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The aim of this thesis is three-fold: i) to investigate the performance of both the Eulerian-Lagrangian model and the Eulerian-Eulerian model to simulate the turbulent gas-particle flow; ii) to investigate the indoor airflows and contaminant particle flows using the Eulerian-Lagrangian model; iii) to develop and validate particle-wall collision models and a wall roughness model for the Eulerian-Lagrangian model and to utilize these models to investigate the effects of wall roughness on the particle flows. Firstly, the Eulerian-Lagrangian model in the software package FLUENT (FLUENT Inc.) and the Eulerian-Eulerian model in an in-house research code were employed to simulate the gas-particle flows. The validation against the measurement for two-phase flow over backward facing step and in a 90-degree bend revealed that both CFD approaches provide reasonably good prediction for both the gas and particle phases. Then, the Eulerian-Lagrangian model was employed to investigate the indoor airflows and contaminant particle concentration in two geometrically different rooms. For the first room configuration, the performances of three turbulence models for simulating indoor airflow were evaluated and validated against the measured air phase velocity data. All the three turbulence models provided good prediction of the air phase velocity, while the Large Eddy Simulation (LES) model base on the Renormalization Group theory (RNG) provided the best agreement with the measurements. As well, the RNG LES model is able to provide the instantaneous air velocity and turbulence that are required for the evaluation and design of the ventilation system. In the other two-zone ventilated room configuration, contaminant particle concentration decay within the room was simulated and validated against the experimental data using the RNG LES model together with the Lagrangian model. The numerical results revealed that the particle-wall coll ision model has a considerable effect on the particle concentration prediction in the room. This research culminates with the development and implementation of particle-wall collision models and a stochastic wall roughness model in the Eulerian-Lagrangian model. This Eulerian-Lagrangian model was therefore used to simulate the gas-particle flow over an in-line tube bank. The numerical predictions showed that the wall roughness has a considerable effect by altering the rebounding behaviours of the large particles and consequently affecting the particles motion downstream along the in-line tube bank and particle impact frequency on the tubes. Also, the results demonstrated that for the large particles the particle phase velocity fluctuations are not influenced by the gas-phase fluctuations, but are predominantly determined by the particle-wall collision. For small particles, the influence of particle-wall collisions on the particle fluctuations can be neglected. Then, the effects of wall roughness on the gas-particle flow in a two-dimensional 90-degree bend were investigated. It was found that the wa ll roughness considerably altered the rebounding behaviours of particles by significantly reducing the 'particle free zone' and smoothing the particle number density profiles. The particle mean velocities were reduced and the particle fluctuating velocities were increased when taking into consideration the wall roughness, since the wall roughness produced greater randomness in the particle rebound velocities and trajectories.

In this thesis, CMs of linear and non-linear multiple antenna receivers, in particular linear minimum mean squared error (LMMSE) and LMMSE with decision feedback (LMMSE-DF), are developed. To develop these CMs, first a simple analytical expression of the distribution of the post processing signal to interference and noise (SINR) of an LMMSE receiver is developed. This expression is then used to develop SINR- and ABER-based CMs. However, the analytical forms of these CMs are derived only for the following scenarios: (i) any number of receive antennas with three users having arbitrary received powers and (ii) two antenna receiver with arbitrary number of equal received power users. For all the other scenarios a semi-analytical CM is used. The PHY abstractions or CMs are next used in the evaluation of a random access cellular network and an ad hoc network. Analytical model of the random access cellular network is developed using the SINR- and ABER-based CM of the LMMSE receiver. The impact of receiver processing is measured in terms of throughput. In this case, the random access mechanism is modeled by a single channel S-Aloha channel access scheme. Another analytical model is developed for single and multi-packet reception in a multi-channel S-Aloha channel access. An emph{ideal} receiver is modeled in this case, i.e. the packet(s) are successfully received as long as the total number of colliding packets is not greater than the number of antennas. Throughput and delay are used as performance metrics to study the impact of different PHY designs. Finally, the SINR-based semi-analytical CMs of LMMSE and LMMSE-DF are used to evaluate the performance of multi-hop ad hoc networks. Throughput is used as the performance evaluation metric. A novel MAC, called S-MAC, is proposed and its performance is compared against another MAC for wireless networks, called CSMA/CA(k).

Dans ce travail, nous nous sommes intéressés à la simulation numérique de suspensions denses d'objets immergés dans un fluide. En s'inspirant d'une méthode de segmentation d'image, nous avons développé une méthode efficace de capture d'interface permettant d'une part de localiser les structures immergées et d'autre part de gérer les contacts numériques entre les structures.Le domaine fluide/structure est représenté à l'aide de trois fonctions labels et deux fonctions distances qui permettent de localiser chaque structure et son plus proche voisin.Les interfaces sont capturées par une seule fonction level set, celle-ci est ensuite transportée par la vitesse du fluide ou par la vitesse de chaque structure. Un algorithme de multi-label fast marching permet de réinitialiser à chaque pas de temps les fonctions labels et distances dans un périmètre proche des interfaces.La gestion des contacts numériques est effectuée grâce à une force répulsive à courte portée prenant en compte l'interaction entre les objets les plus proches.Dans un premier temps, la méthode est appliquée à l'évolution de solides rigides immergés.Un modèle de pénalisation global couplé aux fonctions labels permet de calculer en une seule fois l'ensemble des vitesses des structures rigides. Les résultats obtenus montrent l'efficacité de la méthode à gérer un grand nombre de solides.Nous avons ensuite appliqué la méthode des suspensions de vésicules immergées. Ce type de simulation requiert le calcul des forces élastiques et de courbures exercées sur les membranes. Grâce au modèle proposé, seulement une force élastique et une force de courbure sont calculées pour l'ensemble des membranes à l'aide de la fonction level set et des fonctions labels. / In this work, we propose a method to efficiently capture an arbitrary number of fluid/solid or fluid/fluid interfaces, in a level-set framework. This technique, borrowed from image analysis, is introduced in the context of the interaction of several bodies immersed in a fluid. A configuration of the bodies in the fluid/structure domain is described by three label maps providing the first and second neighbours, and their associated distance functions. Only one level set function captures the union of all interfaces and is transported with the fluid velocity or with a global velocity field which takes into account the velocity of each structure. A multi-label fast marching method is then performed in a narrow-band around the interfaces allowing to update the label and distance functions. Within this framework, the numerical treatment of contacts between the structures is achieved by a short-range repulsive force depending on the distance between the closest bodies.The method is validated through the simulation of a dense suspension of rigid bodies immersed in an incompressible fluid. A global penalization model uses the label maps to follow the solid bodies altogether without a separate computation of each body velocity. Consequently, the method shows its efficiency when dealing with a large number of rigid bodies. We also investigate the numerical simulation of vesicle suspensions for which a computation of elastic and bending forces on membranes is required. In the present model, only one elastic and bending force is computed for the whole set of membranes according to the level set function and the label maps.

Cette thèse porte sur la théorie spectrale d’équations neutroniques partiellement élastiques introduites en 1974 par les physiciens E. W LARSEN et P. F. ZWEIFEL. L’opérateur de collision est alors la somme d’une partie inélastique (correspondant aux modèles neutroniques classiques) et d’une partie élastique qui induit des phénomènes spectraux nouveaux que l’on veut étudier. L’objectif de cette thèse est l’analyse fine de leur spectre asymptotique (la partie du spectre discret qui détermine le comportement asymptotique en temps des problèmes de Cauchy associés). L’étude spectrale de ces modèles partiellement élastiques met en jeu des propriétés spectrales d’opérateurs bornés non compacts et symétrisables. La première partie de la thèse est alors consacrée à la théorie spectrale des opérateurs symétrisables non compacts sur les espaces de Hilbert. Nous donnons une série de résultats d’analyse fonctionnelle sur ces opérateurs. En particulier nous donnons une méthode qui permet d’obtenir toutes les valeurs propres réelles situées à l’extérieur du disque spectral essentiel (i.e le plus petit disque fermé contenant le spectre essentiel) ainsi que des caractérisations variationnelles de ces valeurs propres. La deuxième partie de cette thèse porte sur l’analyse spectrale des modèles cinétiques partiellement élastiques isotropes et homogène en espace (i.e les sections efficaces ne dépendent que du module des vitesses). Nous montrons entre autre que le spectre asymptotique est formé au plus de valeurs propres isolées de multiplicité algébrique finie. Nous montrons aussi que ce spectre ponctuel est réel. Nous démontrons que le nombre des valeurs propres réelles de l’opérateur de transport partiellement élastique augmente indéfiniment avec la taille du domaine spatial. Nous démontrons aussi que toutes ces valeurs propres tendent vers la borne spectrale de l’opérateur partiellement élastique homogène en espace quand la taille du domaine tend vers l’infini. Nous étudions aussi des modèles anisotropes pour lesquels nous étendons la plupart des résultats obtenus pour les modèles isotropes / This thesis is devoted to spectral theory of party elastic neutron transport equations introduced in 1974 by physicists E. LARSEN W and PF ZWEIFEL. The collision operator is then the sum of an inelastic part (corresponding to classical neutron transport models) and an elastic part that induces new spectral phenomena to be studied. The objective of this thesis is the analysis of their asymptotic spectrum (the part of the discrete spectrum that determines the time asymptotic behavior of the associated Cauchy problems). The spectral study of these partly elastic models involves spectral properties of bounded non-compact and symmetrizable operators. Thus the first part of the thesis deals with spectral theory of non compact symmetrizable operators on Hilbert spaces. We give a series of functional analytic results on these operators. In particular we give a method which provides us with all the real eigenvalues located outside the essential spectral disc and provide variational characterizations of these eigenvalues. The second part of the thesis focuses on spectral analysis of partly elastic isotropic and space homogeneous kinetic models (i.e. the cross sections depend only on speed modulus). Among other things, we show that the asymptotic spectrum consists at most of isolated eigenvalues with finite algebraic multiplicity. We also show that this point spectrum is real. Further we show that the number of real eigenvalues of the partly elastic transport operator increases indefinitely with the size of the spatial domain. We show also that all these eigenvalues tend to the spectral bound of the space homogeneous partly elastic operator when the size of domain tends to infinity. Most of these results are also extended to anisotropic models.