A Dinâmica de Fluidos Computacional é uma importante área de pesquisa no contexto da Computação Científica. Através da modelagem e simulação das propriedades de líquidos e gases é possível obter resultados numéricos para diferentes estruturas e fenômenos físicos cotidianos e de grande importância econômica. A evolução dos sistemas computacionais possibilitou a essa área o surgimento de novas técnicas e abordagens de simulação. Uma das técnicas computacionais atualmente empregadas é o Método de Lattice Boltzmann, um método numérico iterativo para a modelagem e simulação mesoscópica da dinâmica de fluxos de fluidos. Diferentes tipos de sistemas físicos podem ser tratados através dessa técnica, como é o caso de fluxos em meios porosos ou de substâncias imiscíveis. No entanto, por causa da dimensão dos sistemas físicos, é necessário adotar estratégias que permitam a obtenção de resultados precisos ou em tempos computacionais aceitáveis. Assim, paralelizar as operações é a solução mais indicada para aumentar o desempenho do método. Uma maneira eficiente de paralelizar um método numérico é fazer uso de técnicas de distribuição de dados refinadas, como é o caso do particionamento em blocos. Tais abordagens de paralelização foram adotadas neste trabalho em implementações bi- e tridimensionais do Método de Lattice Boltzmann, com o intuito de avaliar o ganho de desempenho oferecido através dessa técnica. Além disso, foram definidos os fatores que influenciam as melhores configurações de particionamento. Os resultados obtidos demonstraram que o particionamento em blocos prove um aumento considerável do desempenho das aplicações paralelas, especialmente para a versão tridimensional do método. Para algumas configurações dos estudos de caso os tempos de execução diminuíram em até 30% em relação aos tempos obtidos com o particionamento unidimensional. Já as melhores configurações para a distribuição dos dados em blocos foram aquelas em que a disposição dos dados manteve-se mais quadrada ou cúbica em relação a cada uma das dimensões coordenadas. / Computational Fluid Dynamics is an important research area in the Scientific Computing context. Through the modeling and simulation of liquids and gases properties it is possible to get numerical results for different physical structures and daily phenomena that have great economic importance. The evolution of the computational systems made it possible to develop new techniques and approaches of simulation in this area. One of these techniques currently used is the Lattice Boltzmann Method. This method is an iterative numerical strategy for modeling and simulating mesoscopic dynamics of fluid flows. Different types of physical systems can be simulated through this technique, like immiscible substances and flows in porous media. However, since the dimension of the physical systems is usually large, it is necessary to adopt strategies that allow to get accurate results or results in an acceptable computational time. Thus, the parallelization of the operations is the best alternative to increase the performance of the method. An efficient way to parallelize a numerical method is to make use of refined data distribution techniques, like data partitioning in blocks. Such parallelization approach had been adopted in this work for bi- and three-dimensional implementations of the Lattice Boltzmann Method. The objective of the work was to evaluate the performance enhancement offered through the parallelization. Moreover, another objective is to define the elements that influence the best partitioning configurations. The results shown that data partitioning in blocks provide a considerable performance increase for parallel implementations, especially for the three-dimensional version of the method. For some configurations adopted in the case studies, the execution time was reduced of up to 30% in relation to the one-dimensional partitioning strategy. The best configurations for data distribution in blocks were that where the data disposal are more square or cubical shaped in relation to each one of the coordinate dimensions

A Dinâmica de Fluidos Computacional é uma importante área de pesquisa no contexto da Computação Científica. Através da modelagem e simulação das propriedades de líquidos e gases é possível obter resultados numéricos para diferentes estruturas e fenômenos físicos cotidianos e de grande importância econômica. A evolução dos sistemas computacionais possibilitou a essa área o surgimento de novas técnicas e abordagens de simulação. Uma das técnicas computacionais atualmente empregadas é o Método de Lattice Boltzmann, um método numérico iterativo para a modelagem e simulação mesoscópica da dinâmica de fluxos de fluidos. Diferentes tipos de sistemas físicos podem ser tratados através dessa técnica, como é o caso de fluxos em meios porosos ou de substâncias imiscíveis. No entanto, por causa da dimensão dos sistemas físicos, é necessário adotar estratégias que permitam a obtenção de resultados precisos ou em tempos computacionais aceitáveis. Assim, paralelizar as operações é a solução mais indicada para aumentar o desempenho do método. Uma maneira eficiente de paralelizar um método numérico é fazer uso de técnicas de distribuição de dados refinadas, como é o caso do particionamento em blocos. Tais abordagens de paralelização foram adotadas neste trabalho em implementações bi- e tridimensionais do Método de Lattice Boltzmann, com o intuito de avaliar o ganho de desempenho oferecido através dessa técnica. Além disso, foram definidos os fatores que influenciam as melhores configurações de particionamento. Os resultados obtidos demonstraram que o particionamento em blocos prove um aumento considerável do desempenho das aplicações paralelas, especialmente para a versão tridimensional do método. Para algumas configurações dos estudos de caso os tempos de execução diminuíram em até 30% em relação aos tempos obtidos com o particionamento unidimensional. Já as melhores configurações para a distribuição dos dados em blocos foram aquelas em que a disposição dos dados manteve-se mais quadrada ou cúbica em relação a cada uma das dimensões coordenadas. / Computational Fluid Dynamics is an important research area in the Scientific Computing context. Through the modeling and simulation of liquids and gases properties it is possible to get numerical results for different physical structures and daily phenomena that have great economic importance. The evolution of the computational systems made it possible to develop new techniques and approaches of simulation in this area. One of these techniques currently used is the Lattice Boltzmann Method. This method is an iterative numerical strategy for modeling and simulating mesoscopic dynamics of fluid flows. Different types of physical systems can be simulated through this technique, like immiscible substances and flows in porous media. However, since the dimension of the physical systems is usually large, it is necessary to adopt strategies that allow to get accurate results or results in an acceptable computational time. Thus, the parallelization of the operations is the best alternative to increase the performance of the method. An efficient way to parallelize a numerical method is to make use of refined data distribution techniques, like data partitioning in blocks. Such parallelization approach had been adopted in this work for bi- and three-dimensional implementations of the Lattice Boltzmann Method. The objective of the work was to evaluate the performance enhancement offered through the parallelization. Moreover, another objective is to define the elements that influence the best partitioning configurations. The results shown that data partitioning in blocks provide a considerable performance increase for parallel implementations, especially for the three-dimensional version of the method. For some configurations adopted in the case studies, the execution time was reduced of up to 30% in relation to the one-dimensional partitioning strategy. The best configurations for data distribution in blocks were that where the data disposal are more square or cubical shaped in relation to each one of the coordinate dimensions

Oriunda da etapa de destilação do caldo do caldo da cana-de-açúcar, a vinhaça é um subproduto da produção de etanol. Apesar de seu difundido uso na agricultura canavieira como fertirrigação, sua disposição no solo tem sido questionada quanto a possíveis riscos ambientais. Uma destinação alternativa à vinhaça e seu tratamento anaeróbio, considerado bastante atrativo haja vista a possibilidade de recuperação de energia na forma de biogás, sem interferir em suas qualidades como biofertilizante. Entre os sistemas de tratamento anaeróbios, os reatores de leito fixo têm sido amplamente utilizados devido à sua estabilidade operacional. A modelagem abrangente destes tipos reatores tende a ser complexa de forma que o estudo dos escoamentos em seu interior do reator é vital. Neste contexto, o objetivo deste trabalho foi analisar e simular numericamente a hidrodinâmica de reator de leito fixo de fluxo ascendente tipo APBR (anaerobic packed bed reactor). Em termos gerais, os resultados obtidos por simulação foram confrontados tanto com os correspondentes valores experimentais como com aqueles obtidos a partir dos modelos uniparamétricos comumente usados para representar reatores não ideais. Para tanto, foram empregados dados pré-existentes de ensaios hidrodinâmicos conduzidos no início e no final da operação, com biorreator alimentado com solução-traçador na forma de degrau a vazões de 4,6 L/dia e 2,3 L/dia. Foram considerados os modelos de dispersão de pequena e grande intensidade bem como o modelo de tanques agitados em série. Quanto às simulações numéricas, foi usado o software de CFD (fluidodinâmica computacional)COMSOL Multiphysics ® 4.3b.As curvas DTR obtidas via simulação e com base nos modelos para reatores não ideais foram confrontadas com as curvas obtidas experimentalmente. Para o reator operando com vazão de 2,3 L/dia, nenhum dos modelos propostos mostrou-se adequado quanto ao final da operação, em razão da incapacidade em representar o surgimento de picos de concentração que podem estar associados ao acúmulo de biomassa no interior do biorreator, mas também ao tipo de traçador utilizado para a realização do experimento. As demais curvas DTR sugerem que o reator em questão aproxima-se do tipo pistonado. O simulador CFD representou de forma bem adequada os dados experimentais em comparação com resultados obtidos a partir dos modelos para reatores não ideais. A simulação numérica de biorreatores para tratamento de efluentes mostrou-se, pois, capaz de fornecer informações mais detalhadas e precisas, geralmente úteis a engenharia do processo. Adicionalmente, foi implementado um simulador com base no método de Boltzmann em rede (lattice Boltzmann method, LBM) capaz de simular escoamento laminar bidimensional em regime permanente no interior de um canal. No escopo de uma linha de pesquisa em simulação LBM de biossistemas agroindustriais, trata-se de um esforço inicial quanto à simulação LBM da hidrodinâmica de biorreatores para tratamento de efluentes em geral. / Resulting from sugarcane juice distillation, vinasse is a by-product from ethanol industry. Despite its widespread use as fertirrigation at crops, direct deposition of vinasse into soils has raised environmental issues. Alternatively, it may undergo anaerobic treatment, which is very attractive in view of energy recovery as biogas while preserving vinasse quality as biofertilizer. Among anaerobic treatment systems, fixed-bed reactors come forward due to their operational stability. Their comprehensive modeling is prone to be complex so that the study of fluid flows prevailing inside is fundamental. Accordingly, the goal of this work was to numerically analyze and simulate the hydrodynamics within a particular upflow fixedbed reactor, namely anaerobic packed bed reactor. In general, results from simulations were compared with experimental counterparts as well as against results from well-known single-parameter models for non-ideal reactors. Existing data from hydrodynamic tests were then used, concerning operation at both start-up and shut-down and bioreactor stepwise feeding with tracer solution flow at 4,6 L/day and 2,3 L/day. Non-ideal reactor models comprised either low or high-dispersion together with continuous stirred-tank reactor model while COMSOL Multiphysics ® 4.3b CFD (computational fluid dynamics) software was employed for simulations. Retention time distribution (RTD) curves from simulations and from model calculations were compared to experimental ones. For operation at 2,3 L/day flow, no models proved to be suitable as far as shut-down operation is concerned, due to biomass accumulation inside the bioreactor. Remaining RTD curves suggested that reactor behavior resembles plug-flow type. Compared to non-ideal reactor models, CFD simulations proved to properly reproduce experimental data while being able to provide detailed and accurate information for process engineering towards effluent treatment. Furthermore, a numerical simulator was implemented as based on the lattice Boltzmann method (LBM) in order to deal with two-dimensional steady-state laminar flow inside a channel. As part of research work on LBM simulation of agroindustrial biosystems, aforesaid simulator contributed to LBM simulation of hydrodynamics within bioreactors for wastewater treatment in general.

Le travail présenté dans ce mémoire de thèse porte sur la modélisation discrète de l’évolution régressive du front d’un conduit d’érosion qui peut se produire dans les barrages ou digues en remblai. Des outils numériques ont été développés en se basant sur le couplage entre la méthode des éléments discrets (DEM) et la méthode de Boltzmann sur réseau (LBM) pour la description, respectivement, des phases solide et fluide. L’implémentation de la méthode DEM suit une approche standard de type dynamique moléculaire (DM) et les interactions intergranulaires sont modélisées par des contacts unilatéraux visco-élastiques frottants ou bilatéraux (ponts solides) viscoélastiques, afin de permettre la modélisation d’un sol légèrement cohésif. La méthode LBM est implémentée ici avec des temps de relaxation multiples (MRT) et une condition de rebondissement interpolée pour les frontières solides en mouvement, afin d’améliorer la stabilité numérique des calculs. Le schéma du couplage entre les deux méthodes, ainsi que les critères pour le choix des paramètres numériques des deux méthodes. Pour étudier le phénomène visé, un échantillon représentatif de sol granulaire situé au front d’un conduit d’érosion est d’abord assemblé par une procédure de préparation “à sec”, puis testé dans des conditions saturées sous un chargement hydraulique monotone croissant. L’érosion régressive se produit par amas de grains au niveau du front d’érosion ayant subi au préalable une dégradation due à de nombreuses ruptures de ponts solides en traction. L’autre phénomène important observé est la présence d’arcs associés a` des chaines de forces en compression qui parviennent à maintenir parfois totalement, parfois partiellement l’intégrité du matériau non érodé. / The work reported in this thesis consists in a discrete modelling of the backward front propagation of an erosion pipe, as can take place in embankment dams or dikes. Some numerical tools have been developed to this end, based on the coupling between the Discrete Element Method (DEM) and the Lattice Boltzmann Method (LBM) for the representation of the solid and uid phases, respectively. The implementation of DEM follows a standard molecular dynamics approach and the interaction among grains are regulated by unilteral frictional visco-elastic and breakable visco-elastic bonds, in order to take into account a slightly cohesive soil behaviour. The LBM was implemented according to the Multiple Relaxation Time (MRT) scheme along with an interpolated non-slip conditions for moving boundaries, in order to improve the numerical stability of the calculations. The coupling scheme is described along with the criteria for the numerical parameters of the two methods. A representative specimen of a granular soil located at the front of an erosion pipe is first assembled by a \dry" preparation precedure and then tested under fully-saturated conditions and increasing hydraulic load over time. Backward erosion is takes place in the form of clusters of grain being eroded at the erosion front after a degradation of the material due to the breakage of tensile bonds. The other interesting feature that was observed is the creation of arches of compressive force chains. These arches enabled the specimen to maintain a stable or metastable configuration under the increasing hydraulic load.

Le coefficient d'électrofiltration est simulé par méthode Lattice Boltzmann dans un chenal 2-D sur une grande gamme de salinité. L'influence de la permittivité et de la viscosité est discutée. La validité de l'équation d'Helmholtz Smoluchowski à de forts potentiels zeta est évaluée. Un modèle de conductivité intrinsèque est développé en prenant en compte les variations locales de conductivité, qui ont un impact significatif en la présence d'espèces polyvalentes. Étendu aux conditions non saturées, l'algorithme montre que la densité de charge électrique associée à l'interface eau-air est une composante clé. Le coefficient présente une attitude non monotone, avec une augmentation par rapport à l'état saturé. L'amplitude de cette augmentation dépend de l'état dynamique des bulles, mobiles ou piégées. L'aspect transport multiphasique est complété par une étude numérique de l'impact de la forme des échantillons sur la mesure des lois reliant saturation et pression capillaire en hydrologie. / The electrokinetic coefficient is simulated in a large range of salinities using the Lattice Boltzmann method in a 2-D channel. The effect of permittivity and viscosity is discussed. The validity of the Helmholtz Smoluchowski equation using strong zeta potentials is assessed. A model of bulk fluid conductivity is derived, taking into account the local variations of conductivity which have a significant impact in the presence of polyvalent counterions. Extended to unsaturated conditions, the model shows that the electrical charge density associated to the air-water interface is a key component. The coefficient shows a non monotonous behaviour, with an enhancement compared to the saturated state. The magnitude of this enhancement depends on the dynamic state of the bubbles, moving or entrapped. The multiphase transport aspect is associated to a numerical study of the influence of the sample geometry on the measurement of the capillary pressure / saturation relationships used in hydrology.

La simulation numérique de l’écoulement des fluides et du transfert dechaleur dans les phénomènes multi-échelles est encore très difficile avecles méthodes numériques conventionnelles, e.g. la méthode de Volumes Finis(FVM) etc. Récemment développée pour simuler les écoulements desfluides, le transfert de chaleur et des phénomènes physiques complexes, laméthode de Lattice Boltzmann (LBM) est basée sur la théorie cinétiquedu fluide, qui possède de nombreuse caractéristiques distinctives. Afind’élargir le champ d’application de LBM, cette thèse doctorale a mené destravaux de recherches systématiques sur la combinaison entre LBM et lesméthodes macroscopiques et sur les modèles thermiques et la simulation dela turbulence en utilisant LBM. Les principales contributions de cette thèsesont: 1. Un couplage multi-échelles LBM-FVM est construit pour les écoulementsdu fluide instationnaire et un opérateur de reconstruction g´en´erale entreLBM et FVM est proposé pour le transfert de l’information; 2. Un modèle thermique 3D de LBM est développé pour les écoulements compressibles thermiques à faible nombre de Mach, et un modèle de LBM entièrement compressible avec factorisation symétrique est proposé pour simuler les écoulements fortement compressibles; 3. Un schéma asymptotique de volumes finis LBM et un schéma de LBM basé sur propagation fractionnaire et collision à demi-étape sont proposés pour simuler les écoulements subsoniques à grande vitesse et transsoniques; 4. La simulation des grandes échelles (LES) turbulentes est effectuée et étudiée dans le cadre de LBM thermique. Un modèle de paroi utilisant LBM thermique est développé pour un écoulement à nombre de Reynolds élevé. / The simulation of fluid flows and heat transfer of multiscale phenomena orprocesses is one of the most challenging domains from the theoretical aswell as the numerical modeling point of view. It is difficult to model andsimulate multiscale problems using conventional computational fluid dynamicsmethods. As an approach based on the mesoscopic kinetic equationfor fluids and has many distinctive features, the lattice Boltzmann method(LBM) is a recently developed method for simulating fluid flows, heat transferand complicated physical phenomena. However, the applications of latticeBoltzmann method in actual multiscale problem are still in explorationstage. In order to enlarge the application scope of lattice Boltzmann methodfor multiscale simulation, the present work has conducted systematic researchon combination of LBM and macroscopic methods, thermal lattice Boltzmann models and turbulence simulation using LBM. The major contributions of this dissertation are summarized as follows: 1. A multiscale coupling LBM-FVM is constructed for unsteady fluid flows and a general reconstruction operator between LBM and FVMis proposed for information transfer. 2. A three-dimensional thermal lattice Boltzmann model is developed for thermal compressible flows with variable density in low Machnumber limit. Further more, a fully compressible lattice Boltzmann model with factorization symmetry is proposed for simulating high compressible flow. 3. An asymptotic preserving finite volume scheme LBM and a fractional propagation half step collision LBM are proposed for simulating high subsonic and transonic flows. 4. Large eddy simulation for turbulence is studied in framework of thermallattice Boltzmann method. Wall modeled LES using thermalLBM is developed for high Reynolds number flow.

The main purpose of this thesis was to propose and test a new approach that captures the features of single and multiple bubbles dynamics using the Shan and Chen-type lattice Boltzmann method (LBM). Two dimensional bubbles motions were simulated considering the buoyancy effect for which the topology of the bubble is characterized by the Eötvös (Eo), and Morton (M) numbers. A qualitative and quantitative validation were performed using the Level set method. Bubble shape deformation was captured and analysis based on terminal Reynolds number and degree of circularity show very good agreement with the experimental results and with available simulation results. In sum, this study presents crucial preliminary information to further analyze multiphase fluid flows in various contexts.

Le développement des énergies renouvelables passe par l’exploitation de nouvelles sources d’énergie. La filière hydrolienne, dédiée à la récupération de l’énergie des courants de marée, est proche de l’industrialisation. Cependant, les conditions hydrodynamiques turbulentes des sites hydroliens sont encore mal connues. Cette thèse propose d’examiner à l’échelle locale l’effet des rugosités du fond marin sur la génération de tourbillons hautement énergétiques par la simulation numérique en mécanique des fluides de type méthode de Boltzmann sur réseau. Cette méthode est particulièrement adaptée à la simulation d’écoulements instationnaires sur un domaine de simulation complexe. Dans un premier temps, les phénomènes physiques de détachements tourbillonnaires sur des macro-rugosités canoniques sont décrits. L’appariement de structures tourbillonnaires est mis en évidence dans le processus de formation de tourbillons hautement énergétiques. Dans un deuxième temps, la simulation permet d’observer de tels phénomènes dans le cas d’écoulements environnementaux intégrant une bathymétrie réelle. Ces simulations, validées par rapport à des mesures in situ, mènent à une meilleure compréhension des effets du fond marin sur la turbulence en milieu hydrolien. En particulier, l’importance des failles géologiques dans la génération de turbulence dans la zone d’étude est mise en évidence. / Renewable energy development calls for exploitation of new energy resources. Tidal stream power harvesting is now close to the industrialisation step. Still, turbulent hydrodynamic conditions at tidal sites are not well understood. This thesis aims to investigate the local scale effect of sea bottom roughnesses on energetic vortex generation with computational fluid simulations using the lattice Boltzmann method. This method is highly indicated for unsteady flow simulations of complex domains. First, the physical phenomena involved in vortex emission around canonical macroroughnesses are described. Vortex merging is identified in the generation process of energetic vortices. Then, such physical events are reproduced in the case of environmental flow simulations using a real seabed morphology. These simulations are validated on in situ measured data, and lead to a better understanding of the sea bottom effect on tidal stream site turbulence. They demonstrate the role of geological faults on the local turbulence.

An attempt to numerically predict flow rate of experimental configuration of orifices in transition between molecular and viscous flow regime is described in detail. Discretization of Boltzmann kinetic equation known as lattice-Boltzmann method is derived and applied unfortunately with very little connection to the original experimental problem due to nearly supersonic nature of the experimental setup. Current quite unsatisfactory state of the art of compressible lattice-Boltzmann method is also presented.

Melting and melt segregation are key processes in the geochemical evolution of the Earth. However, mechanism and time scale of melt transport from the source to the surface are still not well understood and are dependent on the grain-scale distribution of melt. A related question is the retention of melt in partially molten regions of the Earths upper mantle. Seismic observations from mid-ocean ridges (MOR) and subduction zones are interpreted to show in-situ melt contents up to 3%, while geochemical observations from MOR basalts are inferred to indicate very efficient extraction of melt (porosities of order 0.1%). Earlier theoretical models of the melt distribution were based on the balance of surface tension between melt and uniform crystalline grains, predicting a simple net- work of melt along three-grain edges. Analyses of experimentally produced samples of olivine and basaltic melt show that the melt geometry is much more complex, and includes wetted two-grain boundaries. I reconstructed the melt geometry of two experimentally produced samples by serial sectioning and 3-D rendering of the pore geometry which demonstrates for the first time that melt exists in thin layers on two-grain boundaries. This confirms the inferences from previous 2-D observations and has significant implications for physical properties of partially molten regions, for example seismic velocities and attenuation. The wetted two-grain boundaries are inferred to be a consequence of continuous grain growth. Due to the complexity of the 3-D melt geometry the perme- ability of partially molten rocks can not be predicted from simple models. I therefore investigated the permeability as a function of porosity for both synthetic and ex- perimentally determined pore geometries using a lattice-Boltzmann method. The calculated permeability is not a simple function of porosity, but increases rapidly at a critical fraction of wetted two-grain boundaries. In order to extrapolate the experimentally based findings to grain sizes expected in natural rocks I examined the geometry of secondary phases inferred to represent relict melt in mantle peridotites from the Krivaja massif in Bosnia. These findings corroborate the experimental observations of wetted two-grain boundaries.