Code verification is the process of ensuring, to the degree possible, that there are no algorithm deficiencies and coding mistakes (bugs) in a scientific computing simulation. In this work, techniques are presented for performing code verification of boundary conditions commonly used in compressible and incompressible Computational Fluid Dynamics (CFD) codes. Using a compressible CFD code, this study assesses the subsonic inflow (isentropic and fixed-mass), subsonic outflow, supersonic outflow, no-slip wall (adiabatic and isothermal), and inviscid slip-wall. The use of simplified curved surfaces is proposed for easier generation of manufactured solutions during the verification of certain boundary conditions involving many constraints. To perform rigorous code verification, general grids with mixed cell types at the verified boundary are used. A novel approach is introduced to determine manufactured solutions for boundary condition verification when the velocity-field is constrained to be divergence-free during the simulation in an incompressible CFD code. Order of accuracy testing using the Method of Manufactured Solutions (MMS) is employed here for code verification of the major components of an open-source, multiphase flow code - MFIX. The presence of two-phase governing equations and a modified SIMPLE-based algorithm requiring divergence-free flows makes the selection of manufactured solutions more involved than for single-phase, compressible flows. Code verification is performed here on 2D and 3D, uniform and stretched meshes for incompressible, steady and unsteady, single-phase and two-phase flows using the two-fluid model of MFIX. In a CFD simulation, truncation error (TE) is the difference between the continuous governing equation and its discrete approximation. Since TE can be shown to be the local source term for the discretization error, TE is proposed as the criterion for determining which regions of the computational mesh should be refined/coarsened. For mesh modification, an error equidistribution strategy to perform r-refinement (i.e., mesh node relocation) is employed. This technique is applied to 1D and 2D inviscid flow problems where the exact (i.e., analytic) solution is available. For mesh adaptation based upon TE, about an order of magnitude improvement in discretization error levels is observed when compared with the uniform mesh. / Ph. D.

Microfluidics has been the focal point of research in various disciplines due to its advantages of portability and cost effectiveness, and the ability to perform complex tasks with precision. In the past two decades microfluidic technology has been used to cool integrated circuits, for exoplanetary chemical analysis, for mimicking cellular environments, and in the design of specialized organ-on-a-chip devices. While there have been considerable advances in the complexity and miniaturization of microfluidic devices, particularly with the advent of microfluidic large-scale integration (mLSI) and microfluidic very-large-scale-integration (mVLSI), in which there are hundreds of thousands of flow channels per square centimeter on a microfluidic chip, there remains an actuation overhead problem: these small, complex microfluidic devices are tethered to extensive off-chip actuation machinery that limit their portability and efficiency. Insects, in contrast, actively and efficiently handle their respiratory air flows in complex networks consisting of thousands of microscale tracheal pathways. This work analytically and experimentally investigates the viability of incorporating some of the essential kinematics and actuation strategies of insect respiratory systems in microfluidic devices. Mathematical models of simplified individual tracheal pathways were derived and analyzed, and insect-mimetic PDMS-based valveless microfluidic devices were fabricated and tested. It was found that not only are these devices are capable of pumping fluids very efficiently using insect-mimetic actuation techniques, but also that the fluid flow direction and magnitude could be controlled via the actuation frequency alone, a feature never before realized in microfluidic devices. These results suggest that insect-mimicry may be a promising direction for designing more efficient microfluidic devices. / Ph. D. / Microfluidics or the study of fluids at the microscale has gained a lot of interest in the recent past due to its various applications starting from electronic chip cooling to biomedical diagnostic devices and exoplanetary chemical analysis. Though there has been a lot of advancements in the functionality and portability of microfluidic devices, little has been achieved in the improvement of the peripheral machinery needed to operate these devices. On the other hand insects can expertly manipulate fluids, in their body, at the microscale with the help of their efficient respiratory capabilities. In the present study we mimic some essential features of the insect respiratory system by incorporating them in microfluidic devices. The feasibility of practical application of these techniques have been tested, at first, analytically by mathematically modeling the fluid flow in insect respiratory tract mimetic microchannels and tubes and then by fabricating, testing and analyzing the functionality of microfluidic devices. The mathematical models, using slip boundary conditions, showed that the volumetric fluid flow through a trachea mimetic tube decreased with the increase in the amount of slip. Apart from that it also revealed a fundamental difference between shear and pressure driven flow at the microscale. The microfluidic devices exhibited some unique characteristic features never seen before in valveless microfluidic devices and have the potential in reducing the actuation overhead. These devices can be used to simplify the operating procedure and subsequently decrease the production cost of microfluidic devices for various applications.

Yes / A novel Lattice-Boltzmann model to simulate gas mixing in anaerobic digestion is developed and described. For the first time, Euler–Lagrange multiphase, non-Newtonian and turbulence modelling are applied jontly with a novel hybrid boundary condition. The model is validated in a laboratory-scale framework and flow patterns are assessed through Particle Imaging Velocimetry (PIV) and innovative Positron-Emission Particle Tracking (PEPT). The model is shown to reproduce the experimental flow patterns with fidelity in both qualitative and quantitative terms. The model opens up a new approach to computational modelling of the complex multiphase flow in anaerobic digesters and offers specific advantages, such as computational efficiency, over an analogous Euler-Lagrange finite-volume computational fluid dynamics approach. / UK EPSRC Grant (EP/R01485X/1, Computational Methods for Anaerobic Digestion Optimization, “CoMAnDO”). The numerical work was performed in the HPC Cirrus EPSRC Tier-2 National HPC Facility, Edinburgh, UK, under a UK EPSRC Tier-2 Research Allocation Panel (RAP) award.

Among the many active materials in use today, piezoelectric composite patches have enabled notable advances in emerging technologies such as disturbance sensing, control of flexible structures, and energy harvesting. The macro fiber composite (MFC), in particular, is well known for its outstanding performance. Multiscale models are typically required for smart-structure design with MFCs. This is due to the need for predicting the macroscopic response (such as tip deflection under a transverse load or applied voltage) while accounting for the fact that the MFC has microscale details. Current multiscale models of the MFC exclusively focus on predicting the macroscopic response with homogenized material properties. There are a limited number of homogenized properties available from physical experiments and various aspects of existing homogenization techniques for the MFC are shown here to be inadequate. Thus, new homogenized models of the MFC are proposed to improve smart-structure predictions and therefore improve device design. It is notable that current multiscale modeling efforts for MFCs are incomplete since, after homogenization, the local fields such as stresses and electric fields have not been recovered. Existing methods for obtaining local fields are not applicable since the electrodes of the MFC are embedded among passive layers. Therefore, another objective of this work was to find the local fields of the MFC without having the computational burden of fully modeling the microscopic features of the MFC over a macroscale area. This should enable smart-structure designs with improved reliability because failure studies of MFCs will be enabled. Large-scale 3D finite element (FE) models that included microscale features were constructed throughout this work to verify the multiscale methodologies. Note that after creating a free account on cdmhub.org, many files used to create the results in this work can be downloaded from https://cdmhub.org/projects/ernestocamarena.<br><br>First, the Mechanics of Structure Genome (MSG) was extended to provide a rigorous analytical homogenization method. The MFC was idealized to consist of a stack of homogeneous layers where some of the layers were homogenized with existing rules of mixtures. For the analytical model, the electrical behavior caused by the interdigitated electrodes (IDEs) was approximated with uniform poling and uniform electrodes. All other assumptions on the field variables were avoided; thus an exact solution for a stack of homogeneous layers was found with MSG. In doing so, it was proved that in any such multi-layered composite, the in-plane strains and the transverse stresses are equal in each layer and the in-plane electric fields and transverse electric displacement are constant between the electrodes. Using this knowledge, a hybrid rule of mixtures was developed to homogenize the entire MFC layup so as to obtain the complete set of effective device properties. Since various assumptions were avoided and since the property set is now complete, it is expected that greater energy equivalence between reality and the homogenized model has been made possible. The derivation clarified what the electrical behavior of a homogenized solid with internal electrodes should be—an issue that has not been well understood. The behavior was verified by large-scale FE models of an isolated MFC patch.<br> <br>Increased geometrical fidelity for homogenization was achieved with an FE-based RVE analysis that accounted for finite-thickness effects. The presented theory also rectifies numerous issues in the literature with the use of the periodic boundary conditions. The procedure was first developed without regard to the internal electrodes (ie a homogenization of the active layer). At this level, the boundary conditions were shown to satisfy a piezoelectric macrohomogeneity condition. The methodology was then applied to the full MFC layup, and modifications were implemented so that both types of MFC electrodes would be accounted for. The IDE case considered nonuniform poling and electric fields, but fully poled material was assumed. The inherent challenges associated with these nonuniformities are explored, and a solution is proposed. Based on the homogenization boundary conditions, a dehomogenization procedure was proposed that enables the recovery of local fields. The RVE analysis results for the effective properties revealed that the homogenization procedure yields an unsymmetric constitutive relation; which suggests that the MFC cannot be homogenized as rigorously as expected. Nonetheless, the obtained properties were verified to yield favorable results when compared to a large-scale 3D FE model.<br> <br>As a final test of the obtained effective properties, large-scale 3D FE models of MFCs acting in a static unimorph configuration were considered. The most critical case to test was the smallest MFC available. Since none of the homogenized models account for the passive MFC regions that surround the piezoelectric fiber array, some of the test models were constructed with and without the passive regions. Studying the deflection of the host substrate revealed that ignoring the passive area in smaller MFCs can overpredict the response by up to 20%. Satisfactory agreement between the homogenized models and a direct numerical simulation were obtained with a larger MFC (about a 5% difference for the tip deflection). Furthermore, the uniform polarization assumption (in the analytical model) for the IDE case was found to be inadequate. Lastly, the recovery of the local fields was found to need improvement.<br><br><br>

Mathematical models describing the Q-switched laser generation, which is a widely used laser technique for producing short intense pulses of light, belong to the class of semi-nonlinear models where only source terms nonlinearly depend on the solution. Numerical methods for solution of systems of semi-nonlinear partial differential equations have been extensively studied in many papers. Schrödinger-type equations, parabolic-type equations or general diffusion-reaction models arise in nonlinear optics. Such differential problems are solved mainly by finite-difference and Galerkin methods. The convergence analysis is based on the stability analysis of the linearized problems. The construction and theoretical analysis of discrete schemes for one-dimensional problem give a basis for a numerical solution of more general two-dimensional and three-dimensional problems where a diffraction process is taken into account. The two-dimensional problem simulates the dynamics of high-power semiconductor lasers. To solve the problems simulating propagation of photon fluxes in the nonlinear disperse medium, the finite-difference time-domain method is used. However, the major drawback of this method is that the computational domain must be sufficiently large. In order to restrict the computational domain and to solve the problem only in the region of interest, special artificial boundary conditions are investigated. The three-dimensional problem simulates an interaction of counter propagating... [to full text] / Disertacijoje nagrinėjami kai kurių lazerių fizikos ir netiesinės optikos uždavinių skaitinės analizės metodai. Tiriami trys pagrindiniai atvejai: bėgančias plokščias bangas aprašantis vienmatis, bėgančias difraguojančias bangas nagrinėjantis dvimatis ir lazerio pluoštų sąveiką netiesinėje Kero terpėje modeliuojantis trimatis modeliai. Šiuos uždavinius sieja pernešimo diferencialinės lygtys dalinėmis išvestinėmis, aprašančios į priešingas puses sklindančias lazerio bangas. Dvimačiame ir trimačiame uždaviniuose sprendžiamos dalinių išvestinių Šrėdingerio (ang. Schrödinger) tipo diferencialinės lygtys. Šiems matematiniams modeliams sudarytos baigtinių skirtumų schemos, atlikta jų analizė ir pagrindimas. Skaitinių eksperimentų realizacijai sukurti lygiagretieji algoritmai, jie yra būtini atliekant didelių resursų reikalaujančius skaičiavimus. Disertaciją sudaro įvadas, keturi skyriai, rezultatų apibendrinimas, naudotos literatūros ir autoriaus publikacijų disertacijos tema sarašai. Įvadiniame skyriuje aptariama tiriamoji problema, darbo aktualumas, aprašomas tyrimų objektas, formuluojamas darbo tikslas bei uždaviniai, aprašoma tyrimų metodika, darbo mokslinis naujumas, darbo rezultatų praktinė reikšmė, ginamieji teiginiai. Įvado pabaigoje pristatomos disertacijos tema autoriaus paskelbtos publikacijos ir pranešimai konferencijose bei disertacijos struktūra. Pirmasis skyrius skirtas mokslinės literatūros apžvalgai ir supažindinimui su netiesinės optikos sąvokomis bei... [toliau žr. visą tekstą]

Disertacijoje nagrinėjami kai kurių lazerių fizikos ir netiesinės optikos uždavinių skaitinės analizės metodai. Tiriami trys pagrindiniai atvejai: bėgančias plokščias bangas aprašantis vienmatis, bėgančias difraguojančias bangas nagrinėjantis dvimatis ir lazerio pluoštų sąveiką netiesinėje Kero terpėje modeliuojantis trimatis modeliai. Šiuos uždavinius sieja pernešimo diferencialinės lygtys dalinėmis išvestinėmis, aprašančios į priešingas puses sklindančias lazerio bangas. Dvimačiame ir trimačiame uždaviniuose sprendžiamos dalinių išvestinių Šrėdingerio (ang. Schrödinger) tipo diferencialinės lygtys. Šiems matematiniams modeliams sudarytos baigtinių skirtumų schemos, atlikta jų analizė ir pagrindimas. Skaitinių eksperimentų realizacijai sukurti lygiagretieji algoritmai, jie yra būtini atliekant didelių resursų reikalaujančius skaičiavimus. Disertaciją sudaro įvadas, keturi skyriai, rezultatų apibendrinimas, naudotos literatūros ir autoriaus publikacijų disertacijos tema sarašai. Įvadiniame skyriuje aptariama tiriamoji problema, darbo aktualumas, aprašomas tyrimų objektas, formuluojamas darbo tikslas bei uždaviniai, aprašoma tyrimų metodika, darbo mokslinis naujumas, darbo rezultatų praktinė reikšmė, ginamieji teiginiai. Įvado pabaigoje pristatomos disertacijos tema autoriaus paskelbtos publikacijos ir pranešimai konferencijose bei disertacijos struktūra. Pirmasis skyrius skirtas mokslinės literatūros apžvalgai ir supažindinimui su netiesinės optikos sąvokomis bei... [toliau žr. visą tekstą] / Mathematical models describing the Q-switched laser generation, which is a widely used laser technique for producing short intense pulses of light, belong to the class of semi-nonlinear models where only source terms nonlinearly depend on the solution. Numerical methods for solution of systems of semi-nonlinear partial differential equations have been extensively studied in many papers. Schrödinger-type equations, parabolic-type equations or general diffusion-reaction models arise in nonlinear optics. Such differential problems are solved mainly by finite-difference and Galerkin methods. The convergence analysis is based on the stability analysis of the linearized problems. The construction and theoretical analysis of discrete schemes for one-dimensional problem give a basis for a numerical solution of more general two-dimensional and three-dimensional problems where a diffraction process is taken into account. The two-dimensional problem simulates the dynamics of high-power semiconductor lasers. To solve the problems simulating propagation of photon fluxes in the nonlinear disperse medium, the finite-difference time-domain method is used. However, the major drawback of this method is that the computational domain must be sufficiently large. In order to restrict the computational domain and to solve the problem only in the region of interest, special artificial boundary conditions are investigated. The three-dimensional problem simulates an interaction of counter propagating... [to full text]

A steepest descent method is constructed for the general setting of a linear differential equation paired with uniqueness-inducing conditions which might yield a generally overdetermined system. The method differs from traditional steepest descent methods by considering the conditions when defining the corresponding Sobolev space. The descent method converges to the unique solution to the differential equation so that change in condition values is minimal. The system has a solution if and only if the first iteration of steepest descent satisfies the system. The finite analogue of the descent method is applied to example problems involving finite difference equations. The well-posed problems include a singular ordinary differential equation and Laplace’s equation, each paired with respective Dirichlet-type conditions. The overdetermined problems include a first-order nonsingular ordinary differential equation with Dirichlet-type conditions and the wave equation with both Dirichlet and Neumann conditions. The method is applied in an investigation of the Tricomi equation, a long-studied equation which acts as a prototype of mixed partial differential equations and has application in transonic flow. The Tricomi equation has been studied for at least ninety years, yet necessary and sufficient conditions for existence and uniqueness of solutions on an arbitrary mixed domain remain unknown. The domains of interest are rectangular mixed domains. A new type of conditions is introduced. Ladder conditions take the uncommon approach of specifying information on the interior of a mixed domain. Specifically, function values are specified on the parabolic portion of a mixed domain. The remaining conditions are specified on the boundary. A conjecture is posed and states that ladder conditions are necessary and sufficient for existence and uniqueness of a solution to the Tricomi equation. Numerical experiments, produced by application of the descent method, provide strong evidence in support of the conjecture. Ladder conditions allow for a continuous deformation from Dirichlet conditions to initial-boundary value conditions. Such a deformation is applied to a class of Tricomi-type equations which transition from degenerate elliptic to degenerate hyperbolic. A conjecture is posed and states that each problem is uniquely solvable and the solutions vary continuously as the differential equation and corresponding conditions vary continuously. If the conjecture holds true, the result will provide a method of unifying elliptic Dirichlet problems and hyperbolic initial-boundary value problem. Numerical evidence in support of the conjecture is presented.

Cette thèse a pour objet le développement d'un modèle numérique de simulation des fluides fondé sur la méthode Smoothed Particle Hydrodynamics (SPH). SPH est une méthode de simulation numérique sans maillage présentant un certain nombre d'avantages par rapport aux méthodes Eulériennes. Elle permet notamment de modéliser des écoulements à surface libre ou interfaces fortement déformées. Ce travail s'adresse principalement à quatre problématiques liées aux fondements de la méthode SPH : l'imposition des conditions aux limites, la prédiction précise des champs de pression, l'implémentation d'un modèle thermique et la réduction des temps de calcul. L'objectif est de modéliser des écoulements industriels complexes par la méthode SPH, en complément de ce qui peut se faire avec des méthodes à maillage. Typiquement, les problèmes visés sont des écoulements 3-D à surface libre ou confinés, pouvant interagir avec des structures mobiles et/ou transporter des scalaires, notamment des scalaires actifs (e.g. température). Dans ce but, on propose ici un modèle SPH incompressible (ISPH) basé sur une représentation semi-analytique des conditions aux limites. La technique des conditions aux limites semi-analytiques permet d'imposer des conditions sur la pression de manière précise et physique, contrairement à ce qui se fait avec des conditions aux limites classiques en SPH. Un modèle k-epsilon a été incorporé à ce nouveau modèle ISPH, à partir des travaux de Ferrand et al. (2013). Un modèle de flottabilité a également été ajouté, reposant sur l'approximation de Boussinesq. Les interactions entre flottabilité et turbulence sont prises en compte. Enfin, une formulation pour les frontières ouvertes dans le nouveau modèle est établie. La validation du modèle en 2-D a été réalisée sur un ensemble de cas-tests permettant d'estimer les capacités de prédiction du nouveau modèle en ce qui concerne les écoulements isothermes et non-isothermes, laminaires ou turbulents. Des cas confinés sont présentés, ainsi que des écoulements à surface libre (l'un d'eux incluant un corps solide mobile dans l'écoulement). La formulation pour les frontières ouvertes a été testée sur un canal de Poiseuille plan laminaire et sur deux cas de propagation d'une onde solitaire. Des comparaisons sont présentées avec des méthodes à maillage, ainsi qu'avec un modèle SPH quasi-incompressible (WCSPH) avec le même type de conditions aux limites. Les résultats montrent que le modèle permet de représenter des écoulements dans des domaines à géométrie complexe, tout en améliorant la prédiction des champs de pression par rapport à la méthode WCSPH. L'extension du modèle en trois dimensions a été réalisée dans un code massivement parallèle fonctionnant sur carte graphique (GPU). Deux cas de validation en 3-D sont proposés, ainsi que des résultats sur un cas simple d'application en 3-D / In this work a numerical model for fluid flow simulation was developed, based on the Smoothed Particle Hydrodynamics (SPH) method. SPH is a meshless Lagrangian Computational Fluid Dynamics (CFD) method that offers some advantages compared to mesh-based Eulerian methods. In particular, it is able to model flows presenting highly distorted free-surfaces or interfaces. This work tackles four issues concerning the SPH method : the imposition of boundary conditions, the accuracy of the pressure prediction, the modelling of buoyancy effects and the reduction of computational time. The aim is to model complex industrial flows with the SPH method, as a complement of what can be done with mesh-based methods. Typically, the targetted problems are 3-D free-surface or confined flows that may interact with moving solids and/or transport scalars, in particular active scalars (e.g. the temperature). To achieve this goal, a new incompressible SPH (ISPH) model is proposed, based on semi-analytical boundary conditions. This technique for the representation of boundary conditions in SPH makes it possible to accurately prescribe consistent pressure boundary conditions, contrary to what is done with classical boundary conditions in SPH. A k-epsilon turbulence closure is included in the new ISPH model. A buoyancy model was also added, based on the Boussinesq approximation. The interactions between buoyancy and turbulence are modelled. Finally, a formulation for open boundary conditions is proposed in this framework. The 2-D validation was performed on a set of test-cases that made it possible to assess the prediction capabilities of the new model regarding isothermal and non-isothermal flows, in laminar or turbulent regime. Confined cases are presented, as well as free-surface flows (one of them including a moving body in the flow). The open boundary formulation was tested on a laminar plane Poiseuille flow and on two cases of propagation of a solitary wave. Comparisons with mesh-based methods are provided with, as well as comparisons with a weakly-compressible SPH (WCSPH) model using the same kind of boundary conditions. The results show that the model is able to represent flows in complex boundary geometries, while improving the pressure prediction compared to the WCSPH method. The extension of the model to 3-D was done in a massively parallel code running on a Graphic Processing Unit (GPU). Two validation cases in 3-D are presented, as well as preliminary results on a simple 3-D application case

Ao longo da última década o método adjunto tem sido consolidado como uma das mais versáteis e bem sucedidas ferramentas de otimização aerodinâmica e projeto inverso na Dinâmica dos Fluidos Computacional. Ele se tornou uma área de pesquisa por si só, criando uma grande variedade de aplicações e uma literatura prolífica. Entretanto, alguns aspectos relevantes do método permanecem ainda relativamente pouco explorados na literatura. Como é o caso das condições de contorno adjuntas e, mais especificamente, com respeito a fronteiras permeáveis. Esta dissertação discute detalhadamente uma nova forma de tratar o problema de contorno, que tem como objetivo assegurar que as equações adjuntas sejam bem-postas. O principal objetivo da otimização aerodinâmica consiste na tentativa de minimizar (ou maximizar) uma determinada medida de mérito. As aplicações de projeto inverso são desenvolvidas para escoamentos Euler 2-D ao redor de aerofólios, representados com a parametrização CST (Class-Shape function Transformation) proposta por Kulfan e Bussoletti (2006), em regime de vôo transônico e com domínio discretizado por malhas não-estruturadas de triângulos através de um ciclo de projeto, que utiliza o método steepest descent como algoritmo de busca da direção que minimiza (ou maximiza) a função de mérito. As equações adjuntas são derivadas na sua formulação contínua e suas condições de contorno são determinadas por equações diferenciais características adjuntas e relações de compatibilidade compatíveis com as variações realizáveis da física do escoamento. As variáveis adjuntas são, então, vistas como forças de vínculo generalizadas, que asseguram a realizabilidade de variações do escoamento. / Over the last decade the adjoint method has been consolidated as one of the most versatile and successful tools of aerodynamic optimization and inverse design in Computational Fluid Dynamics. It has become a research area of its own, spawning a large variety of applications and a prolific literature. Yet, some relevant aspects of the method remain relatively less explored in the literature. Such is the case with the adjoint boundary conditions and, more specifically, with regard to permeable boundaries. This dissertation discusses at length a novel approach to the boundary problem, which aims at ensuring the well-posedness of the adjoint equations. The main goal of aerodynamic optimization consists in attempting to minimize (or maximize) a certain mesure of merit. The inverse design applications are developed for 2-D Euler flows around airfoils, represented with the CST (Class-Shape function Transformation) parameterization proposed by Kulfan and Bussoletti (2006), in the transonic flight regime and domain discretized by triangle unstructured meshes in a design loop which makes use of the steepest descent method as search direction that minimizes (or maximizes) the mesure of merit. Adjoint equations are derived in the continuous formulation and their boundary conditions are determined by adjoint characteristic differential equations and compatibility relations. The latter are derived so as to be compatible with the realizable variations of physical quantities. The adjoint variables are seen as generalized constraint forces, which ensure the realizability of flow variations.

La crise environnementale a conduit l’industrie automobile à faire face à des contraintes croissantes tandis que les limitations drastiques de polluants entrent en vigueur. Afin de réduire les émissions polluantes issues de la combustion, l’une des solutions adoptées est de post-traiter les fumées à l’aide de systèmes de post-traitement catalytique à l’image du catalyseur 3 voies (TWC) pour les moteurs à essence ou le catalyseur d’oxydation (DOC)pour les moteurs diesel. Ces appareils présentent une structure en nid d’abeille constituée d’un réseau de canaux à l’échelle millimétrique appelés monolithes et dont les parois intérieures sont recouvertes d’une fine couche de métal précieux aux propriétés catalytiques. Les polluants sont transformés via l’interaction entre les molécules présentes dans la phase gaz et les sites actifs du métal précieux. Etant donné les conditions laminaires d’écoulement au sein des monolithes, un mélange faible et une diffusion moléculaire limitée peuvent être rencontrés au voisinage de la paroi réactive. Le taux de conversion des polluants peut être alors insuffisant pour des conditions opératoires données. Dans le but d’optimiser les transferts,des obstacles peuvent être introduits par déformation mécanique des parois du canal catalytique au cours du processus de fabrication.Les simulations numériques peuvent contribuer à l’émergence de solutions innovantes basées sur une compréhension et une maitrise profonde des phénomènes sous-jacents. Afin d’atteindre cet objectif, le premier élément clé a été de formuler et d’intégrer dans le code de dynamique des fluides AVBP une approche numérique combinant d’une part des conditions aux limites dédiées à la prise en compte de parois réactives,et d’autre part, la résolution de la cinétique chimique gaz et surface via un solveur d’EDP.L’approche a permis la prise en compte de la cinétique détaillée et l’interaction entre la phase gaz et les parois réactives. L’outil développé a été validé en premier lieu à l’aide de calculs de réacteurs hétérogènes zéro-dimensionnels. Les résultats ont montré un parfait accord avec le solveur de référence SENKIN. L’approche a été validée ensuite en l’appliquant à la simulation de deux canaux réactifs aux parois planes et en comparant les résultats numériques aux résultats expérimentaux de Dogwiler et al. L’approche développée s’est révélée être capable de reproduire les principales caractéristiques de la combustion catalytique pour différents points de fonctionnement. Enfin, l’outil développé a été appliqué à l’étude de l’impact de l’introduction d’obstacles pariétaux sur les taux de conversion des systèmes catalytiques. Les résultats ont permis d’ouvrir des perspectives très intéressantes quant à la contribution de la CFD2D et de la chimie hétérogène détaillée à l’optimisation du design des systèmes de post traitement catalytique. En particulier, l’étude de l’influence des obstacles pariétaux a montré que le design de la géométrie des monolithes constitue un fort potentiel d’optimisation de l’efficacité des systèmes de conversion catalytique et ce, à moindre coût grâce à une utilisation optimisée du métal précieux rendue possible par une meilleure interaction entre l'écoulement, les réactions chimiques dans la phase gaz et la paroi réactive. / The environmental emergency has led automotive industry to deal with growing constraints as drastic regulations of pollutant emissions are emerging. In order to reduce emissions resulting from the combustion process, one of the solution adopted is to post process pollutants by the means of catalytic after-treatment systems such as three-way converters (TWC) for gasoline applications oroxidation catalysts (DOC) for Diesel applications. These devices present a honeycomb shape which consists in a grid of millimeter-scale narrow channels called monoliths whose interior wall are coated with precious metals presenting catalytic properties.Pollutants are converted through the chemical interaction involving gas-phase molecules and active precious metal sites. Given the laminar flow encountered within these monoliths, weak mixing and molecular diffusion could occur near the catalytic walls. Pollutant conversion rates may therefore prove insufficient for certain operating conditions. In order to promote transfers, obstacles could be introduced by mechanically deforming the channel wall during the manufacturing process. Numerical simulations can contribute to the emergence of innovative technologies based on a profound understanding and mastering of the underlying phenomena that simulation allows. In order to achieve this goal, a first key element was the formulation and integration into the AVBP CFD code of a numerical approach combining specific boundary conditions for reactive walls and ODE solvers for the gas phase and surface chemistry.The approach allowed to account for detailed kinetics and the interplay between the reactive surface and the gas-phase. The resulting tool was first validated using a zero-dimensional heterogeneous reactor computations. The results were shown to perfectly match the ones obtained with the reference kinetic solver SENKIN.Furthermore, the approach was then validated by applying it to the simulation of two planar reactive channel flows, and comparing the predictions with experimental findings of Dogwiler et al.. The developed approach proved to be able of reproducing main features of the catalytic combustion observed for different operating points. Finally, the developed tool was applied to explore the impact of introducing wall obstacles on the conversion rate of catalytic devices. The resulting findings have proved to open very interesting perspectives for contributing to the optimization of the design of catalytic converters using 2D CFD and detailed heterogeneous chemistry. In particular, the study of the impact of wall obstacles indicates the potential for contributing to further increase the efficiency of catalytic converters via the design of monolith geometries that would allow a more efficient and thus less costly usage of Pt-coating as a consequence of optimized interactions between the gas flow, gas phase chemistry and surface chemistry.