A avaliação de recursos minerais necessita da delimitação prévia de domínios estacionários para cálculo dos volumes do depósito mineral. O conhecimento a respeito dos processos geológicos de formação do depósito são traduzidos em modelos geológicos, essenciais para o planejamento da produção e à tomada de decisões a respeito da tecnologia e os recursos a empregados no empreendimento. A indústria mineral, normalmente, considera a incerteza dos teores na avaliação de recursos, entretanto a incerteza relacionada ao modelo geológico geralmente não é avaliada. Essa incerteza está relacionada a localização do limite entre domínios geológicos, e é uma da principal fonte de incerteza do empreendimento mineral. A incerteza do modelo geológico deve ser avaliada devido o potencial impacto no volume de recursos do depósito, e consequentemente na lucratividade do empreendimento. Esta dissertação busca avaliar a incerteza associada ao modelo geológico, através de três metodologias que possibilitam construir múltiplas realizações para domínios geológicos. Um banco de dados real com alta complexidade é utilizado na construção dos estudos de caso de cada metodologias e os resultados comparados com o modelo determinístico utilizado como referência. Dentre os métodos, a metodologia do parâmetro da incerteza C representou melhor a incerteza volumétrica, e portanto, foi selecionado para gerar o modelo geológico final, e demonstrar a importância da avaliação da incerteza na construção de modelos geológicos. / The evaluation of mineral resources requires the prior delimitation of a stationary domain geologically controlled. The knowledge about the ore genesis and geological processes involved are translated into geological models, essential for planning the production and decision-making regarding the technology and resources applied in the enterprise. The mineral industry usually considers the grade uncertainty in the evaluation of resources, however the uncertainty related to the geological model is generally under evaluated. This uncertainty related to the location of the boundary between geological domains is the great source of uncertainty in the mineral enterprise. The geological model uncertainty should be assessed due to the potential impact on the volume of deposit, and consequently the profitability of the enterprise. This dissertation evaluates the uncertainty associated to the geological model, through three methodologies that generate multiple realizations for geological domains. A real database with high geological complexity is used in the construction of the case studies for each methodology and the results compared to the deterministic model used as a benchmark. Among the methods, the uncertainty calculation methodology C was selected to generate the final geological model, and to demonstrate the importance of uncertainty evaluation in the construction of geological models.

La modélisation structurale consiste à approximer les structures géologiques du sous-sol en un modèle numérique afin d'en visualiser la géométrie et d'y effectuer des calculs d'estimation et de prédiction. L'approche implicite de la modélisation structurale utilise des données de terrain interprétées pour construire une fonction volumétrique sur le domaine d'étude qui représente la géologie. Cette fonction doit honorer les observations, interpoler entre ces dernières, et extrapoler dans les zones sous-échantillonnées tout en respectant les concepts géologiques. Les méthodes actuelles portent cette interpolation soit sur les données, soit sur un maillage. Ensuite, le problème de modélisation est posé selon la discrétisation choisie : par krigeage dual sur les points de donnée ou en définissant un critère de rugosité sur les éléments du maillage. Dans cette thèse, nous proposons une formulation continue de la modélisation structurale par méthodes implicites. Cette dernière consiste à minimiser une somme de fonctionnelles arbitraires. Les contraintes de donnée sont imposées avec des fonctionnelles discrètes, et l'interpolation est contrôlée par des fonctionnelles continues. Cette approche permet de (i) développer des liens entre les méthodes existantes, (ii) suggérer de nouvelles discrétisations d'un même problème de modélisation, et (iii) modifier le problème de modélisation pour mieux honorer certains cas géologiques sans dépendre de la discrétisation. Nous portons également une attention particulière à la gestion des discontinuités telles que les failles et les discordances. Les méthodes existantes nécessitent soit la création de zones volumétriques avec des géométries complexes, soit la génération d'un maillage volumétrique dont les éléments sont conformes aux surfaces de discontinuité. Nous montrons, en explorant des méthodes sans maillage locales et des concepts de réduction de maillage, qu'il est possible d'assurer l'interpolation des structures tout en réduisant les contraintes liées à la gestion des discontinuités. Deux discrétisations de notre problème de minimisation sont suggérées : l'une utilise les moindres carrés glissants avec des critères optiques pour la gestion des discontinuités, et l'autre utilise des fonctions issues de la méthode des éléments finis avec le concept de nœuds fantômes pour les discontinuités. Une étude de sensibilité et une comparaison des deux méthodes sont proposées en 2D, ainsi que quelques exemples en 3D. Les méthodes développées dans cette thèse ont un grand impact en termes d'efficacité numérique et de gestion de cas géologiques complexes. Par exemple, il est montré que notre problème de minimisation au sens large apporte plusieurs solutions pour la gestion de cas de plis sous-échantillonnés et de variations d'épaisseur dans les couches stratigraphiques. D'autres applications sont également présentées tels que la modélisation d'enveloppe de sel et la restauration mécanique. / Implicit structural modeling consists in approximating geological structures into a numerical model for visualization, estimations, and predictions. It uses numerical data interpreted from the field to construct a volumetric function on the domain of study that represents the geology. The function must fit the observations, interpolate in between, and extrapolate where data are missing while honoring the geological concepts. Current methods support this interpolation either with the data themselves or using a mesh. Then, the modeling problem is posed depending on these discretizations: performing a dual kriging between data points or defining a roughness criterion on the mesh elements. In this thesis, we propose a continuous formulation of implicit structural modeling as a minimization of a sum of generic functionals. The data constraints are enforced by discrete functionals, and the interpolation is controlled by continuous functionals. This approach enables to (i) develop links between the existing methods, (ii) suggest new discretizations of the same modeling problem, and (iii) modify the minimization problem to fit specific geological issues without any dependency on the discretization. Another focus of this thesis is the efficient handling of discontinuities, such as faults and unconformities. Existing methods require either to define volumetric zones with complex geometries, or to mesh volumes with conformal elements to the discontinuity surfaces. We show, by investigating local meshless functions and mesh reduction concepts, that it is possible to reduce the constraints related to the discontinuities while performing the interpolation. Two discretizations of the minimization problem are then suggested: one using the moving least squares functions with optic criteria to handle discontinuities, and the other using the finite element method functions with the concept of ghost nodes for the discontinuities. A sensitivity analysis and a comparison study of both methods are performed in 2D, with some examples in 3D. The developed methods in this thesis prove to have a great impact on computational efficiency and on handling complex geological settings. For instance, it is shown that the minimization problem provides the means to manage under-sampled fold structures and thickness variations in the layers. Other applications are also presented such as salt envelope surface modeling and mechanical restoration.

This thesis deals with Large Eddy Simulation (LES) of impinging air jets. The impinging jet configuration features heated circular jets impinging onto a flat plate. The problem addressed here is of generic nature, with applications in many engineering devices, such as cooling of components in gas turbines, in cars and electronic devices. The flow is inherently unsteady and contains relatively slowly varying coherent structures. Therefore, LES is the method of choice when the Reynolds number is large enough to exclude Direct Numerical Simulations (DNS). The present LES model is a basic model without explicit Sub-Grid-Scale (SGS) modeling and without explicit filtering. Instead, the numerical scheme is used to account for the necessary amount of dissipation. By using the computational grid as a filter the cutoff wavenumber depends explicitly on the grid spacing. The underlying computational grid is staggered and constructed in a Cartesian coordinate system. Heat transfer is modeled by the transport equation for a passive scalar. This is possible due to the negligible influence of buoyancy which implies constant density throughout the flow field. The present method provides accurate results for simple geometries in an efficient manner. A great variety of inlet conditions have been considered in order to elucidate how the dynamics of the flow and heat transfer are affected. The considered studies include top-hat and mollified mean velocity profiles subjected to random and sinusoidal perturbations and top-hat profiles superimposed with solid body rotation. It has been found that the shape of the mean inlet velocity profile has a decisive influence on the development of the flow and scalar fields, whereas the characteristics of the imposed artificial disturbances (under consideration) have somewhat weaker effect. In order to obtain results unequivocally comparable to experimental data on turbulent impinging jets both space and time correlations of the inflow data must be considered, so also the spectral content. This is particularly important if the region of interest is close to the velocity inlet, i.e. for small nozzle-to-plate spacings. Within this work mainly small nozzle-toplate spacings are considered (within the range of 0.25 and 4 nozzle diameters), which emphasizes the importance of the inflow conditions. Thus, additional to the basic methods also turbulent inflow conditions, acquired from a precursor pipe simulation, have been examined. Both for swirling and non-swirling flows. This method emulates fully developed turbulent pipe flow conditions and is the best in the sense of being well defined, but it demands a great deal of computing power and is also rather inflexibility. In case of the basic randomly perturbed methods the top-hat approach has been found to produce results in closest agreement with those originating from turbulent inlet conditions. In the present simulations the growth of individual instability modes is clearly detected. The character of the instability is strongly influenced by the imposed boundary conditions. Due to the lack of correlation random superimposed fluctuations have only a weak influence on the developing flow field. The shape of the mean profile, on the other hand, influences both the growth rate and the frequency of the dominant modes. The top-hat profile yields a higher natural frequency than the mollified. Furthermore, for the top-hat profile coalescence of pairs of vortices takes place within the shear-layer of the axial jet, whereas for the mollified profile (for the considered degree of mollification) it takes place within the wall jet. This indicates that the transition process is delayed for smoother profiles. The amount of wall heat transfer is directly influenced by the character of the convective vortical structures. For the mollified cases wall heat transfer originates predominantly from the dynamics of discrete coherent structures. The influence from eddy structures is low and hence Reynolds analogy is applicable, at least in regions of attached flow. The top-hat and the turbulent inflow conditions yield a higher rate of incoherent small scale structures. This strongly affects the character of wall heat transfer. Also the applied level of swirl at the velocity inlet has significant influence on the rate of heat transfer. The turbulence level increases with swirl, which is positive for heat transfer, and so also the spreading of the jet. The latter effect has a negative influence on wall heat transfer, particularly in the center most regions. This however depends also on the details of the inflow data. / QC 20100831

Recently a periodic surface model was developed to assist geometric construction in computer-aided nano-design. This implicit surface model helps create super-porous nano structures parametrically and support crystal packing. In this thesis, a new approach for pathway search in phase transition simulation of crystal structures is proposed. The approach relies on the interpolation of periodic loci surface models. Respective periodic plane models are reconstructed from the positions of individual atoms at the initial and final states, and surface correspondence is found using a Simulated Annealing-like algorithm. With geometric constraints imposed based on physical and chemical properties of crystals, two surface interpolation methods are used to approximate the intermediate atom positions on the transition pathway in the full search of the minimum energy path. This hybrid approach integrates geometry information in configuration space and physics information to allow for efficient transition pathway search. The methods are demonstrated by examples of FeTi, VO2, and FePt. Additionally, two new particle swarm optimization (PSO) algorithms are developed and applied to crystal structure relaxation of the initial and final states. The PSO algorithms are integrated into the Quantum-Espresso open-source software package and tested against the default Broyden-Fletcher-Goldfarb-Shanno relaxation method.

Cette thèse s’intéresse à la synthétisation de paysages naturels, et plus particulièrement, à leur portion céleste. L’aspect du ciel est gouverné par de nombreux phénomènes atmosphériques parmi lesquels les nuages jouent un rôle prépondérant car ils sont fréquemment présents et couvrent de grandes étendues. Même sans considérer directement le ciel, la densité des nuages leur permet de modifier intensément l’illumination globale d’un paysage. Les travaux de cette thèse se concentrent donc principalement sur l’édition, la modélisation et l’animation d’étendues nuageuses aux dimensions d’un paysage. Comme la simulation thermodynamique de la formation des nuages est difficilement contrôlable et que les détails du volume simulés sont rapidement limités, nous proposons plutôt une méthode par génération procédurale. Nous érigeons un modèle léger de paysage nuageux sous forme d’une hiérarchie de fonctions. Les détails les plus fins sont obtenus par composition de bruits procéduraux et reproduisent les formes de différents genres de nuages. La présence nuageuse à grande échelle est quant à elle décrite à haut niveau et à différents instants par des cartes dessinées par l’utilisateur. Ces cartes discrètes sont transformées en primitives implicites statiques ensuite interpolées par métamorphose en prenant en compte le relief et les vents pour produire des trajectoires cohérentes. Le champ implicite obtenu par mélange des primitives interpolantes constitue le champ spatiotemporel de densité nuageuse. Des images sont finalement synthétisées par rendu du milieu participatif atmosphérique selon notre propre implémentation exécutée en parallèle sur carte graphique / This thesis focusses on the synthetization of natural landscapes, and more particularly on their celestial part. The aspect of the sky is governed by plenty of atmospheric phenomena, among which clouds play a major role for they are recurrent and widespread. Even without directly considering the sky, the density of the clouds allows them to intensely modify the global illumination of a landscape. The work of this thesis thus focuses mainly on the editing, modelling and animation of cloud areas of landscape dimensions.Because the thermodynamic simulation of cloud formation is hard to control and its maximum resolution quickly limits the details of the simulated volume, we propose instead a procedural generation method. We build a lightweight cloudscape model as a hierarchy of functions. The finest details are obtained by composing procedural noises and reproduce the specific shapes of different kinds of clouds. The large-scale cloud presence is described at a high level and at different times by maps drawn by the user. These discrete maps are transformed into implicit static primitives and then interpolated by morphing, accounting for relief and winds in order to produce coherent trajectories. The implicit field obtained by mixing the interpolating primitives represents the spatiotemporal field of cloud density. Images are finally synthesized by rendering of the atmospheric participative medium according to our own implementation, executed in parallel on a graphic card

We present an implicit approach for constructing smooth isolated or interconnected 3-D inscribed volumes which can be employed for volumetric modeling of various kinds of spongy or porous structures, such as volcanic rocks, pumice stones, Cancellus bones *, liquid or dry foam, radiolarians, cheese, and other similar materials. The inscribed volumes can be represented in their normal or positive forms to model natural pebbles or pearls, or in their inverted or negative forms to be used in porous structures, but regardless of their types, their smoothness and sizes are controlled by the user without losing the consistency of the shapes. We introduce two techniques for blending and creating interconnections between these inscribed volumes to achieve a great flexibility to adapt our approach to different types of porous structures, whether they are regular or irregular. We begin with a set of convex polytopes such as 3-D Voronoi diagram cells and compute inscribed volumes bounded by the cells. The cells can be irregular in shape, scale, and topology, and this irregularity transfers to the inscribed volumes, producing natural-looking spongy structures. Describing the inscribed volumes with implicit functions gives us a freedom to exploit volumetric surface combinations and deformations operations effortlessly / Graduate