Understanding how the water produced in an operating polymer electrolyte membrane fuel cell (PEMFC) is transported in cathode catalyst layer (CCL) is crucial to improving performance and efficiency. In this thesis, a multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) is employed to simulate the high density ratio, multiphase water transport in in the CCL. The three-dimensional structure of the catalyst layer is reconstructed based on experimental data acquired with a dual beam scanning electron microscope/focused ion beam system and a stochastic method using lower order statistical functions (e.g. porosity and two point correlation functions). Simulations of the water transport dynamics are performed to examine the effect of a range of physical parameters: wettability, viscosity ratio, pressure gradient, and surface tension. The water penetration patterns in the catalyst layers reveal a complex fingering process and transition of the water transport pattern from a capillary fingering regime to a stable displacement regime is observed when the wettability potential of the catalyst layer changes. The second part of the analysis focuses on quantifying the impact of liquid water distribution and accumulation in the catalyst layer on effective transport properties by coupling two numerical methods: the two-phase LBM is used to determine equilibrium liquid water distribution, and then a finite volume-based pore-scale model (FV-PSM) is used to compute transport of reactant and charged species in the CL accounting for the impact of liquid water saturation .The simulated results elucidate and quantify the significant impact of liquid water on the effective oxygen and water vapor diffusivity, and thermal conductivity in CLs. / Graduate

The fluid-structure interactions of wall-mounted slender structures, such as cilia, filaments, flaps, and flags, play an important role in a broad range of physical processes: from the coherent waving motion of vegetation, to the passive flow control capability of hair-like surface coatings. While these systems are ubiquitous, their coupled nonlinear response exhibits a wide variety of behaviours that is yet to be fully understood, especially when multiple structures are considered. The purpose of this work is to investigate, via numerical simulation, the fluid-structure interactions of arrays of slender structures over a range of input conditions. A direct modelling approach, whereby the individual structures and their dynamics are fully resolved, is realised via a lattice Boltzmann-immersed boundary model, which is coupled to two different structural solvers: an Euler-Bernoulli beam model, and a finite element model. Results are presented for three selected test cases - which build in scale from a single flap in a periodic array, to a small finite array of flaps, and finally to a large finite array - and the key behaviour modes are characterised and quantified. Results show a broad range of behaviours, which depend on the flow conditions and structural properties. In particular, the emergence of coherent waving motions are shown to be closely related to the natural frequency of the array. Furthermore, this behaviour is associated with a lock-in between the natural frequency of the array and the predicted frequency of the fluid instabilities. The original contributions of this work are: the development and application of a numerical tool for direct modelling of large arrays of slender structures; the characterisation of the behaviour of slender structures over a range of input conditions; and the exposition of key behaviour modes of slender structures and their relation to input conditions.

Les méthodes de Boltzmann sur réseaux (LBM) ont été appliquées avec beaucoup de succès aux écoulements hydrodynamiques en milieux poreux. Cependant, la limitation de ces méthodes aux écoulements hydrodynamiques et isothermes, les rendent insuffisantes pour simuler des écoulements de gaz dans des milieux micro-poreux. Dans ce cas, il est en effet fréquent que le libre parcours moyen des molécules du gaz, soit du même ordre de grandeur que la taille des pores dans lesquels il s’écoule. De tels écoulements ne seront alors plus en régime hydrodynamique, mais dans des régimes qualifiés de glissement et de transitionnel ; régimes pour lesquels les LBM standards ne sont plus valides. D’autre part, le caractère isotherme des LBM les rendent inutilisables, par exemple dans le cas où le gaz subit une détente à travers le milieu. Il est nécessaire, pour décrire de tels écoulements et phénomènes, de se placer au niveau cinétique. La démarche proposée repose sur la décomposition de la fonction de distribution sur la base des polynômes d’Hermite et l’emploi de la quadrature de Gauss-Hermite associée à cette projection. L’aspect systématique de ce développement amène naturellement à considérer divers ordres d’approximation de l’équation de Boltzmann-BGK sous diverses quadratures. Il résulte alors de ces différentes approximations toute une famille de discrétisations de l’équation de Boltzmann-BGK, dont les LBM classiques ne sont qu’un membre. La détermination de l’approximation la plus adaptée est réalisée par analyse systématique des résultats obtenus aux différents ordres d’approximation. Ces méthodes sont testées avec succès dans des cas modèles. / The lattice Boltzmann method (LBM) have been applied very successfully to hydrodynamic flows in porous media. However, the limitation of these methods to isothermal and hydrodynamic flows, make them inadequate to simulate gas flows in micro-porous media. Indeed, in these conditions, the mean free path of the molecules could be of the same magnitude order as the pore size in which gas flows. Such flows will not be in hydrodynamic regime, but in regimes qualified of, slip or transitional ; for which the LBM are no longer valid. On the other hand, the isothermal character of LBM make them unusable, for example, in the case where the gas undergoes expansion through the media. It is then necessary, to take the kinetic point of view to describe such flows and phenomena. The proposed approach is based on the decomposition of the distribution function on the Hermite polynomials basis and the use of Gauss-Hermite quadrature associated with this projection. The systematic nature of this development naturally leads to consider different order of approximation of the Boltzmann-BGK equation in various quadratures. It then follows from these various approximations, a family of discretizations of the Boltzmann-BGK equation, whose classical LBM are a member. Determining the most suitable approximation is achieved by systematic analysis of the results obtained with different approximation orders. These methods are successfully tested in model cases.

Cette thèse a pour but de définir et de développer des solutions informatiques de manière à permettre la mise en place de simulations physiques sur des domaines de simulation très grands tels qu'un site industriel comme le terminal méthanier de Dunkerque. Le modèle d'écoulement mis en place est basé sur la méthode de Boltzmann sur réseau et permet de gérer de nombreux cas de simulation. Différentes architectures de calculs sont étudiées dans ce travail de thèse. L'utilisation du processeur central ainsi que de processeurs graphiques pour la parallélisation des calculs est abordée. Des solutions sont mises en place de manière à obtenir une parallélisation efficace du modèle de calcul sur plusieurs GPUS pouvant calculer en parallèle. Une approche de maillage progressif du maillage de simulation est également abordée pour gérer dynamiquement la quantité de mémoire nécessaire pour simuler en fonction des besoins de la simulation et de sa progression. Son intégration sur une architecture de calcul composée de plusieurs processeurs graphiques est également mise en avant. Finalement, une solution de type "Out-of-core" a été mise en place pour traiter des cas où la mémoire liée aux processeurs graphiques est insuffisante pour simuler. En effet, les processeurs graphiques disposent généralement d'une quantité de mémoire nettement inférieure à celle de la RAM du processeur central. La mise en place d'un système d'échange efficace entre les processeurs graphiques et la RAM est donc essentielle. / This thesis has for goal to define and develop solutions in order to achieve physical simulations on large simulation domains such as industrial sites (Dunkerque LNG Terminal). The simulation model is based on the lattice Boltzmann method (LBM) and allows to treat several simulation cases. The use of several computing architectures are studied in this work. The use of a multicore central processing unit (CPU) and also several graphics processing units (GPUS) is considered. An efficient parllelization of the simulation model is obtained by the use of several GPUS able to calculate in parallel. A progressive mesh algorithm is also defined in order to automatically mesh the simulation domain according to fluids propagation. Its integration on a multi-GPU architecture is studied. Finally, an "out-of-core" method is introduced in order to handle cases that require more memory than all GPUS have. Indeed, GPU memory is generally significantly inferior to the CPU memory. The definition of an exchange system between GPUS and the CPU is therefore essential.

L'objectif de cette thèse est de développer et d'analyser des techniques numériques basées sur la méthode e Boltzmann sur réseau (LBM) pour résoudre des systèmes non linéaires de type advection-réaction-diffusion provenant de la physique et de la biologie. Avec la LBM, des problèmes portant sur des quantités moyennées densité, potentiel, vitesse, etc) sont exprimés à l'échelle particulaire. Nous approchons la solution de l'équation e Boltzmann relative au comportement d'un champs de particules puis nous recomposons les quantités moyennées solutions des équations traitées. Dans un premier temps, nous développons un cadre général approprié permettant de traiter plusieurs types de systèmes non linéaires (paraboliques, elliptiques, ou couplées ' variables réelles ou complexes), avec des applications à des modèles tels que Burger-Fisher, écoulement de fluides en milieu poreux, Helmoltz, Patlar-Keller-Segel, ou encore Schrodinger. Pour chaque problème, nous analysons le comportement asymptotique de la méthode, quand le nombre de Knudsen tend vers zéro (par le développement de Chapman-Enskog) et nous effectuons l'analyse numérique de la convergence et de la stabilité de la méthode. Dans un deuxième temps, nous nous intéressons à un problème réaliste d'électrophysiologie cardio-vasculaire. Nous adaptons la méthode LBM développée pour approcher les solutions d'un système de type bidomaine permettant de simuler le comportement de potentiels électriques et les interactions ioniques ans la région du myocarde. L'étude et la modélisation d'un tel type de problème est un enjeu sanitaire majeur ans le traitement des pathologies liées par exemple à l'arythmie cardiaque. Notre but étant d'obtenir des comportements réalistes, nous introduisons au sein de ce système bidomaine des opérateurs de retard afin de tenir compte des temps de retard dans les transmissions de signaux. Une fois l'existence et l'unicité de la solution démontrées, nous proposons une série de simulations avec des paramètres physiques et biologiques réalistes afin de valider la méthode proposée. / In this thesis, we develop and analyze numerical techniques based on the lattice Boltzmann method LBM) for solving systems of nonlinear advection-diffusion-reaction equations from physics and biology. Wi BM, problems relating to averaged quantities (density, potential, velocities, etc.) are expressed at the particle scale. We approach the solution of Boltzmann equation relating to the behavior of a particle field and then we recompose the averaged quantities solutions of treated systems. In the first part, we develop an appropriate general framework to deal with several types of non-linear systems (parabolic, elliptic, or coupled, with real or complex variables), with applications to models such as Burger-Fisher, fluid flow in a porous medium, Helmoltz, Patlar-Keller-Segel, or Schrodinger. For each problem, we analyze the asymptotic behavior of the method, when the number of Knudsen tends to zero (by the development of Chapman-Enskog) and we perform the numerical analysis of convergence and stability of the method. In the second part, we have taken an interest in a realistic problem of cardio-vascular electrophysiology. We adapt the developed LBM method to approach e solutions of a bidomain type system for simulating the behavior of electrical potentials and ionic interactions in myocardial region. The study and modeling of this type of problem is a major health issue in the treatment of pathologies related, for example, to cardiac arrhythmia. Since our goal is to obtain realistic behaviors, we introduce time-delay operators into this coupled system in order to take into account delay in signal transmissions. Once the existence and uniqueness of solution have been demonstrated, we propose a series of simulations with realistic physical and biological parameters to validate the proposed method.

In this thesis work fluid flow and heat transfer in two-dimensional microchannels are studied numerically. A computer code based on Lattice Boltzmann Method (LBM) is developed for this purpose. The code is written using MATLAB and Jacket software and has the important feature of being able to run parallel on Graphics Processing Units (GPUs). The code is used to simulate flow and heat transfer inside micro and macro channels. Obtained velocity profiles and Nusselt numbers are compared with the Navier-Stokes based analytical and numerical results available in the literature and good matches are observed. Slip velocity and temperature jump boundary conditions are used for the micro channel simulations with Knudsen number values covering the slip flow regime. Speed of the parallel version of the developed code running on GPUs is compared with that of the serial one running on CPU and for large enough meshes more than 14 times speedup is observed.

In this dissertation, we explore direct-forcing immersed boundary methods (IBM) under the framework of the lattice Boltzmann method (LBM), which is called the direct-forcing immersed boundary-lattice Boltzmann method (IB-LBM). First, we derive the direct-forcing formula based on the split-forcing lattice Boltzmann equation, which recovers the Navier-Stokes equation with second-order accuracy and enables us to develop a simple and accurate formula due to its kinetic nature. Then, we assess the various interface schemes under the derived direct-forcing formula. We consider not only diffuse interface schemes but also a sharp interface scheme. All tested schemes show a second-order overall accuracy. In the simulation of stationary complex boundary flows, we can observe that the sharper the interface scheme is, the more accurate the results are. The interface schemes are also applied to moving boundary problems. The sharp interface scheme shows better accuracy than the diffuse interface schemes but generates spurious oscillation in the boundary forcing terms due to the discontinuous change of nodes for the interpolation. In contrast, the diffuse interface schemes show smooth change in the boundary forcing terms but less accurate results because of discrete delta functions. Hence, the diffuse interface scheme with a corrected radius can be adopted to obtain both accurate and smooth results. Finally, a direct-forcing immersed boundary method (IBM) for the thermal lattice Boltzmann method (TLBM) is proposed to simulate non-isothermal flows. The direct-forcing IBM formulas for thermal equations are derived based on two TLBM models: a double-population model with a simplified thermal lattice Boltzmann equation (Model 1) and a hybrid model with an advection-diffusion equation of temperature (Model 2). The proposed methods are validated through natural convection problems with stationary and moving boundaries. In terms of accuracy, the results obtained from the IBMs based on both models are comparable and show a good agreement with those from other numerical methods. In contrast, the IBM based on Model 2 is more numerically efficient than the IBM based on Model 1. Overall, this study serves to establish the feasibility of the direct-forcing IB-LBM as a viable tool for computing various complex and/or moving boundary flow problems.

This thesis deals with the lattice-Boltzmann method (LBM) in combination with other methods to solve thermal flow problems. The three primary, current approaches for thermal lattice-Boltzmann method (TLBM) will be introduced. The three approaches are the multispeed approach by McNamara and Alder , the passive scalar approach by Shan, and the thermal distribution model proposed by He et al. Shi et al. simplified the thermal distribution model for incompressible thermal flows. The model proposed by Shi et al. was simulated and compared to a hybrid LBM and energy equation model proposed by Khiabani et al. The thermal lattice-Boltzmann method will be compared to the temperature fields generated by the energy equation of the hybrid method. To determine which method is better suited from computer simulations the two will be compared for computational demands, and the speed of both convergence and computation.

The dynamics of fiber orientation is of great interest for efforts to predict the microstructure and material properties of a suspension flow system. In this research a fiber-level, hybrid simulation method, LBM‒EBF (coupled lattice‒Boltzmann method with the external boundary force method) is undertaken to advance the current understanding of the hydrodynamic interaction induced rotational diffusion mechanism for rigid fibers in semidilute suspension of low Reynolds number flow. The LBM‒EBF simulations correctly predict the orbit constant distribution of fibers in a sheared semidilute suspension flow. It is demonstrated that an anisotropic, weak rotary diffusion model can fit the orbit constant distribution very well, but it can not describe the asymmetry in Stokes flow observed in semidilute suspension. The rotational diffusion process is then characterized with a three dimensional spatial tensor representation of the rotational diffusivity. A scalar measure of the rotational diffusion‒'scalar Folgar‒Tucker constant', C[subscript I], is extracted from this tensor. The study provides substantial numerical evidence that the range of C[subscript I] (0.0038 to 0.0165) obtained by Folgar&Tucker (J. reinf. plast. and comp, v.3, 1984) in a semidilute regime is overly diffusive, and that the correct magnitude is of O(10⁻⁴). The study reveals that the interactions among fibers become more frequent with either the decrease of fiber aspect-ratio, r[subscript p] (keeping nL³ constant, where n is the fiber number density, and L is the fiber length) or with the increase of nL³ (keeping r[subscript p] constant) in the semidilute regime, which in consequence causes an increase in C[subscript I]. The rheological properties of sheared semidilute suspension are also computed with direct LBM‒EBF simulations. The LBM‒EBF investigation is extended to characterize the fiber orientation in a linearly contracting channel similar to a paper machine 'headbox'. It is found that the rotational diffusion is the predominant term over the strain rate in the semidilute regime for a low Reynolds number flow, and it results in a decreasing trend of rotational Peclet number, Pe, along the contraction centerline. Lastly, in order to improve the numerical consistency of the existing LBM‒EBF approach, a modification to the body force term in the LB equation is suggested, which can recover the exact macroscopic hydrodynamics from the mesoscale.

To develop or engineer artificial tissues in tissue engineering, a detailed knowledge of the in vitro culture process including cell and tissue growth inside porous scaffolds, nutrient transport, and the shear stress acting on the cells is of great advantage. It has been shown that obtaining such information by means of experimental techniques is exceedingly difficult and in some ways impossible. Mathematical modelling and computational simulation based on computational fluid dynamics (CFD) has emerged recently to be a promising tool to characterize the culture process. However, due to the complicated structure of porous scaffolds, modelling and simulation of the in vitro cell culture process has been shown to be a challenging task. Furthermore, due to the cell growth during the culture process, the geometry of the scaffold structure is not constant, but changes with time, which makes the task even more challenging. To overcome these challenges, the research presented in this thesis is aimed at developing a CFD-based mathematical model and multi-time scale computational framework for culturing cell-scaffold constructs placed in perfusion bioreactors. To predict the three-dimensional (3D) cell growth in a porous tissue scaffold placed inside a perfusion bioreactor, a model is developed based on the continuity and momentum equations, a convection-diffusion equation and a suitable cell growth equation, which characterize the fluid flow, nutrient transport and cell growth, respectively. To solve these equations in a coupled fashion, an in-house FORTRAN code is developed based on the multiple relaxation time lattice Boltzmann method (MRT LBM), where the D3Q19 MRT LBM and D3Q7 MRT LBM models have been used for the fluid flow and mass transfer simulation, respectively. In the model cell growth equation, the transport of nutrients, i.e. oxygen and glucose, as well as the shear stress induced on the cells are considered for predicting the cell growth rate. In the developed model and computational framework, the influence of the dynamic strand surface on the local flow and nutrient concentration has been addressed by using a two-way coupling between the cell growth and local flow field and nutrient concentration, where a control-volume method within the LBM framework is applied. The simulation results provide quantification of the biomechanical environment, i.e. fluid velocity, shear stress and nutrient concentration inside the bioreactor. The final simulation applied the cell growth model to the culture of a three-zone tissue scaffold where the scaffold strands were initially seeded with cells. The prediction for the 3D cell growth rate indicates that the increase in the cell volume fraction is much higher in the front region of the scaffold due to the higher nutrient supply. The higher cell growth in the front zone reduces the permeability of the porous scaffold and significantly reduces the nutrient supply to the middle and rear regions of the scaffold, which in turn limit the cell growth in those regions. However, implementation of a bi-directional perfusion approach, which reverses the flow direction for second half of the culture period, is shown to significantly improve the nutrient transport inside the scaffold and increase the cell growth in the rear zone of the scaffold. The results in this study also demonstrate that the developed mathematical model and computational framework are capable of realistically simulating the 3D cell growth over extended culture periods. As such, they represent a promising tool for enhancing the growth of tissues in perfusion bioreactors.