O método de Lattice-Boltzmann (MLB) vem ganhando destaque nas últimas décadas pela sua capacidade de solução de escoamentos complexos como escoamentos multifásicos e multicomponentes, meios porosos e magnetohidrodinâmicos. Também existem extensões do método para a solução de problemas de advecção-difusão, que permitem acoplamento dessa metodologia para a solução numérica do conjunto de equação Navier-Stokes-Fourier. No trabalho presente, os objetivos iniciais podem ser resumidos no estudo dos conceitos básicos necessários para entender a derivação do método a partir da teoria cinética e estudo do método de Lattice Boltzmann, com operador de colisão mais simples conhecido como operador BGK, para problemas bidimensionais térmicos e fluidodinâmicos. A implementação numérica do método foi realizada em linguagem C, Matlab e CUDA C, com foco na solução de cinco problemas incompressíveis e laminares em regime permanente, conhecidos na literatura: equação viscosa de Burgers, escoamento de Poiseuille com transferência de calor, convecção natural em uma cavidade quadrada, regimes de convecção natural, forçada e mista em uma cavidade com uma das fronteiras móvel, e por fim, convecção forçada em uma cavidade ventilada, com uma entrada e uma saída. Além disso, um pequeno estudo no tempo computacional utilizando três implementações distintas foram testadas: implementação em série, uso de interpolações entre malhas grosseiras como condição inicial para malhas mais refinadas, e por fim, a adição da implementação do código em paralelo. Os ganhos de tempo entre a primeira e segunda estratégia ficaram entre 1.5 e 6, ao passo que o código paralelizado mostrou-se entre 20 e 25 vezes mais rápido que a segunda estratégia testada, comprovando o benefício de utilizar o processamento em paralelo em unidades gráficas. Os resultados obtidos para os problemas foram comparados com outros trabalhos da literatura, mostrando boa concordância para os primeiros quatro problemas estudados. Para a cavidade ventilada, diferenças relativas de até 15.7% no coeficiente de troca de calor e de até 28.38% para o coeficiente de queda de pressão adimensional foram observadas. Análises a respeito dos termos de erros do método apresentado, e a utilização de outras metodologias com método de Lattice Boltzmann, como por exemplo, o emprego de outros operadores de colisão, para trazerem mais estabilidade e precisão, podem elucidar melhor as divergências observados entre o trabalho presente e outros trabalhos da literatura. / Lattice-Boltzmann Method (LBM) has gained attention over last decades due to its performance in solving complex flows such as multiphase and multicomponent flow, porous media and magnetohydrodynamics. There are also further techniques which makes LBM able to solve advection-difussion problems, which allows coupling this methodology to solve Navier-Stokes-Fourier equations. In this work, initial goals are, in a few words, studying main concepts required to understand numerical method origins from kinectic thery, and studying the method implemetantion to solve 2D fluid dynamic and thermal problems. Numerical implemetation was written in C, CUDA C and Matlab languages, keeping in focus five different cases of laminar incompressible flows in steady state: viscous Burgers\' equation, thermal Poiseuille, natural convection in square cavities, natural, forced and mixed convection in a lid driven cavity, and, finally, forced convection in a ventilated cavity, with one inlet and outlet ports. Besides that, a quick study regarding impact in simulation time of three distinct approaches was conducted. First approach consists in implementing a serial code, the second in using interpolation for coarser grids results as initial condition for finer meshes, and the last one is adding parallelized code implementation. Time gains between first and second approach range from 1.5 to 6, while parallelized code was able to converge from 20 to 25 times faster than second approach, confirming great benefits in using graphics processing units. Results obtained from numerical solutions of problems were compared with other works from literature, and a good agreement among them was observed, specially in the first four problems studied. In ventilated cavity problem, relative differences up to 15.7% in heat transfer coefficient and up to 28.38% in dimensionless pressure drop coefficient were observed. A further error terms analysis of method used in this work, and use of distinct approaches, such as different collision operators, in order to increase numerical solution stability and accurarcy, may shed a light on results divergences observed between this work and others from literature.

Modelling the ice accretion in glaze regime for the supercooled large droplets is one of the most challenging problems in the aircraft icing field. The difficulties are related to the presence of the liquid water film on the surface in the glaze regime and also the phenomena associated with SLD conditions, specifically the splashing and re-impingement. The steady improvement of simulation methods and the increasing demand for highly optimised aircraft performance, make it worthwhile to try to get beyond the current level of modelling accuracy. A semi-empirical method has been presented to characterize the thin water film in the icing problem based on both analytical and experimental approaches. The experiments have been performed at the Cranfield icing facilities. Imaging techniques have been used to observe and measure the features of the thin water film in the different conditions. A series of numerical simulations based on an inviscid VOF model have been performed to characterize the splashing process for different water film to droplet size ratios and impact angles. Based on these numerical simulations and the proposed methods to estimate the thin water film thickness, a framework has been presented to model the effects of the splashing in the icing simulation. These effects are the lost mass from the water film due to the splashing and the re-impingement of the ejected droplets. Finally, a new framework to study the solidification process of the thin water film has been explored. This framework is based on the lattice Boltzmann method and the preliminary results showed the capabilities of the method to model the dynamics, thermodynamics and the solidification of the thin water film.

Reactive Transport Models (RTMs) provide quantitative tools to analyze the interaction between transport and biogeochemical processes in subsurface environments such as aquatic sediments and groundwater flow. A tremendous amount of research has shown the role and impact of scaling behavior of the reactive systems which stems from geologic heterogeneity. Depending on the kinetics of the reactions, different types of formulations have been proposed to describe reactions in RTMs. We introduce a novel quantitative criteria on the range of validity of local equilibrium assumption (LEA) in aquatic sediments with irreversible heterogeneous sorption reactions. Then we present a one-dimensional (1-D) early diagenetic module, MATSEDLAB, developed in MATLAB. The module provides templates for representing the reaction network, boundary conditions and transport regime, which the user can modify to fit the particular early diagenetic model configuration of interest. We describe the theoretical background of the model and introduce the MATLAB pdepe solver, followed by calibration and validation of the model by a number of theoretical and empirical applications. Finally, we introduce a new pore-scale model using lattice Boltzmann (LB) approach. It uses an iterative scheme for the chemical transport-reaction part and recent advances in the development of optimal advection-diffusion solvers within the lattice Boltzmann method framework. We present results for the dissolution and precipitation of a porous medium under different dynamical conditions, varying reaction rates and the ratio of advective to diffusive transport (Pe, Peclet number) for linear reactions. The final set of calculations considers sorption reactions on a heterogeneous porous medium. We use our model to investigate the effect of heterogeneity on the pore-scale distribution of sorption sites and the competition between three different sorption reactions.

Modelling the ice accretion in glaze regime for the supercooled large droplets is one of the most challenging problems in the aircraft icing field. The difficulties are related to the presence of the liquid water film on the surface in the glaze regime and also the phenomena associated with SLD conditions, specifically the splashing and re-impingement. The steady improvement of simulation methods and the increasing demand for highly optimised aircraft performance, make it worthwhile to try to get beyond the current level of modelling accuracy. A semi-empirical method has been presented to characterize the thin water film in the icing problem based on both analytical and experimental approaches. The experiments have been performed at the Cranfield icing facilities. Imaging techniques have been used to observe and measure the features of the thin water film in the different conditions. A series of numerical simulations based on an inviscid VOF model have been performed to characterize the splashing process for different water film to droplet size ratios and impact angles. Based on these numerical simulations and the proposed methods to estimate the thin water film thickness, a framework has been presented to model the effects of the splashing in the icing simulation. These effects are the lost mass from the water film due to the splashing and the re-impingement of the ejected droplets. Finally, a new framework to study the solidification process of the thin water film has been explored. This framework is based on the lattice Boltzmann method and the preliminary results showed the capabilities of the method to model the dynamics, thermodynamics and the solidification of the thin water film.

No description available.

This thesis focuses on the lattice-Boltzmann method (LBM) and its ability to simulate immiscible two-phase flow. We introduce the main lattice-Boltzmann-based approaches for analyzing two-phase flow: the color-fluid model by Gunstensen, the interparticle-potential model by Shan and Chen, the free-energy model by Swift and Orlandini, and the mean-field model by He. The first objective is to assess the ability of these methods to maintain continuity at the interface of two fluids, especially when the two fluids have different viscosities or densities. Continuity issues have been mentioned in the literature but have never been quantified. This study presents a critical comparison of the four lattice-Boltzmann-based approaches for analyzing two-phase flow by analyzing the results of the two-phase Poiseuille flow for different viscosity ratios and density ratios. The second objective is to present the capability of the most recent version of the color-fluid model for simulating 3D flows. This model allows direct control over the surface tension at the interface. We demonstrate the ability of this model to simulate surface tension effects at the interface (Laplace bubble test), stratified two-phase flows Poiseuille two-phase flow), and bubble dynamics (the free rise of a bubble in a quiescent viscous fluid).

Many industrial processes use biological agents as catalysts. In this context, the study of the cellular metabolism becomes relevant for planning the best strategies (environmental and/or genetic modifications) to manipulate the cell in order to maximise the production of a metabolite of interest and minimise the by-products one. This increases the yield of the fermentation and reduces the cost of product recovery; thereby the profitability of the process is improved. The intracellular reactions are carried out in a complex, crowded and heterogeneous medium composed by solid components (macromolecules, ions, enzymes, small solutes, etc.) in a fluid phase called cytoplasm, all of them enclosed within the cellular membrane. The interactions among the intracellular components (as well as with the extracellular environment) determine the behaviour of the organism. The modelling and simulations of these interactions help the understanding of the metabolism. The aim of this thesis is to provide generic tools for the analysis and simulation of metabolic systems under the intracellular environmental conditions. In particular, this research focuses on the estimation of metabolic fluxes and the simulation of the diffusion process. The stoichiometric models have been widely used for the calculation of unmeasured fluxes in a metabolic network, assuming the system is at steady state. The addition of thermodynamic constraints allows only the prediction of fluxes that go in the direction of the Gibbs free energy drop. The Gibbs free energy change ( ) depends on the (intracellular) environmental conditions and determine the direction, feasibility and reversibility of the reactions involved in the pathways. The thermodynamically constrained stoichiometric model proposed here allows the estimation of the range of fluxes of a metabolic network, where the information about the presence of the enzymes that catalyse the reactions can be incorporated (if available). The effect of considering a zero flux reaction as blocked or at equilibrium on the flux predictions was investigated, as well as the environmental conditions ionic strength, temperature and pH. Additionally, since the solid components within the cell occupy about 40% of its total volume, these crowding conditions could alter the thermodynamic feasibility of the pathways. For this reason, the thermodynamically constrained stoichiometric model is extended to incorporate the crowding effect. The case study used in this work is the central carbon metabolic network of Actinobacillus succinogenes for the production of succinic acid from glycerol, a by-product in the biodiesel manufacture. Moreover, the crowding conditions also affect the diffusion of the molecules. The prokaryotic cells have been widely used in fermentation processes for the production of metabolites of interest. In this type of cells the diffusion is the primary mean of the particles’ motion, so that the diffusion reduction due to the crowding conditions could affect the possibility of encounter among the reactants, decreasing the reactions’ rate and therefore the yield of the process. A methodology based on the Lattice Boltzmann Method (LBM) and the Scaled Particle Theory (SPT) is presented in this thesis for fast simulations of the diffusion of hard-disk molecules in 2D crowded systems, which also allows evaluating the effect of the molecules’ size on their diffusion.

<div>The thesis includes two application studies of computational fluid dynamics. The first is new and efficient drug delivery to the posterior part of the eye, a growing health necessity worldwide. Current treatment of eye diseases, such as age related macular degeneration (AMD), relies on repeated intravitreal injections of drug-containing solutions. Such a drug delivery has significant drawbacks, including short drug life, vital medical service, and high medical costs. In this study, we explore a new approach of controlled drug delivery by introducing unique porous implants. Computational</div><div>modeling contains physiological and anatomical traits. We simulate the IgG1 Fab drug delivery to the posterior eye to evaluate the effectiveness of the porous implants to control the drug delivery. The computational model was validated by established computation results from independent studies and experimental data. Overall, the results indicate that therapeutic drug levels in the posterior eye are sustained for</div><div>eight weeks, similar to those performed with intravitreal injection of the same drug. We evaluate the effects of the porous implant on the time evaluation of the drug concentrations in the sclera, choroid, and retina layers of the eye. Subsequent simulations were carried out with varying porosity values of a porous episcleral implant.</div><div>Our computational results reveal that the time evolution of drug concentration is distinctively correlated to drug source location and pore size. The response of this porous implant for controlled drug delivery applications was examined. A correlation between porosity and fluid properties for the porous implants was revealed in this study. The second application lays in the computational modeling of the oscillating flow in rectangular ducts. This computational study has further applications in investigating the fluid flow motion in bodily organs. It can be useful in studying the</div><div>response of bone cells to the wall shear stress in the human body. </div>

[pt] Neste trabalho aplicamos o método Lattice Boltzmann (LBM) para simular os processos de reações químicas que ocorrem na interação entre o fluido e a fase sólida, modificando o meio poroso. Para isso apresentaremos como o método LBM aborda a simulação do escoamento de fluido em um meio poroso irregular para os casos de um ou mais fluidos incluindo o processo de dissolução química. A partir dos processos anteriores, propomos uma modificação onde a dissolução possa ocorrer como uma característica do fluido que interage com a fase sólida. Ao abordar a dissolução como característica da interação do fluido com a fase sólida, é possível ter uma maior compreensão de como o fluido pode modificar a geometria do meio poroso e impactar nas mudanças de fluxo. A proposta de modificação foi avaliada em alguns casos em que o fluxo no meio poroso é bem definido: o canal aberto, canal com cilindros e em um meio poroso de geometria complexa. A proposta foi estendida para a simulação em um meio poroso 3D, onde analisamos como a dissolução foi impactada pela presença de forças externas como a gravidade. / [en] In this work, we apply the Lattice Boltzmann (LBM) method to simulate the chemical reaction processes that occur in the interaction between the fluid and the solid phase, modifying the porous medium. For this, we will present how the LBM method approaches fluid flow simulation in an irregular porous medium for cases of one or more fluids, including the chemical dissolution process. Based on the previous processes, we propose a modification where dissolution can occur as a characteristic of the fluid that interacts with the solid phase. By approaching dissolution as a characteristic of the interaction of the fluid with the solid phase, it is possible to better understand how the fluid can modify the geometry of the porous medium and impact the flow changes. The modification proposal was evaluated in some cases where the flow in the porous medium is well defined: the open channel, a channel with cylinders, and a porous medium with complex geometry. The proposal was extended to the simulation in a 3D porous medium, where we analyzed how the dissolution was impacted by external forces such as gravity.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24167号 / 理博第4858号 / 新制||理||1695(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 早川 尚男, 教授 佐々 真一, 教授 山本 潤 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM