Le comportement des matériaux multiphasiques couvre une multitude de phénomènes qui suscitent un grand intérêt dans le domaine scientifique et professionnel. Les propriétés mécaniques de ces types de matériau trouvent leur origine dans les phases dont ils sont composés, leur distribution et interaction. Un nouveau modèle hydrodynamique couplé est présenté dans ce travail de thèse, à appliquer à l'analyse de l'hydrodynamique des milieux granulaires saturés. Le modèle associe la méthode des éléments discrets (DEM) pour la modélisation de la phase solide, avec une formulation en volumes finis, à l'échelle des pores (PFV), du problème de l'écoulement. Une importance particulière est donné à la description de l'interaction entre les phases, avec la détermination des forces fluides à appliquer sur chacune des particule, tout en assurant un coût de calcul abordable, qui permet la modélisation de plusieurs milliers des particules en trois dimensions. Le milieux est considéré saturé par un fluide incompressible. Les pores et leur connectivité est basée sur une triangulation régulière des assemblages. L'analogie de cette formulation avec la théorie classique de Biot est présenté. Le modèle est validé par la comparaison des résultats numériques obtenus pour un problème de consolidation d'un sol granulaire avec la solution analytique de Terzaghi. Une approche pour analyser l'hydrodynamique d'un sédiment granulaire est finalement présenté. La reproduction du phénomène de liquéfaction d'un sol est également présentée. / The behaviour of multiphase materials covers a wide range of phenomena of interest to both scientists and engineers. The mechanical properties of these materials originate from all component phases, their distribution and interaction. A new coupled hydromechanical model is presented in this work, to be applied to the analysis of the hydrodynamics of saturated granular media. The model associates the discrete element method (DEM) for the solid phase, and a pore-scale finite volume (PFV) formulation of the flow problem. The emphasis of this model is, on one hand, the microscopic description of the interaction between phases, with the determination of the forces applied on solid particles by the fluid; on the other hand, the model involve affordable computational costs, that allow the simulation of thousands of particles in three dimensional models. The medium is assumed to be saturated of an incompressible fluid. Pore bodies and their connections are defined locally through a regular triangulation of the packings. The analogy of the DEM-PFV model and the classic Biot's theory of poroelasticity is discussed. The model is validated through comparison of the numerical result of a soil consolidation problem with the Terzaghi's analytical solution. An approach to analyze the hydrodynamic of a granular sediment is finally presented. The reproduction of the phenomenon of soil liquefaction is analysed and discussed.

Made available in DSpace on 2014-06-11T19:23:39Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-09-08Bitstream added on 2014-06-13T19:09:39Z : No. of bitstreams: 1 lacerda_jf_me_ilha.pdf: 4631781 bytes, checksum: cad33ad7c5cac9de6cec08fd94b419e7 (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Nesse trabalho resolve-se numericamente o escoamento em difusores radiais, os quais têm sido utilizados como modelo para o estudo do escoamento em válvulas automáticas de compressores de refrigeração. As equações governantes do escoamento, escritas no sistema de coordenadas cilíndricas, são resolvidas utilizando um código numérico baseado no Método dos Volumes Finitos. O Método da Fronteira Imersa, em conjunto com o Modelo Físico Virtual, foi implementado no código numérico e utilizado para representar a região sólida imersa no escoamento. Inicialmente, o código numérico foi utilizado para resolver o problema do escoamento em torno de um cilindro de base quadrada, como parte do processo de validação do código. O confronto dos resultados numéricos com dados da literatura indicou a validação parcial do código. Posteriormente, realizou-se um estudo preliminar do comportamento da solução do escoamento no difusor radial em relação a diversos parâmetros geométricos e de simulação numérica, com o objetivo de identificar a configuração numérica capaz de fornecer, simultaneamente, resultados satisfatórios com o menor custo computacional. Usando esta configuração, o código numérico foi validado através da comparação dos resultados da distribuição de pressão sobre o disco frontal (palheta) do difusor com dados experimentais da literatura, para duas distâncias entre disco frontal e disco inferior (assento), s=0,02 e 0,025 cm, e números de Reynolds variando entre 1500 e 2500. As comparações entre esses resultados mostraram que a metodologia utilizada é adequada para estudar o problema. Finalmente, a geometria do disco inferior foi modificada através da inserção de um chanfro com três ângulos de inclinação (30, 45 e 60º), com o objetivo de avaliar sua influência sobre o comportamento da distribuição de pressão sobre o disco frontal... / In this work the flow in radial diffusers, which have been used as a model to study the flow in refrigeration compressors valves, is solved numerically. The governing equations, written in cylindrical coordinates, are solved using a numerical code based on the Finite Volume Method. The Immersed Boundary Method, with the Virtual Physical Method, was implemented in the numerical code and used to represent the solid region immersed in the flow. Initially, the numerical code was used to solve the flow around a square base cylinder, as part of the code validation. The comparison of the numerical results with literature data indicated the partial validation of the code. Afterwards it was performed a preliminary study of the behavior of the flow solution in the radial diffuser relating to several geometrical and numerical parameters, with the objective of identifying a configuration capable of providing, simultaneously, satisfactory results with the smaller computational cost. Using this configuration, the numerical code was validated through the comparison with experimental pressure distribution on the frontal disk (reed) for two gaps between the frontal disk and inferior disk (seat), s=0.020 and 0.025 cm, and Reynolds numbers varying between 1500 and 2500. These comparisons have shown that the implemented methodology is suitable to study this problem. Finally, the inferior disk geometry was modified by inserting a chamfer with three inclination angles (30, 45 e 60º), with the objective of evaluating its influence on the pressure distribution on the frontal disk. The decreasing of the total pressure gradient through the flow for increasing inclination angles indicates less amount of energy to drive the flow. This is an important result that can be used to design refrigeration compressors with lower compression power

Orientador: José Luiz Gasche / Banca: Sérgio Said Mansur / Banca: Aristeu da Silveira Neto / Resumo: Nesse trabalho resolve-se numericamente o escoamento em difusores radiais, os quais têm sido utilizados como modelo para o estudo do escoamento em válvulas automáticas de compressores de refrigeração. As equações governantes do escoamento, escritas no sistema de coordenadas cilíndricas, são resolvidas utilizando um código numérico baseado no Método dos Volumes Finitos. O Método da Fronteira Imersa, em conjunto com o Modelo Físico Virtual, foi implementado no código numérico e utilizado para representar a região sólida imersa no escoamento. Inicialmente, o código numérico foi utilizado para resolver o problema do escoamento em torno de um cilindro de base quadrada, como parte do processo de validação do código. O confronto dos resultados numéricos com dados da literatura indicou a validação parcial do código. Posteriormente, realizou-se um estudo preliminar do comportamento da solução do escoamento no difusor radial em relação a diversos parâmetros geométricos e de simulação numérica, com o objetivo de identificar a configuração numérica capaz de fornecer, simultaneamente, resultados satisfatórios com o menor custo computacional. Usando esta configuração, o código numérico foi validado através da comparação dos resultados da distribuição de pressão sobre o disco frontal (palheta) do difusor com dados experimentais da literatura, para duas distâncias entre disco frontal e disco inferior (assento), s=0,02 e 0,025 cm, e números de Reynolds variando entre 1500 e 2500. As comparações entre esses resultados mostraram que a metodologia utilizada é adequada para estudar o problema. Finalmente, a geometria do disco inferior foi modificada através da inserção de um chanfro com três ângulos de inclinação (30, 45 e 60º), com o objetivo de avaliar sua influência sobre o comportamento da distribuição de pressão sobre o disco frontal... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: In this work the flow in radial diffusers, which have been used as a model to study the flow in refrigeration compressors valves, is solved numerically. The governing equations, written in cylindrical coordinates, are solved using a numerical code based on the Finite Volume Method. The Immersed Boundary Method, with the Virtual Physical Method, was implemented in the numerical code and used to represent the solid region immersed in the flow. Initially, the numerical code was used to solve the flow around a square base cylinder, as part of the code validation. The comparison of the numerical results with literature data indicated the partial validation of the code. Afterwards it was performed a preliminary study of the behavior of the flow solution in the radial diffuser relating to several geometrical and numerical parameters, with the objective of identifying a configuration capable of providing, simultaneously, satisfactory results with the smaller computational cost. Using this configuration, the numerical code was validated through the comparison with experimental pressure distribution on the frontal disk (reed) for two gaps between the frontal disk and inferior disk (seat), s=0.020 and 0.025 cm, and Reynolds numbers varying between 1500 and 2500. These comparisons have shown that the implemented methodology is suitable to study this problem. Finally, the inferior disk geometry was modified by inserting a chamfer with three inclination angles (30, 45 e 60º), with the objective of evaluating its influence on the pressure distribution on the frontal disk. The decreasing of the total pressure gradient through the flow for increasing inclination angles indicates less amount of energy to drive the flow. This is an important result that can be used to design refrigeration compressors with lower compression power / Mestre

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho apresenta um estudo teórico e numérico sobre os erros que ocorrem nos cálculos de gradientes em malhas não estruturadas constituídas pelo diagrama de Voronoi, malhas estas, formadas também pela triangulação de Delaunay. As malhas adotadas, no trabalho, foram as malhas cartesianas e as malhas triangulares, esta última é gerada pela divisão de um quadrado em dois ou quatro triângulos iguais. Para tal análise, adotamos a escolha de três metodologias distintas para o cálculo dos gradientes: método de Green Gauss, método do Mínimo Resíduo Quadrático e método da Média do Gradiente Projetado Corrigido. O texto se baseia em dois enfoques principais: mostrar que as equações de erros dadas pelos gradientes podem ser semelhantes, porém com sinais opostos, para pontos de cálculos em volumes vizinhos e que a ordem do erro das equações analíticas pode ser melhorada em malhas uniformes quando comparada as não uniformes, nos casos unidimensionais, e quando analisada na face de tais volumes vizinhos nos casos bidimensionais. / This work presents a theoretical and numerical study on the errors that occur in the calculation of gradients on unstructured meshes Voronoi type, these meshes, also formed by Delaunay triangulation. The meshes adopted in the work were cartesian and triangular meshes, the latter is formed by dividing a square in two or four equal triangles. For this analysis, we adopt the choice of three different methodologies for the calculation of gradients: Green Gauss method, weighted least-squares method and mean value of the projected gradients method. The text is based on two main approaches: to show that the equations of errors given by the gradients may be similar, but with opposite signs, for calculation point in opposite volumes. And show that the order of the error of the analytical equations can be improved in uniform mesh when compared to not uniform, the one-dimensional case, and when viewed from the opposite face of such volumes for the two-dimensional case.

L’objet de cette thèse est l’étude de la séparation membranaire de l’air appliquée à la réduction desémissions d’oxyde d’azote (NOx) des moteurs Diesel. Il a en effet été démontré précédemment quel’utilisation d’air dopé en azote pour la combustion Diesel entrainait une diminution des émissions deNOx. Les travaux présentés ici ont consisté à produire des outils de modélisation d’un module deséparation membranaire des gaz de type fibres creuses et à valider expérimentalement ces outils.Deux approches de modélisation ont été retenues, une approche génie chimique a conduit à unmodèle monodimensionnel applicable en régime stationnaire ; une approche dynamique des fluidesa permis de développer un modèle bidimensionnel valable en régime transitoire. Le premier modèlea été utilisé pour le dimensionnement de modules, le second pour simuler les performances deséparation de ces modules. Par ailleurs, l’influence du taux de dopage en azote de l’air sur la quantitéde NOx émis a été numériquement étudiée à l’aide d’un outil commercial. Enfin, la possibilitéd’implanter un tel module sur un moteur Diesel de série et les paramètres limitants ont été étudiés àl’aide d’un code commercial et d’un modèle développé par Renault. / The purpose of this work is the study of the air membrane separation applied to the reduction ofnitrogen oxides (NOx) emissions of Diesel engines. As a matter of fact, previous works proved thatusing nitrogen-doped air in Diesel combustion led to lower NOx emissions. The study presentedherein consisted in developing a set of modeling tools simulating a gas separation hollow fibersmembrane module and in experimentally validating these tools. A chemical engineering approachresulted in a monodimensional model suitable for stationary regime; a flow dynamic approach led toa bidimensional model dedicated to transitory regime. The first model was used to design modulessize, the second one to simulate separation performances of these modules. Beside, the impact ofnitrogen doping on NOx emissions was numerically studied with a commercial software. Finally, thefeasibility of the introduction of such a module in a mass-produced Diesel engine was investigatedwith a model developed at Renault on a commercial software.

The consumption of energy is a main factor that determines the viability of any industrial process. Thermal dehydration is responsible for a high consumption of energy. In developed countries, 9 to 25% of the energy consumption of the national industry is attached to thermal dehydration. Thus, studying the dehydration process shows itself very promisor. In biological products, dehydration has a specific importance, the product conservation. The organic matter of the product and its water create a propitious medium for microorganisms proliferation that will deteriorate the product, making the product inappropriate for consumption. In this work, the modeling and simulation of a convective dehydration process using a diffusive-convective differential model solved by the finite volumes numeric method for predicting the behavior of the mean moisture content during the dehydration, defining molecular mass transfer and convective coefficients, and drawing moisture profiles of the interior of the solid. To evaluate the influence of internal and external resistances, the mass transfer Biot number was obtained. The implementation of the models of this work were made in Python using its scientific models for solving differential equations. This tool has been utilized because it is open source, has simple implementation when compared to other programming languages and has performance when performing simulations. As study of cases, experimental data of assisted convective dehydration by ultrasound of apple (Malus domestica L. var Royal Gala) cubes with 8 mm under the following operation conditions: 1, 2, 3 and 5 m/s for dehydration velocities, air flow temperature of 45ÂC and 60ÂC, presence and absence of ultrasound during the dehydration process and presence and absence of the pre-treatment with ultrasounds. The apple cubes of the experiments have 25 Â1g of mass. The dehydration has been performed until the removal of 80% of the initial mass of the cubes. The parameters, diffusivity and mass transfer coefficient, have been adjusted by Levenberg-Marquardt non-linear regression method. The results obtained in the simulations showed that the implemented model is very promisor, because it represents accurately the process. The values for diffusivity and mass transfer coefficient herein obtained were plausible. The influence of the air flow velocity, temperature and ultrasounds assistance and ultrasounds pre-treatments have been analyzed. / O consumo de energia à um fator determinante na viabilidade de qualquer processo industrial. A desidrataÃÃo tÃrmica à responsÃvel por um alto consumo de energia tÃrmica. Em paÃses desenvolvidos, o consumo da energia da indÃstria nacional à atribuÃdo, em mÃdia, entre 9-25% a desidrataÃÃo tÃrmica. Assim, o estudo do processo de secagem se mostra bastante promissor. Em produtos biolÃgicos, a secagem tem uma importÃncia especÃfica, a conservaÃÃo do produto, pois a matÃria orgÃnica do produto e a Ãgua presente nele torna este um local propÃcio para a proliferaÃÃo de micro-organismos que irÃo deteriorar o produto, tornando-o inapropriado para consumo. Neste trabalho, realizou-se a modelagem e simulaÃÃo do processo de secagem convectiva utilizando modelo diferencial difusivo-convectivo resolvido pelo mÃtodo numÃrico dos volumes finitos para predizer o comportamento do conteÃdo de umidade mÃdio durante a secagem de cubos, definir os coeficientes de transferÃncia de massa molecular e convectivo e encontrar os perfis do conteÃdo de umidade no interior do sÃlido. Para avaliar a influÃncia das resistÃncias interna e externa, o nÃmero de Biot de Massa foi obtido. A implementaÃÃo dos modelos deste trabalho foi realizada na ferramenta livre Python utilizando seus mÃdulos cientÃficos de resoluÃÃo de equaÃÃes diferenciais. Esta ferramenta foi utilizada porque à livre, implementaÃÃo simples, quando comparada com outras linguagens e possui alta performance nas simulaÃÃes. Como estudos de caso, utilizaram-se dados experimentais da secagem convectiva assistida por ultrassom de cubos de maÃà (Malus domestica L. var Royal Gala) com 8 mm de aresta nas seguintes condiÃÃes operacionais: velocidades de secagem: 1, 2, 3 e 5 m/s; temperatura do ar de secagem: 45 ÂC e 60 ÂC; presenÃa e ausÃncia de ultrassom durante a secagem; presenÃa e ausÃncia de etapa de prÃ-tratamento com ultrassom. Os cubos de maÃà dos experimentos tinham, em mÃdia, 25Â1 g. A secagem foi realizada atà que as amostras perdessem 80% da massa inicial. Os parÃmetros, difusividade e coeficiente de transferÃncia de massa, foram ajustados por regressÃo nÃo linear pelo mÃtodo de Levenberg-Marquardt. Os resultados obtidos nas simulaÃÃes mostraram que o modelo implementado à promissor, pois representa bem o processo. Os valores obtidos da difusividade e coeficiente de transferÃncia de massa foram plausÃveis. Analisou-se a influÃncia da velocidade do ar de secagem, da temperatura, da assistÃncia do ultrassom no processo e da utilizaÃÃo de uma etapa de prÃ-tratamento com ultrassom no processo de secagem.

Orientador: Milton Mori, Marcos A. d'Avila / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-06T05:47:36Z (GMT). No. of bitstreams: 1 Santos_CelsoMurilodos_M.pdf: 3396606 bytes, checksum: 6f04eb0860468401aa6369dba2b5c839 (MD5) Previous issue date: 2005 / Resumo: Colunas de bolhas são equipamentos de simples operação, mas que apresentam uma fluidodinâmica complexa. Seu funcionamento básico é dado pela injeção de um gás (fase dispersa) na base da coluna em um meio líquido (fase contínua). Elas são empregadas nas mais diversas áreas industriais, como processos de química fina, reações de oxidação, reações de alquilação, síntese de Fischer-Tropsch, tratamento de efluentes, reações de fermentação e produção de proteínas, e mais recentemente, em cultura de células. Neste trabalho foram realizadas simulações tridimensionais do escoamento transiente em coluna de bolhas utilizando o pacote computacional de CFD CFX® 5.7 (ANSYS®). Este pacote utiliza o método dos volumes finitos para solucionar as equações governantes de transporte em escoamento multifásico, utilizando a abordagem Euleriana-Euleriana, que mostrou-se adequada para este estudo. Os estudos de casos foram feitos para verificar a influência das propriedades da fase contínua (viscosidade e tensão superficial), da fase dispersa (diâmetro das bolhas) e dos modelos de arraste ... Observação: O resumo, na íntegra, poderá ser visualizado no texto completo da tese digital / Abstract: Bubble columns are equipments of simple operation, but presents a complex fluidodynamic. Its basic operation consists of the injection of a gas (disperses phase) in the bottom of the column in a liquid medium (continuous phase). As reactors, they are used in a variety of chemical processes, such as Fischer-Tropsch synthesis, oxidation reactions, alkylation reactions, effluent treatment, fermentation, reactions, protein production, and more recently, in cell cultures. In this work, three-dimensional simulations of the transient flow in bubble columns was performed using the computational package CFD CFX® 5.7 (ANSYS®). This package uses the finite volumes method to solve the governing equations of transport in multiphase flow using the Eulerian-Eulerian approach, which showed to be adequate for this study. The case studies were carried out in order to verify the influence of the properties of the continuous phase (viscosity and superficial tension), the dispersed phase (diameter of the bubbles) and the drag models ... Note: The complete abstract is available with the full electronic digital thesis or dissertations / Mestrado / Desenvolvimento de Processos Químicos / Mestre em Engenharia Química

We develop and analyse explicit in time schemes for the computation of compressible flows, based on staggered in space. Upwinding is performed equation by equation only with respect to the velocity. The pressure gradient is built as the transpose of the natural divergence. For the barotropic Euler equations, the velocity convection is built to obtain a discrete kinetic energy balance, with residual terms which are non-negative under a CFL condition. We then show that, in 1D, if a sequence of discrete solutions converges to some limit, then this limit is the weak entropy solution. For the full Euler equations, we choose to solve the internal energy balance since a discretization of the total energy is rather unnatural on staggered meshes. Under CFL-like conditions, the density and internal energy are kept positive, and the total energy cannot grow. To obtain correct weak solutions with shocks satisfying the Rankine-Hugoniot conditions, we establish a kinetic energy identity at the discrete level, then choose the source term of the internal energy equation to recover the total energy balance at the limit. More precisely speaking, we prove that in 1D, if we assume the L∞ and BV-stability and the convergence of the scheme, passing to the limit in the discrete kinetic and internal energy equations, we show that the limit of the sequence of solutions is a weak solution. Finally, we consider the computation of radial flows, governed by Euler equations in axisymetrical (2D) or spherical (3D) coordinates, and obtain similar results to the previous sections. In all chapters, we show numerical tests to illustrate for theoretical results. / We develop and analyse explicit in time schemes for the computation of compressible flows, based on staggered in space. Upwinding is performed equation by equation only with respect to the velocity. The pressure gradient is built as the transpose of the natural divergence. For the barotropic Euler equations, the velocity convection is built to obtain a discrete kinetic energy balance, with residual terms which are non-negative under a CFL condition. We then show that, in 1D, if a sequence of discrete solutions converges to some limit, then this limit is the weak entropy solution. For the full Euler equations, we choose to solve the internal energy balance since a discretization of the total energy is rather unnatural on staggered meshes. Under CFL-like conditions, the density and internal energy are kept positive, and the total energy cannot grow. To obtain correct weak solutions with shocks satisfying the Rankine-Hugoniot conditions, we establish a kinetic energy identity at the discrete level, then choose the source term of the internal energy equation to recover the total energy balance at the limit. More precisely speaking, we prove that in 1D, if we assume the L∞ and BV-stability and the convergence of the scheme, passing to the limit in the discrete kinetic and internal energy equations, we show that the limit of the sequence of solutions is a weak solution. Finally, we consider the computation of radial flows, governed by Euler equations in axisymetrical (2D) or spherical (3D) coordinates, and obtain similar results to the previous sections. In all chapters, we show numerical tests to illustrate for theoretical results.

Dans les installations nucléaires, les explosions, qu’elles soient d’origine interne ou externe, peuvent entrainer la rupture du confinement et le rejet de matières radioactives dans l’environnement. Il est donc fondamental, dans un cadre de sûreté de modéliser ce phénomène. L’objectif de cette thèse est de contribuer à l’élaboration de schémas numériques performants pour résoudre ces modèles complexes. Les travaux présentés s’articule autour de deux axes majeurs : le développement de schémas volumes finis consistants pour les équations d’Euler compressible qui modélise les ondes de choc et celui de schémas performants pour la propagation d’interfaces comme le front de flamme lors d'une déflagration. La discrétisation spatiale est de type mailles décalées pour tous les schémas développés. Les schémas pour les équations d'Euler se basent sur une formulation en énergie interne qui permet de préserver sa positivité ainsi que celle de la masse volumique. Un bilan d'énergie cinétique discret peut être obtenu et permet de retrouver un bilan d'énergie totale par l'ajout d'un terme de correction dans le bilan d'énergie interne. Le schéma ainsi construit est consistant au sens de Lax avec les solutions faibles entropiques des équations continues. On utilise les propriétés des équations de type Hamilton-Jacobi pour construire une classe de schémas volumes finis performants sur une large variété de maillages modélisant la propagation du front de flamme. Ces schémas garantissent un principe du maximum et possèdent des propriétés importantes de monotonie et consistance qui permettent d'obtenir un résultat de convergence. / In nuclear facilities, internal or external explosions can cause confinement breaches and radioactive materials release in the environment. Hence, modeling such phenomena is crucial for safety matters. The purpose of this thesis is to contribute to the creation of efficient numerical schemes to solve these complex models. The work presented here focuses on two major aspects: first, the development of consistent schemes for the Euler equations which model the blast waves, then the buildup of reliable schemes for the front propagation, like the flame front during the deflagration phenomenon. Staggered discretization is used in space for all the schemes. It is based on the internal energy formulation of the Euler system, which insures its positivity and the positivity of the density. A discrete kinetic energy balance is derived from the scheme and a source term is added in the discrete internal energy balance equation to preserve the exact total energy balance. High order, MUSCL-like interpolators are used in the discrete momentum operators. The resulting scheme is consistent (in the sense of Lax) with the weak entropic solutions of the continuous problem. We use the properties of Hamilton-Jacobi equations to build a class of finite volume schemes compatible with a large number of meshes to model the flame front propagation. These schemes satisfy a maximum principle and have important consistency and monotonicity properties. These latters allows to derive a convergence result for the schemes based on Cartesian grids.

Les maillages volumiques sont très répandus en informatique graphique, en visualisation scientifique et en calcul numérique. Des opérations de subdivision, de simplification ou de remaillage sont parfois utilisées afin d’accélérer les traitements sur ces maillages. Afin de maîtriser la complexité de l’objet et des traitements numériques qui lui sont appliqués, une solution consiste alors à le représenter à différentes échelles. Les modèles existants sont conçus pour des approches spécifiques rendant leur utilisation limitée aux applications pour lesquelles ils ont été pensés. Nos travaux de recherche présentent un nouveau modèle pour la représentation de maillages multirésolutions en dimension quelconque basé sur le formalisme des cartes combinatoires. Nous avons d’abord appliqué notre modèle aux volumes de subdivision multirésolutions. Dans ce cadre, nous présentons plusieurs algorithmes de raffinement d’un maillage grossier initial. Ces algorithmes supportent des hiérarchies obtenues par subdivision régulière et adaptative. Nous proposons ensuite deux représentations, opposés en terme de coût spatial et temporel, pour ce modèle. / Volume meshes are widespread in computer graphics, scientific visualization and numerical computation. Subdivision, simplification or remeshing operations are sometimes used to speed up processing of these meshes. A solution to manage the complexity of the object and numerical processing applied to it consist in presenting this object at different scales. Nevertheless, existing models are designed for specific approaches making them limited to applications for which they were designed. Our research work present a new model for the representation of multiresolution meshes in any dimension based on the combinatorial maps model. We first applied our model to the multiresolution subdivision volumes. In this framework, we present several refinement algorithms of an initial coarse mesh. These algorithms support hierarchies obtained by regular and adaptive subdivision. Finally, we propose two representations, opposed in term of time and space complexity, of this model.