No contexto de Dinâmica de Fluidos Computacional, métodos de simulação de objetos imersos em Malhas Cartesianas têm se mostrado vantajosos tanto em termos de Custo Computacional quanto em termos de precisão numérica. Entretanto, a representação física de objetos imersos nesses domínios computacionais impõe a perda de validade dos esquemas de Diferenças Finitas empregados, na região das superfícies introduzidas. Este trabalho analisa um Método de Interfaces Imersas quanto ao desempenho em aplicações a esquemas de solução numérica de Alta Ordem de precisão. Através de Testes de Refinamento de Malha, é feita a apreciação da ordem de decaimento dos erros das soluções numéricas em comparação com as soluções analíticas para 2 problemas unidimensionais. O primeiro envolve a solução da Equação de Calor unidimensional sujeita a uma Condição Inicial Unitária, e o segundo relaciona-se ao cálculo das duas primeiras derivadas espaciais das funções analíticas Seno e Tangente Hiperbólica. Também é promovida uma análise de forma fragmentária do método, a fim de individualizar a contribuição dos elementos envolvidos no comportamento das soluções geradas. Os resultados obtidos indicam eventuais alterações na ordem de precisão dos esquemas de Diferenças Finitas originalmente aplicados. Esse comportamento e visto como uma dependência que o método escolhido apresenta em relação a função discretizada. Por fim, são elaboradas considerações sobre restrições de aplicabilidade do método escolhido. / In the Computational Fluid Dynamics context, methods for simulating immersed objects in Cartesian Grids have shown advantages regarding both Computational Cost and numerical precision. Nevertheless, the physical representation of immersed objects within these computational domains leads to the loss of validity of the emplyed Finite Dierence Schemes near the immersed surfaces. This work analizes a Immersed Interface Method regarding its performance in High Order Schemes applications. The error decay order for numerical solutions of two 1D problems is observed. The rst problem relates to the solution of the Heat Equation subjected to the unitary initial condition. The second relates to the computation of the rst two derivatives of analytical functions Sin and Hyperbolic Tangent. It\'s also conducted a fragmentary analysis, which is intended to identify the contribution of each element of this method to the character of the generated solution. The results indicate some eventual changes in the Order of the Finite Dierences Schemes employed. This behaviour is regarded as a dependency of this method to the nature of the discretized function. Finaly, some remarks regarding restrictions to this method\'s applicability are made.

No contexto de Dinâmica de Fluidos Computacional, métodos de simulação de objetos imersos em Malhas Cartesianas têm se mostrado vantajosos tanto em termos de Custo Computacional quanto em termos de precisão numérica. Entretanto, a representação física de objetos imersos nesses domínios computacionais impõe a perda de validade dos esquemas de Diferenças Finitas empregados, na região das superfícies introduzidas. Este trabalho analisa um Método de Interfaces Imersas quanto ao desempenho em aplicações a esquemas de solução numérica de Alta Ordem de precisão. Através de Testes de Refinamento de Malha, é feita a apreciação da ordem de decaimento dos erros das soluções numéricas em comparação com as soluções analíticas para 2 problemas unidimensionais. O primeiro envolve a solução da Equação de Calor unidimensional sujeita a uma Condição Inicial Unitária, e o segundo relaciona-se ao cálculo das duas primeiras derivadas espaciais das funções analíticas Seno e Tangente Hiperbólica. Também é promovida uma análise de forma fragmentária do método, a fim de individualizar a contribuição dos elementos envolvidos no comportamento das soluções geradas. Os resultados obtidos indicam eventuais alterações na ordem de precisão dos esquemas de Diferenças Finitas originalmente aplicados. Esse comportamento e visto como uma dependência que o método escolhido apresenta em relação a função discretizada. Por fim, são elaboradas considerações sobre restrições de aplicabilidade do método escolhido. / In the Computational Fluid Dynamics context, methods for simulating immersed objects in Cartesian Grids have shown advantages regarding both Computational Cost and numerical precision. Nevertheless, the physical representation of immersed objects within these computational domains leads to the loss of validity of the emplyed Finite Dierence Schemes near the immersed surfaces. This work analizes a Immersed Interface Method regarding its performance in High Order Schemes applications. The error decay order for numerical solutions of two 1D problems is observed. The rst problem relates to the solution of the Heat Equation subjected to the unitary initial condition. The second relates to the computation of the rst two derivatives of analytical functions Sin and Hyperbolic Tangent. It\'s also conducted a fragmentary analysis, which is intended to identify the contribution of each element of this method to the character of the generated solution. The results indicate some eventual changes in the Order of the Finite Dierences Schemes employed. This behaviour is regarded as a dependency of this method to the nature of the discretized function. Finaly, some remarks regarding restrictions to this method\'s applicability are made.

Este trabalho pode ser dividido em três etapas principais. Inicialmente é proposta uma formulação estabilizada do método dos elementos finitos (MEF) para solução de problemas de escoamento incompressível governado pela equação de Navier-Stokes. Esta formulação foi implementada em um código computacional e testada através de diversos exemplos numéricos. Alguns elementos finitos com diferentes pares de função de interpolação da velocidade e pressão, consagrados na literatura, e também elementos finitos menos populares, foram investigados e seus resultados e performance comparados. A segunda etapa consiste na formulação do problema estrutural. Buscou-se por uma formulação dinâmica, não linear, capaz de simular movimentos complexos de estruturas sujeitas a grandes deslocamentos e grandes deformações durante longos intervalos de tempo. A etapa final deste trabalho é a proposição de um método para solução de problemas de Interação Fluido Estrutura (IFE) que utiliza o conceito de fronteiras imersas como alternativa a abordagens ALE (Arbitrary Lagrangian Eulerian) clássicas. Elementos Finitos Generalizados, juntamente com Multiplicadores de Lagrange, são utilizados para prover descontinuidade nos campos de velocidade e pressão do fluido ao longo da interface com a estrutura. O acoplamento dos dois problemas é realizado utilizando um método implícito e alternado (staggered scheme), que possui a vantagem de permitir, facilmente, a implementação de códigos computacionais desenvolvidos para resolver isoladamente o problema fluido e/ou estrutural. / This work is divided in three parts. Initially, it is presented a stabilized Finite Element Method formulation to solve fluid flow problems governed by the incompressible Navier-Stokes Equations. This formulation was implemented in a computer code and validated throughout several numeric simulations. Some well-known finite elements with different pairs of velocity/pressure approximations, as well as some other less popular elements, were investigated and their performance compared. The second part describes the Structural Problem formulation. This formulation is able to simulate nonlinear dynamic problems involving large displacements and finite strains during long period of time. In the final part of this work, it is proposed a Fluid-Structure Interaction method based on an immersed interface approach in opposition to classical ALE (Arbitrary Lagrangian Eulerian) approaches. Generalized Finite Elements, together with Lagrange Multipliers, are used to provide velocity and pressure discontinuities on the fluid domain across the immersed interface. To couple both fluid and structural problems, an implicit staggered scheme is adopted, which allows the easy implementation of already developed black box computer codes.

Les énergies fossiles sont largement utilisées depuis les années 1900 pour satisfaire l’augmentation mondiale de la demande d’énergie. Cependant, la combustion est un procédé qui libère des polluants comme le CO2 et les NOx. Un des principaux challenges du 21ème siècle est de réduire ces émissions et les constructeurs automobiles sont impliqués dans cette course. Pour augmenter le rendement des moteurs à pistons, des solutions techniques, tels que le "downsizing", sont développées. Cette technique consiste à réduire la cylindrée des moteurs tout en maintenant leurs performances grâce à un turbocompresseur qui permet d’augmenter la masse enfermée dans la chambre de combustion. Malheureusement, l’augmentation de la pression dans les cylindres induite par le turbocompresseur est à l’origine de combustions anormales : des variations cycles à cycles importantes apparaissent, les gaz frais peuvent s’auto-allumer (allumage avant le claquage de la bougie) entrainant des phénomènes de cliquetis ou de rumble. La Simulation aux Grandes Echelles (SGE) a déjà prouvé qu’elle était un outil fiable pour prédire ces combustions anormales. Cependant ces calculs reposent sur des modèles pour prédire la propagation de la flamme dans la chambre de combustion. Ces modèles sont généralement issus de corrélations réalisées dans des cas où la turbulence est supposée homogène et isotrope. Définir théoriquement ou numériquement une telle turbulence est relativement simple mais expérimentalement la tâche est plus délicate. Cette thèse s’intéresse à un dispositif classiquement utilisé: une enceinte fermée dans laquelle la turbulence est générée par des ventilateurs. L’objectif de ce travail est donc double: 1. caractériser la turbulence générée dans ce type d’enceinte pour vérifier si elle est homogène et isotrope. 2. caractériser finement la combustion, laminaire et turbulente, afin d’enrichir les connaissances dans ce domaine et ainsi améliorer les modèles utilisés. Une première étude sur la propagation des flammes laminaires a été menée. Elle présente les effets de l’étirement et du confinement sur la vitesse de flamme laminaire. La principale difficulté pour la simulation de l’enceinte complète consiste à trouver une méthode numérique permettant de reproduire précisément l’écoulement généré par un ventilateur mais aussi d’en gérer plusieurs simultanément. Deux méthodes ont alors été testées. Premièrement, une méthode type Frontières Immergées a été implémentée dans le code de calcul AVBP. Malgré les bons résultats obtenus sur des cas tests simples, cette méthode ne s’est pas montrée adaptée pour reproduire précisément l’écoulement généré par un seul ventilateur. Une autre approche, provenant du monde du calcul des turbomachines, et basée sur le couplage de codes (appelée MISCOG), a quant à elle démontré ses capacités à le faire et est donc utilisée pour calculer l’écoulement généré par les six ventilateurs à l’intérieur de l’enceinte. L’écoulement non réactif est d’abord analysé: les résultats montrent qu’il existe une zone d’environ 6 cm de diamètre au centre de l’enceinte dans laquelle la vitesse moyenne de l’écoulement est proche de zéro et dans laquelle la turbulence est quasiment homogène et isotrope. Enfin, le pré-mélange de gaz frais est allumé en déposant un noyau de gaz chauds au centre de l’enceinte et la phase de propagation turbulente est analysée. En particulier, il est montré que la température des gaz brulés déposés au moment de l’allumage est un paramètre critique. / Fossil energy is widely used since the 1900s to satisfy the global increasing energy demand. However, combustion is a process releasing pollutants such as CO2 and NOx. One of the major challenges of the 21th century is to reduce these emissions and car manufacturers are involved in this race. To increase fuel efficiency of piston engines, some technical solutions are developed such as ‘downsizing’. It consists in reducing the engine size while maintaining its performances using a turbocharger to increase the trapped mass in the combustion chamber. Unfortunately, downsizing can lead to abnormal combustions: intense cycle to cycle variations can appear, the fresh mixture can auto-ignite (ignition before spark-plug ignition) leading to knock or rumble. Large Eddy Simulation has proven to be a reliable tool to predict these abnormal combustions in real engines. However, such computations are performed using models to predict the flame propagation in the combustion chamber. Theses models are generally based on correlations derived in cases where turbulence is assumed to be homogeneous and isotropic. Defining theoretically or numerically such a turbulence is a simple task but experimentally it is more challenging. This thesis focuses on a apparatus used in most experimental systems: fans stirred vessel. The objective of this work is twofold: 1. characterize the turbulence generated inside the vessel to check wether it is homogeneous and isotropic or not, 2. finely characterize laminar and turbulent combustion in this setup in order to increase the knowledge in this field, and thereby improve models used. First, a laminar flame propagation study has been conducted to address both confinement and curvature effects on the laminar flame speed in a spherical configuration. The main difficulty to perform the simulation of the whole configuration consists in finding a numerical method able to compute accurately the flow generated by one fan and able to handle six fans simultaneously too. Two numerical methodologies have been tested. First an Immersed Boundaries method was implemented. Despite good results obtained on academic test cases, this method was shown to be unadapted to compute accurately the flow generated by one fan. On the other hand, a numerical approach, coming from turbomachinery calculations and based on code coupling (called MISCOG), demonstrates its ability to do it and it is used to compute the flow generated by the six fans inside the closed vessel. Non-reacting flow is first analyzed and reveals a zone at the vessel center of around 6 cm of diameter where mean velocity is near zero and turbulence is almost homogeneous and isotropic. After that, the premixed fresh mixture is ignited depositing a hot gases kernel at the vessel center and the turbulent propagation phase is analyzed. In particular, it is shown that the amount of energy deposited at ignition is a critical parameter.

Este trabalho pode ser dividido em três etapas principais. Inicialmente é proposta uma formulação estabilizada do método dos elementos finitos (MEF) para solução de problemas de escoamento incompressível governado pela equação de Navier-Stokes. Esta formulação foi implementada em um código computacional e testada através de diversos exemplos numéricos. Alguns elementos finitos com diferentes pares de função de interpolação da velocidade e pressão, consagrados na literatura, e também elementos finitos menos populares, foram investigados e seus resultados e performance comparados. A segunda etapa consiste na formulação do problema estrutural. Buscou-se por uma formulação dinâmica, não linear, capaz de simular movimentos complexos de estruturas sujeitas a grandes deslocamentos e grandes deformações durante longos intervalos de tempo. A etapa final deste trabalho é a proposição de um método para solução de problemas de Interação Fluido Estrutura (IFE) que utiliza o conceito de fronteiras imersas como alternativa a abordagens ALE (Arbitrary Lagrangian Eulerian) clássicas. Elementos Finitos Generalizados, juntamente com Multiplicadores de Lagrange, são utilizados para prover descontinuidade nos campos de velocidade e pressão do fluido ao longo da interface com a estrutura. O acoplamento dos dois problemas é realizado utilizando um método implícito e alternado (staggered scheme), que possui a vantagem de permitir, facilmente, a implementação de códigos computacionais desenvolvidos para resolver isoladamente o problema fluido e/ou estrutural. / This work is divided in three parts. Initially, it is presented a stabilized Finite Element Method formulation to solve fluid flow problems governed by the incompressible Navier-Stokes Equations. This formulation was implemented in a computer code and validated throughout several numeric simulations. Some well-known finite elements with different pairs of velocity/pressure approximations, as well as some other less popular elements, were investigated and their performance compared. The second part describes the Structural Problem formulation. This formulation is able to simulate nonlinear dynamic problems involving large displacements and finite strains during long period of time. In the final part of this work, it is proposed a Fluid-Structure Interaction method based on an immersed interface approach in opposition to classical ALE (Arbitrary Lagrangian Eulerian) approaches. Generalized Finite Elements, together with Lagrange Multipliers, are used to provide velocity and pressure discontinuities on the fluid domain across the immersed interface. To couple both fluid and structural problems, an implicit staggered scheme is adopted, which allows the easy implementation of already developed black box computer codes.

Ces travaux portent sur la modélisation et la simulation numérique des effets du déplacement d'un corps indéformable dans un écoulement multiphasique compressible. Ils se placent dans le cas où plusieurs objets sont en mouvement ou dans le cas où un objet est en mouvement dans un milieu aux géométries complexes. L'étude ne peut alors pas être placée dans le référentiel lié à l'objet en mouvement. Le modèle est basé sur une méthode multiphasique à interfaces diffuses où les différentes phases sont en équilibre mécanique. Le système régissant l'écoulement fluide est augmenté d'une équation d'advection. Cette dernière s'applique sur une fonction Level Set dont le niveau zéro permet de localiser le mobile dans l'espace. Des termes de couplage sont ajoutés au membre de droite des équations d'évolution de la quantité de mouvement et de l'énergie totale. Ces termes sont composés d'un facteur du type pénalisation et d'un facteur du type relaxation de vitesses. Cette nouvelle méthode permet de simuler des cas complexes où peuvent interagir des mobiles à hautes vitesses, des ondes de choc et des interfaces liquide/gaz. / This work deals with modelling and the numerical simulation of the effects of a moving rigid body on a multiphase flow. Here more than one object is moving, or an object is moving in a complex geometry domain. So the reference frame linked to the moving body can't be used. The model is build on a multiphase diffuse interface method with mechanical equilibrium. An advection equation is added. It applies on a Level Set function used to track the moving body. Coupling terms are added to the momentum equation and to the total energy equation. These terms are made of a penalization factor and a velocity relaxation factor. This new method allows to simulate complex cases where can interact high velocity objects, shock waves and liquid / gas interfaces.

Une méthode de frontières immergées est développée pour la simulation d’écoulements compressibles et validée au travers de cas-tests spécifiques (réflexion d’ondes acoustiques et quantification de la conservation de la masse dans des canaux inclinés). La simulation aux grandes échelles (LES) d’une cavité transsonique est ensuite présentée. Le bouclage aéro-acoustique, très sensible aux conditions aux limites, est reproduit avec précision par la LES dans le cas où les parois sont immergées dans un maillage structurée. La comparaison des stratégies de modélisation de sous-maille pour cet écoulement transsonique et l’adaptation des filtres en présence de frontières immergées sont également discutées. Le rôle, souvent sous-estimé, du schéma de viscosité artificiel, est quantifié.Dans la dernière partie du manuscrit, des études sont réalisées pour aider au dimensionnement d’un nouveau concept de chambre de combustion où la flamme est stabilisée par la recirculation de gaz brûlés dans une cavité (chambre TVC pour Trapped Vortex Combustor). La modélisation de la combustion turbulente est basée sur une chimie tabulée, couplée à une fonction densité de probabilité présumée (PCM-FPI). L’étude de la dynamique de la flamme est réalisée pour diverses conditions de fonctionnement (débit de l’écoulement principal et présence ou non d’un swirl). Les spécificités de mise en œuvre de la simulation d’un écoulement de ce type sont discutées et un soin particulier est apporté au traitement de la condition de sortie, qui constitue un point sensible de la chaîne de modélisation. Les phénomènes d’instabilités et de retour de la flamme sont mis en évidence ainsi que les modifications à apporter au dispositif afin de minimiser ces effets. L’existence d’un cycle limite acoustique est souligné et une formule permettant d’anticiper le niveau des fluctuations de pression est proposée et validée. Une correction au modèle PCM-FPI est présentée afin de préserver la vitesse de flamme et d’assurer une reproduction plus précise de la dynamique de flamme. / An immersed boundary method has been developed for the simulation of compressible flow and validated with reference test cases (pressure wave reflection and quantification of mass conservation for various inclined channels). Large Eddy Simulation (LES) of a transonic cavity is then presented. The aeroacoustic feedback loop, which is highly sensitive to the boundary conditions, was accurately reproduced where the walls are immersed inside a structured grid. The comparison between the modeling approaches for this transonic flow and the correction of the filtering operation near immersed boundaries are also discussed. The often underestimated role of the numerical artificial dissipation is also quantified.In the last part of this manuscript, many studies are realized to help in the design of a new combustion chamber for Trapped Vortex Combustor (TVC). The turbulent combustion model is based on tabulated chemistry and a presumed probability density function (PCM-FPI) method.The flame dynamics is studied for various operating conditions (flowrate of the main flow and presence of swirl motion). Details concerning the realization of such a flow are discussed and special care is taken for the treatment of the most sensitive outlet boundary condition. The phenomena of combustion instabilities and of flame backflow are highlighted along with the modifications to be made for the device to minimize these effects. The existence of a acoustic limit cycle is emphasized and a formula is proposed and validated to anticipate the level of pressure fluctuations. Finally a correction to the PCM-FPI model is suggested to preserve the flame front speed and to ensure a more accurate description of the flame dynamics.