A Large Eddy-Simulation code, based on a mesh transparent algorithm, for hybrid unstructured meshes is presented to deal with complex geometries that are often found in engineering flow problems. While tetrahedral elements are very effective in dealing with complex geometry, excessive numerical diffusion often affects results. Thus, prismatic or hexahedral elements are preferable in regions where turbulence structures are important. A second order reconstruction methodology is used since an investigation of a higher order method based upon Lele's compact scheme has shown this to be impractical on general unstructured meshes. The convective fluxes are treated with the Roe scheme that has been modified by introducing a variable scaling to the dissipation matrix to obtain a nearly second order accurate centred scheme in statistically smooth flow, whilst retaining the high resolution TVD behaviour across a shock discontinuity. The code has been parallelised using MPI to ensure portability. The base numerical scheme has been validated for steady flow computations over complex geometries using inviscid and RANS forms of the governing equations. The extension of the numerical scheme to unsteady turbulent flows and the complete LES code have been validated for the interaction of a shock with a laminar mixing layer, a Mach 0.9 turbulent round jet and a fully developed turbulent pipe flow. The mixing layer and round jet computations indicate that, for similar mesh resolution of the shear layer, the present code exhibits results comparable to previously published work using a higher order scheme on a structured mesh. The unstructured meshes have a significantly smaller total number of nodes since tetrahedral elements are used to fill to the far field region. The pipe flow results show that the present code is capable of producing the correct flow features. Finally, the code has been applied to the LES computation of the impingement of a highly under-expanded jet that produces plate shock oscillation. Comparison with other workers' experiments indicates good qualitative agreement for the major features of the flow. However, in this preliminary computation the computed frequency is somewhat lower than that of experimental measurements.

Nous présentons de nouveaux schémas numériques pour l'approximation de problèmes de diffusion hétérogène et anisotrope sur des maillages généraux. Sous des hypothèses correspondant aux cas industriels, nous montrons qu'un premier schéma, qui est centré sur les mailles, possède un petit stencil et converge dans le cas de tenseurs discontinus. La preuve de la convergence repose sur des propriétés de consistance des gradients discrets issus du schéma. Dans une seconde partie, nous proposons des méthodes de correction non linéaire du schéma initial pour obtenir le principe du maximum. L'efficacité de ces schémas est étudiée sur des tests numériques ayant fait l'objet de bancs d'essais d'une grande variété de schémas de volumes finis. Les comparaisons avec les schémas volumes finis classiques montrent l'apport de ces schémas en termes de précision. Nous montrons ainsi le bon comportement de ces schémas sur des maillages déformés, et le maintien de la précision des schémas non-linéaires, alors que les oscillations ont été supprimées / We present a new scheme for the discretization of heterogeneous anisotropic diffusion problems on general meshes. With light assumptions, we show that the algorithm can be written as a cell-centered scheme with a small stencil and that it is convergent for discontinuous tensors. The key point of the proof consists in showing both the strong and the weak consistency of the method. Besides, we study non-linear corrections to correct the FECC scheme, in order to satisfy the discrete maximum principle (DMP).The efficiency of the scheme is demonstrated through numerical tests of the 5th & 6th International Symposium on Finite Volumes for Complex Applications - FVCA 5 & 6. Moreover, the comparison with classical finite volume schemes emphasizes the precision of the method. We also show the good behaviour of the algorithm for nonconforming meshes. In addition, we give some numerical tests to check the existence for the non-linear FECC schemes

Les ondes de batillage générées par l’avancement des bateaux détruisent les rives des voies navigables et accélèrent les phénomènes d’érosion aussi bien au niveau des berges qu’au niveau du fond du canal. Leurs caractéristiques cinématiques dépendent de la vitesse, de l’enfoncement, du chargement du bateau et également de la profondeur de la voie navigable. En outre, les masses d’eau accélérées par l’immersion des bateaux et par leur système propulsif, induisent la remise en suspension d’une grande quantité de sédiments et provoquent l’érosion du fond de la voie navigable.Dans cette thèse, un modèle numérique 3D est présenté pour simuler la génération de ces ondes de batillage. Ce modèle, basé sur les équations de Navier-Stokes (RANS), a été couplé à un modèle d’advection-diffusion 3D pour caractériser la répartition et le mode de transport sédimentaire au passage du bateau. Ce couplage est mis en oeuvre avec prise en compte des effets des hélices du système propulsif du bateau. / Ship-generated waves in restricted waterways lead to the stream banks erosion and cause environmental damage which harms fish, plants, benthos, plankton, etc. They also alter the channel morphology because of the resuspension and transport of bed material by accelerated flows caused by moving-ships. The magnitude of these waves depends mainly on the geometrical and kinematical parameters of the convoy.The objective of this study is to predict the relationship between these geometrical and kinematical parameters and the amplitude of ship-generated waves as well as the water plane drawdown. Numerical simulations are conducted by solving the 3-dimensional Navier-Stokes equations along with the k-ε model for turbulent processes. The results are compared firstly with the empirical models and secondly with experimental measurements performed by the French Compagnie Nationale of Rhône (CNR). The exitance of the propeller increases the sediment in suspension. Therefore, the relationships between the re-suspended sediments and the advancing speeds of the convoy, the wakes generated by the moving convoy, as well as the number of barges are studied by adding 3D advection-diffusion equation and a propeller model.

[pt] Uma investigação da capacidade de previsão de modelos de turbulência baseados na modelagem estatística clássica e de grandes escalas é apresentada. A modelagem estatística clássica de turbulência (média de Reynolds) foi analisada, através da solução de escoamentos complexos, como, por exemplo, o escoamento turbulento em degrau (backstep). Especial atenção foi dada aos modelos kapa-epsilon de baixo Reynolds e as variantes renormalizadas (RNG). O comportamento dos vários termos da equação da energia cinética turbulenta na região da parede foram analisados em detalhes, especialmente o termo de difusão de pressão. Avaliou-se a importância da correta modelagem do termo de difusão de pressão sobre as predições dos modelos de baixo número de Reynolds, nas regiões de recirculação. Alguns modelos, propostos na literatura para o termo de difusão de pressão, foram também avaliados teórica e numericamente. A capacidade de previsão da metodologia de simulação de grandes escalas (LES por Large Eddy Simulation) também foi realizada. O desempenho do modelo de Smagorinsky para prever escoamentos limitados por fronteiras sólidas foi avaliado do ponto de vista computacional. Utilizou-se o método de volumes finitos para integrar tanto as equações médias de Reynolds quanto as equações LES. O escoamento turbulento em canal foi resolvido de modo bidimensional e tridimensional. Já o escoamento em degrau (backstep) foi resolvido exclusivamente de modo bidimensional, enquanto o escoamento em um duto de seção quadrada foi simulado de modo tridimensional. Os resultados foram comparados com aqueles obtidos pelos modelos de baixo Reynolds, analisando-se a relação custo-benefício. / [en] An investigation of turbulence models prediction capacity based on classical statistical modeling and large eddy simulation (LES) is presented. The classical statistical modeling (average of Reynolds) was analyzed, by investigating the solution of complex flows, as, for example, the turbulent flow past a backwardfacing- step (backstep). Special attention was given to low Reynolds number k-e models and models derived by renormalization group theory (RNG). The behavior of the different terms in the turbulent kinetic energy equation in the near wall region was examined in details, specially the pressure diffusion term. It was evaluated the importance of the correct modeling of the pressure diffusion term on the predictions of the low Reynolds number models, in recirculating flows. A few models, proposed in the literature for the pressure diffusion term, were also evaluated theoretically and numerically. The prediction capacity of large eddy simulation (LES) technique was also investigated. The ability of Smagorinsky model to predict complex limited wall flows was analyzed from a computational standpoint. The finite-volume method was employed to integrate both the Reynolds average and LES equations. The fully developed turbulent channel flow was solved in two- dimensional and three-dimensional numerical simulations. The turbulent flow over a backward-facing-step was computed exclusively in a twodimensional manner, while the fully developed turbulent flow in a straight square duct was simulated in a three-dimensional manner. The results were compared with those obtained by the low Reynolds models, analyzing the cost-benefit relation.

Este trabalho tem como propósito investigar como a variação geométrica de determinados parâmetros envolvidos na construção de uma geometria bifurcada de seção circular, em forma de Y, afeta a resistência ao escoamento, tanto de fluidos newtonianos como não newtonianos. As geometrias estudadas foram construídas utilizando-se o princípio do Design Construtal. Os parâmetros variados foram a relação entre os comprimentos dos dutos pais e filhos, a relação entre os diâmetros dos mesmos dutos, e o ângulo central da estrutura em forma de Y. Para as relações geométricas lineares foram utilizados os valores de 0,5; 0,6; 0,7; 0,8; 0,9 e 1, enquanto para os ângulos, foram utilizados os valores de 155°, 135°, 115°, 95°, 75°, 45°, 25° e 10°. Os fluidos utilizados foram do tipo newtoniano e não newtoniano, dentre estes últimos, foram estudados fluidos pseudoplásticos e dilatantes. O trabalho foi realizado através de simulações numéricas, implementadas com a utilização do software comercial Ansys Fluent, o qual resolve as equações governantes através do método dos volumes finitos. As malhas utilizadas foram do tipo poliédrica. Os resultados indicam que há uma diferença em relação ao que se espera da literatura para as relações entre os diâmetros e os comprimentos. A Lei Hess-Murray indica que estas relações ótimas seriam de 2-1/3 para as relações entre os diâmetros e comprimentos. No presente trabalho, foram determinadas relações entre os diâmetros próximas de 0,6, e entre os comprimentos, iguais a 1. Os ângulos ótimos ficaram localizados no intervalo entre 100° e 135°. / This work aims to investigate how the geometric variation of certain parameters involved in the construction of a bifurcated Y-shaped circular cross-section geometry affects the flow resistance of both Newtonian and non-Newtonian fluids. The geometries studied were constructed using the Constructal Design principle. The parameters were the relationship between the lengths of the daughter and parent ducts, the relationship between the diameters of the same ducts, and the central angle of the Y-shaped structure. For the linear geometric relations, values of 0.5; 0.6; 0.7; 0.8; 0.9 and 1 where used, for the angles, the values of 155 °, 135 °, 115 °, 95°, 75 °, 45 °, 25 ° and 10 ° were used. The fluids used were of the Newtonian and non-Newtonian type, among the latter, pseudo plastic and dilatant fluids were studied. The work was carried out through numerical simulations, implemented with the commercial software Ansys Fluent, which solves the governing equations through the finite volume method. The meshes used were of the polyhedral type. The results indicate that there is a difference in relation to what is expected from the literature for the relationships between diameters and lengths. The Hess-Murray Law indicates that these optimal relations would be 2-1/3 for the relationships between diameters and lengths. In the present work, relationships between the diameters close to 0,6 were found and s equal to 1 between the lengths. The optimum angles were located in the range between 100 ° and 135 °.

Wave-based models of sound propagation can be used to predict and synthesize sounds as they would be heard naturally in room acoustic environments. The numerical simulation of such models with traditional time-stepping grid-based methods can be an expensive process, due to the sheer size of listening environments (e.g., auditoriums and concert halls) and due to the temporal resolution required by audio rates that resolve frequencies up to the limit of human hearing. Finite difference methods comprise a simple starting point for such simulations, but they are known to suffer from approximation errors that may necessitate expensive grid refinements in order to achieve sufficient levels of accuracy. As such, a significant amount of research has gone into designing finite difference methods that are highly accurate while remaining computationally efficient. The problem of designing and using accurate finite difference schemes is compounded by the fact that room acoustics models require complex boundary conditions to model frequency-dependent wall impedances over non-trivial geometries. The implementation of such boundary conditions in a numerically stable manner has been a challenge for some time. Stable boundary conditions for finite difference room acoustics simulations have been formulated in the past, but generally they have only been useful in modelling trivial geometries (e.g., idealised shoebox halls). Finite volume methods have recently been shown to be a viable solution to the problem of complex boundary conditions over non-trivial geometries, and they also allow for the use of energy methods for numerical stability analyses. Finite volume methods lend themselves naturally to fully unstructured grids and they can simplify to the types of grids typically used in finite difference methods. This allows for room acoustics simulation models that balance the simplicity of finite difference methods for wave propagation in air with the detail of finite volume methods for the modelling of complex boundaries. This thesis is an exploration of these two distinct, yet related, approaches to wave-based room acoustic simulations. The overarching theme in this investigation is the balance between accuracy, computational efficiency, and numerical stability. Higher-order and optimised schemes in two and three spatial dimensions are derived and compared, towards the goal of finding accurate and efficient finite difference schemes. Numerical stability is analysed using frequency-domain analyses, as well as energy techniques whenever possible, allowing for stable and frequency-dependent boundary conditions appropriate for room acoustics modelling. Along the way, the use of non-Cartesian grids is investigated, geometric relationships between certain finite difference and finite volume schemes are explored, and some problems associated to staircasing effects at boundaries are considered. Also, models of sound absorption in air are incorporated into these numerical schemes, using physical parameters that are appropriate for room acoustic scenarios.

A representação de malhas por meio de estrutura de dados e operadores topológicos e um dos focos principais da modelagem geométrica, onde permite uma implementação robusta e eficiente de mecanismos de refinamento adaptativo, alinhamento de células e acesso as relações de incidência e adjacência entre os elementos da malha, o que é de grande importância na maioria das aplicações em mecânica dos fluidos. No caso de malhas não estruturadas, a não uniformidade da decomposição celular e melhor representada por uma estrategia mais sofisticada, que são as estruturas de dados topológicas. As estruturas de dados topológicas indexam elementos de uma malha representando relações de incidência e adjacência entre elementos, garantindo acesso rápido às informações. Um dos aspectos mais comuns aos problemas tratados pela mecânica dos fluidos computacional é a complexidade da geometria do domínio onde ocorre o escoamento. O uso de estruturas de dados para manipular malhas computacionais e de grande importância pois realiza de modo eficiente as consultas às informações da malha e centraliza todas as operações sobre a malha em um único módulo, possibilitando sua extensão e adaptação em diversas situações. Este trabalho visou explorar o acoplamento de uma estrutura de dados topológica, a Mate Face, em um módulo simulador existente, de modo a gerenciar todos os acessos à malha e dispor operações e iteradores para pesquisas complexas nas vizinhanças de cada elemento na malha. O módulo simulador resolve as equações governantes da mecânica dos fluidos através da técnica de volumes finitos. Foi utilizada uma formulação que atribui os valores das propriedades aos centroides dos volumes de controle, utiliza métodos de alta ordem, os esquemas ENO e WENO, que tem a finalidade de capturar com eficiência descontinuidades presentes em problemas governados por equações diferenciais parciais hiperbólicas. As equações de Euler em duas dimensões representam os escoamentos de interesse no presente trabalho. O acoplamento da estrutura de dados Mate Face ao simulador foi realizada através da criação de uma biblioteca desenvolvida que atua como uma interface de comunicação entre os dois módulos, a estrutura de dados e o simulador, que foram implementados em diferentes linguagens de programação. Deste modo, todas as funcionalidades existentes na Mate Face tornaram-se acessíveis ao simulador na forma de procedimentos. Um estudo sobre malhas dinâmicas foi realizado envolvendo o método das molas para movimentação de malhas simulando-se operações de arfagem. A idéia foi verificar a aplicabilidade deste método para auxiliar simulações de escoamentos não estacionarios. Uma outra vertente do trabalho foi estender a estrutura Mate Face de forma a representar elementos não suportados a priori, de modo a flexibilizar o seu uso em simulações de escoamentos baseados no método de volumes finitos espectrais. O método dos volumes espectrais e utilizado para se obter alta resolução espacial do domínio computacional, que também atribui valores das propriedades aos centroides dos volumes de controle, porém, os volumes de controle são particionados em volumes menores de variadas topologias. Assim, uma extensão da Mate Face foi desenvolvida para representar a nova malha para a aplicação do método, representando-se cada particionamento localmente em cada volume espectral. Para todas as etapas deste trabalho, realizaram-se experimentos que validaram a utilizaação da estrutura de dados Mate Face junto a métodos numéricos. Desta forma, a estrutura pode auxiliar as ferramentas de simulações de escoamentos de fluidos no gerenciamento e acesso à malha computacional / The storage and access of grid files by data structures and topologic operators is one of the most important goals of geometric modeling research field, which allows an efficient and stable implementation of adaptive refinement mechanisms, cells alignment and access to incidence and adjacency properties from grid elements, representing great concernment in the majority of applications from fluid mechanics. In the case of non-structured grids, the cellular decomposition if non-uniform and is better suited by a more sophisticated strategy - the topologic data structs. The topologic data structs index grid elements representing incidence and adjacency properties from grid elements, ensuring quick access to information. One of most common aspects from problems solved by computational fluid mechanic is the complexity of the domain geometry where the fluid ows. The usage of data structures to manipulate computational grids is of great importance because it performs efficiently queries on grid information and centers all operations to the grid on a unique module, allowing its extension and flexible usage on many problems. This work aims at exploring the coupling of a topologic data structure, the Mate Face, on a solver module, by controlling all grid access providing operators and iterators that perform complex neighbor queries at each grid element. The solver module solves the governing equations from fluid mechanics though the finite volume technique with a formulation that sets the property values to the control volume centroids, using high order methods - the ENO and WENO schemes, which have the purpose of efficiently capture the discontinuities appearing in problems governed by hyperbolic conservation laws. The two dimensional Euler equations are considered to represent the flows of interest. The coupling of the Mate Face data structure to the solver module was achieved by a creation of a library that acts as an interface layer between both modules, the Mate Face and the solver, which had been implemented using different programming languages. Therefore, all Mate Face class methods are available to the solver module though the interface library in the form of procedures. A study of dynamic grids was made by using spring methods for the moving grid under pitch movement case. The goal was to analyze the applicability of such method to aid non stationary simulations. Another contribution of this work was to show how the Mate Face can be extended in order to deal with non-supported types of elements, allowing it to aid numeric simulations using the spectral finite volume method. The spectral nite volume method is used to obtain high spatial resolution, also by setting the property values to the control volume centroids, but here the control volumes are partitioned into smaller volumes of different types, from triangles to hexagons. Then, an extension of the Mate Face was developed in order to hold the new generated grid by the partitioning specfied by the spectral finite volume method. The extension of Mate Face represents all partitioned elements locally for each original control volume. For all implementations and proposals from this work, experiments were performed to validate the usage of the Mate Face along with numeric methods. Finally, the data structure can aid the fluid flow simulation tools by managing the grid file and providing efficient query operators

This work investigates numerically the process of Teflon ablation using a finite-volume discretization, implicit time integration and a domain decomposition method in three-dimensions. The interest in Teflon stems from its use in Pulsed Plasma Thrusters and in thermal protection systems for reentry vehicles. The ablation of Teflon is a complex process that involves phase transition, a receding external boundary where the heat flux is applied, an interface between a crystalline and amorphous (gel) phase and a depolymerization reaction which happens on and beneath the ablating surface. The mathematical model used in this work is based on a two-phase model that accounts for the amorphous and crystalline phases as well as the depolymerization of Teflon in the form of an Arrhenius reaction equation. The model accounts also for temperature-dependent material properties, for unsteady heat inputs and boundary conditions in 3D. The model is implemented in 3D domains of arbitrary geometry with a finite volume discretization on unstructured grids. The numerical solution of the transient reaction-diffusion equation coupled with the Arrhenius-based ablation model advances in time using implicit Crank-Nicolson scheme. For each time step the implicit time advancing is decomposed into multiple sub-problems by a domain decomposition method. Each of the sub-problems is solved in parallel by Newton-Krylov non-linear solver. After each implicit time-advancing step, the rate of ablation and the fraction of depolymerized material are updated explicitly with the Arrhenius-based ablation model. After the computation, the surface of ablation front and the melting surface are recovered from the scalar field of fraction of depolymerized material and the fraction of melted material by post-processing. The code is verified against analytical solutions for the heat diffusion problem and the Stefan problem. The code is validated against experimental data of Teflon ablation. The verification and validation demonstrates the ability of the numerical method in simulating three dimensional ablation of Teflon.

L’objectif de cette thèse est de proposer une méthode permettant d’optimiser la stratégie de maintenance d’un système multi-composants. Cette nouvelle stratégie doit être adaptée aux conditions d’utilisation et aux contraintes budgétaires et sécuritaires. Le vieillissement des composants et la complexité des stratégies de maintenance étudiées nous obligent à avoir recours à de nouveaux modèles probabilistes afin de répondre à la problématique. Nous utilisons un processus stochastique issu de la Fiabilité Dynamique nommé processus markovien déterministe par morceaux (Piecewise Deterministic Markov Process ou PDMP). L’évaluation des quantités d’intérêt (fiabilité, nombre moyen de pannes...) est ici réalisé à l’aide d’un algorithme déterministe de type volumes finis. L’utilisation de ce type d’algorithme, dans ce cadre d’application, présente des difficultés informatiques dues à la place mémoire. Nous proposons plusieurs méthodes pour repousser ces difficultés. L’optimisation d’un plan de maintenance est ensuite effectuée à l’aide d’un algorithme de recuit simulé. Cette méthodologie a été adaptée à deux systèmes ferroviaires utilisés par la SNCF, l’un issu de l’infrastructure, l’autre du matériel roulant. / The aim of this work is to propose a methodology to optimize a multi-components system maintenance. This new maintenance strategy must be adapted to budget and safety constraints and operating conditions. The aging of components and the complexity of studied maintenance strategies require us to use new probabilistic models in order to address the problem. A stochastic process from Dynamic Reliability calculations are here established by using a deterministic algorithm method based on a finite volume scheme. Using this type of algorithm in this context of application presents difficulties due to computer memory space. We propose several methods to counter these difficulties. The optimization of a maintenance plan is then performed using simulated annealing algorithm. This methodology was used to optimize the maintenance of two rail systems used by the French national railway company (SNCF).

Simulations of fluid flows over complex geometries are typically solved using a solution technique known as the overset meshing method. The geometry is meshed using grid types appropriate to the local geometry in a patchwork fashion, rather than meshing the entire geometry with one type of mesh. The strand-Cartesian approach is a simplification of this process. While high-order accurate solvers on Cartesian grids are simple to implement, strand grids are usually restricted to second-order accuracy, resulting in poor quality solutions. Flux correction is a high-order accurate solution method, specifically designed for use on strand grids. The flux correction method on strand grids is evaluated in conjunction with an overset Cartesian grid. Fundamental studies are considered which demonstrate the effectiveness of high-order methods in solving practical flows of interest.