methods, another popular new trend in engineering applications is the Discontinuous Galerkin (DG) method, i.e. discontinuous finite elements presenting many interesting numerical properties in terms of dispersion and dissipation, errors convergence rates, advection schemes, mesh adaptation, etc. The method is especially efficient at high polynomial orders. The motivation for this PhD research is therefore to investigate the use of the high-order DG method for geophysical flow modeling. A first part of the thesis is devoted to the mesh adaptation using the DG method. The inter-element jumps of the fields are used as error estimators. New mesh size fields or polynomial orders are then derived and local h- or p-adaptation is performed. The technique is applied to standard benchmarks and computations in more realistic domains as the Gulf of Mexico. A second part deals with the use of the high order DG method with high-order representation of geometrical features. On one hand, a method is proposed to deal with complex representations of the coastlines. Computations are performed using high-order mappings around the Rattray island, located in the Great Barier Reef. Numerical results are then compared to in-situ measurements. On the other hand, a new method is proposed to deal with curved manifolds in order to represents oceanic or atmospheric flows on the sphere. The approach is based on the use of a local high-order non-orthogonal basis, and is equivalent to the use of vectorial shape and test functions to represent the vectorial conservation laws on the manifold's surface. A method is finally proposed to analyze the dispersion and dissipation properties of any numerical scheme on any kind of grid, possibly unstructured. The DG method is then compared to other techniques as the mixed non-conforming linear elements, and the impact of unstructured meshes is studied.