La descripción del flujo de fluidos involucra la solución de las ecuaciones de Navier-Stokes compresible, un problema muy complejo cuya estructura matemática no es del todo comprendida. Por lo tanto, mediante análisis asintótico, se pueden derivar modelos simplificados bajo ciertas hipótesis sobre el problema hechas en términos de parámetros adimensionales que miden la importancia relativa de los diferentes procesos físicos. Los flujos a baja velocidad se pueden describir por diferentes modelos que incluyen las ecuaciones de Navier Stokes incompresible cuya matemática es mucho mas conocida. Sin embargo, algunos flujos importantes no se pueden considerar incompresibles debido a la presencia de efectos térmicos. En esta clase de problemas se pueden derivar otra clase de ecuaciones simplificadas: las ecuaciones de Boussinesq y las ecuaciones de bajo numero de Mach.La complejidad de estos problemas matemáticos hace que su solución numérica sea muy difícil. En estos problemas el método de los elementos finitos es inestable, lo que en la práctica implica soluciones numéricas que presentan oscilaciones nodo a nodo de naturaleza no física. En las ecuaciones de Navier Stokes incompresible, dos fuentes bien conocidas de inestabilidad son la condición de incompresibilidad y la presencia del término convectivo. Muchas técnicas de estabilización utilizadas hoy en día se basan en la separación de escalas, descomponiendo la incógnita en una parte gruesa inducida por la discretización del domino y una parte fina de subescala. Modelar la subescala y su influencia conduce a un problema modificado para la escala gruesa que resulta estable.Aunque las técnicas de estabilización son ampliamente utilizadas hoy en día, importantes problemas permanecen abiertos. Contribuyendo a su comprensión, en este trabajo se analizan varios aspectos del modelado de las subescalas. Para problemas escalares de segundo orden, se encuentra la dependencia de la subescala con el tamaño de la malla en el caso general de mallas anisótropas. Estas ideas son extendidas a sistemas de ecuaciones para considerar el problema de Oseen. También se analiza el modelado de las subescalas en problemas transitorios, obteniendo un mejor esquema de integración temporal para el problema de escala gruesa. Para considerar flujos a baja velocidad, se presenta la extensión de estas técnicas a problemas no lineales acoplados, lo que esta íntimamente relacionado con el problema del modelado de la turbulencia, que es un tema en si mismo.Los flujos acoplados térmicamente, aparte del interés intrínseco que merecen, son importantes desde un punto de vista ingenieril. Una solución precisa del problema de flujo es necesaria para definir las cargas térmicas sobre las estructuras, que en muchos casos responden fuertemente, haciendo el problema acoplado. Esta clase de problemas, que motivaron este trabajo, incluyen la respuesta estructural en el caso de un incendio. / A general description of a fluid flow involves the solution of the compressible Navier-Stokes equations, a very complex problem whose mathematical structure is not well understood. Therefore, simplified models can be derived by asymptotic analysis under some assumptions on the problem, made in terms of dimensionless parameters that measure the relative importance of different physical processes. Low speed flows can be described by several models including the incompressible Navier Stokes equations whose mathematical structure is much better understood. However many important flows cannot be considered as incompressible, even at low speed, due to the presence of thermal effects. In such kind of problems another class of simplified equations can be derived: the Boussinesq equations and the Low Mach number equations.The complexity of these mathematical problems makes their numerical solution very difficult. For these problems the standard finite element method is unstable, what in practice means that node to node oscillations of non physical nature may appear in the numerical solution. In the incompressible Navier Stokes equations, two well known sources of numerical instabilities are the incompressibility constraint and the presence of the convective terms. Many stabilization techniques used nowadays are based on scale separation, splitting the unknown into a coarse part induced by the discretization of the domain and a fine subgrid part. The modelling of the subgrid scale and its influence leads to a modified coarse scale problem that now can be shown to be stable. Although stabilization techniques are nowadays widely used, important problems remain open. Contributing to their understanding, several aspects of the subgrid scale modelling are analyzed in this work. For second order scalar problems, the dependence of the subgrid scale on the mesh size, in the general anisotropic case, is clarified. These ideas are extended to systems of equations to consider the Oseen problem. The modelling of the subgrid scales in transient problems is also analyzed, leading to an improved time discretization scheme for the coarse scale problem. To consider low speed flow models, the extension of these techniques to nonlinear and coupled problems is presented, something that is intimately related to the problem of turbulence modelling, which a entire subject on its own right. Thermally coupled flow problems, despite the intrinsic interest they deserve, are important from an engineering point of view. An accurate solution of a flow problem is needed to define thermal loads on structures which, in many cases have a strong response, making the problem coupled. This kind of problems, that motivated this work, include the problem of a structural response in the case of fires.

Les buts principaux recherchés de la présente thèse visent au développement et à l’expertise d’une méthodologie de simulation numérique des problèmes d’interactions fluides-structures. Afin de cerner progressivement le problème étudié, nous nous sommes intéressés en premier lieu à la simulation numérique des écoulements autour d’obstacles solides, plus particulièrement au phénomène d’éclatements tourbillonnaires dans la zone de sillage d’obstacles de différentes formes. Nous avons utilisé la méthode des éléments finis en adoptant la technique de stabilisation GLS (Galerkin Least-Square). Pour le traitement de la turbulence, nous avons opté pour la méthode LES (Large-Eddy Simulation) en utilisant le filtre de Smagorinsky. En deuxième phase, nous nous sommes intéressés aux écoulements en milieux déformables. Nous avons entrepris la formulation ALE (Arbitrairement Lagrangienne Eulérienne) en considérant un maillage déformable. Pour la mise à jour de la grille du maillage dynamique, nous avons utilisé une approche pseudo-élastique. Afin d’expertiser la méthodologie mise en oeuvre, nous avons choisi d’aborder le problème des ballottements à la surface libre de réservoirs partiellement remplis de liquide. En dernière partie, nous nous sommes intéressés au comportement vibratoire d’un corps solide sous l’effet d’un écoulement de fluide. Par l’utilisation d’un algorithme de couplage totalement implicite basé sur la méthode de Gauss-Seidel par Bloc, nous avons abordé le phénomène des instabilités aéroélastiques des ponts à haubans. Pour la validation du modèle numérique traitant les interactions fluides-structures par les données expérimentales, nous nous sommes intéressés au comportement vibratoire d’une maquette sectionnelle d’un tablier de pont réel sous l’effet d’un vent soufflant uniforme. / The main goals sought by this thesis target the development and expertise of a methodology for numerical simulation of fluid-structure interactions problems. In order to identify the studied problem progressively, we are interested primarily in numerical simulation of flows around bluff bodies, especially the phenomenon of vortex shedding in the wake zone of a bluff body of different shapes. We used the finite element method by adopting the stabilized GLS (Galerkin Least-Square) technique. For the treatment of turbulence, we opted the LES (Large-Eddy Simulation) method using the Smagorinsky filter. In the second phase, we were interested in flows in deformable media. We undertook the ALE (Arbitrary Lagrangian Eulerian) formulation by considering a deformable mesh. To update the grid of the dynamic mesh, we used a pseudo-elastic approach. To appraise the implemented methodology, we decided to approach the problem of sloshing at the free surface of a tank partially filled with liquid. In the final part, we were interested in vibration behavior of a solid body under the effect of fluid flow. By using a fully implicit coupling algorithm based on a relaxed Bloc Gauss-Seidel method, we studied the phenomenon of aeroelastic instability of cable-stayed bridges. To validate the numerical model treating fluid-structure interactions by experimental data, we investigated the vibration behavior of a real deck sectional model under the effect of a uniform wind.

Neste trabalho é apresentado a modelagem mecânica e numérica de um escoamento elastoviscoplástico tixotrópico, em termos dos campos de velocidade, pressão, tensão e parâmetro de estrutura. A discretização numérica é feita pelo Método de Elementos Finitos Estabilizado, também conhecido como Galerkin Mínimos Quadrados (GMQ), através de elementos quadrangulares bilineares. O clássico problema da cavidade é utilizado nas simulações, a fim de comparar a formulação e o código utilizados com os resultados conhecidos na literatura. Além disso, apresenta-se o estudo de materiais elasto-viscoplástico tixotrópico em uma contração abrupta na escala 4:1, utilizando a formulação descrita e uma nova função viscosidade para fluidos viscoplásticos, denominada função Viscoplástica Harmônica (VPH). Resultados envolvendo a função VPH são introduzidos e discutidos pela primeira vez nesta tese e apresenta um ótimo ajuste de curva, quando comparada com outras funções disponíveis na literatura. Além da fácil implementação, essa função também apresenta um platô para as altas e baixas viscosidades que são fisicamente realistas, visto que não é possível uma viscosidade infinita ou nula. O menor tempo computacional é também uma característica perceptível nas simulações usando a nova função viscoplástica, isso é um atributo do seu equacionamento que não depende de um termo exponencial, como outros modelos. O estudo de qualidade de malha também é apresentado a fim de garantir a escolha do domínio discreto adequado. Apesar do uso de elementos de ordem inferior, o método GMQ mostrou-se estável na aproximação numérica de todos os problemas dispostos, garantindo até mesmo a análise sobre os efeitos da cinemática, da elasticidade e da tixotropia no escoamento dos fluidos dentro da contração abrupta. / In this work the mechanical and numerical modeling of a thixotropic elasto-viscoplastic flow in terms of the velocity, pressure, stress and structure parameter is presented. Numerical discretization is done by the Stabilized Finite Element Method, also known as Galerkin Least Squares (GLS), through bilinear quadrangular elements. The classical liddriven cavity problem is used in the simulations in order to compare the formulation and code used with the results in the literature. In addition, the study of elasto-viscoplastic thixotropic materials in a 4:1 abrupt contraction using the described formulation and a new viscosity function for viscoplastic fluids, called the Harmonic Viscoplastic Function (HVP), is presented. Results involving the HVP function are introduced and discussed for the first time in this thesis and present a better curve fit when compared to other functions available in the literature. Besides to easy implementation, this function also features a plateau for high and low viscosities that are physically realistic, since infinite or zero viscosity is not possible. The shortest computational time is also a perceptible feature in the simulations using the new viscoplastic function, this is an attribute of its equation that does not depend on an exponential term like other models. The mesh quality study is also presented in order to ensure the choice of the appropriate discrete domain. Despite the use of lower-order elements, the GLS method proved to be stable in the numerical approximation of all the problems, guaranteeing even the analysis of the effects of kinematics, elasticity and thixotropy on fluid flow within the abrupt contraction.

Neste trabalho é apresentado a modelagem mecânica e numérica de um escoamento elastoviscoplástico tixotrópico, em termos dos campos de velocidade, pressão, tensão e parâmetro de estrutura. A discretização numérica é feita pelo Método de Elementos Finitos Estabilizado, também conhecido como Galerkin Mínimos Quadrados (GMQ), através de elementos quadrangulares bilineares. O clássico problema da cavidade é utilizado nas simulações, a fim de comparar a formulação e o código utilizados com os resultados conhecidos na literatura. Além disso, apresenta-se o estudo de materiais elasto-viscoplástico tixotrópico em uma contração abrupta na escala 4:1, utilizando a formulação descrita e uma nova função viscosidade para fluidos viscoplásticos, denominada função Viscoplástica Harmônica (VPH). Resultados envolvendo a função VPH são introduzidos e discutidos pela primeira vez nesta tese e apresenta um ótimo ajuste de curva, quando comparada com outras funções disponíveis na literatura. Além da fácil implementação, essa função também apresenta um platô para as altas e baixas viscosidades que são fisicamente realistas, visto que não é possível uma viscosidade infinita ou nula. O menor tempo computacional é também uma característica perceptível nas simulações usando a nova função viscoplástica, isso é um atributo do seu equacionamento que não depende de um termo exponencial, como outros modelos. O estudo de qualidade de malha também é apresentado a fim de garantir a escolha do domínio discreto adequado. Apesar do uso de elementos de ordem inferior, o método GMQ mostrou-se estável na aproximação numérica de todos os problemas dispostos, garantindo até mesmo a análise sobre os efeitos da cinemática, da elasticidade e da tixotropia no escoamento dos fluidos dentro da contração abrupta. / In this work the mechanical and numerical modeling of a thixotropic elasto-viscoplastic flow in terms of the velocity, pressure, stress and structure parameter is presented. Numerical discretization is done by the Stabilized Finite Element Method, also known as Galerkin Least Squares (GLS), through bilinear quadrangular elements. The classical liddriven cavity problem is used in the simulations in order to compare the formulation and code used with the results in the literature. In addition, the study of elasto-viscoplastic thixotropic materials in a 4:1 abrupt contraction using the described formulation and a new viscosity function for viscoplastic fluids, called the Harmonic Viscoplastic Function (HVP), is presented. Results involving the HVP function are introduced and discussed for the first time in this thesis and present a better curve fit when compared to other functions available in the literature. Besides to easy implementation, this function also features a plateau for high and low viscosities that are physically realistic, since infinite or zero viscosity is not possible. The shortest computational time is also a perceptible feature in the simulations using the new viscoplastic function, this is an attribute of its equation that does not depend on an exponential term like other models. The mesh quality study is also presented in order to ensure the choice of the appropriate discrete domain. Despite the use of lower-order elements, the GLS method proved to be stable in the numerical approximation of all the problems, guaranteeing even the analysis of the effects of kinematics, elasticity and thixotropy on fluid flow within the abrupt contraction.

There are two big challenges which restrict the extensive application of fully coupled geomechanics-reservoir modeling. The first challenge is computational effort. Consider a 3-D simulation combining pressure and heat diffusion, elastoplastic mechanical response, and saturation changes; each node has at least 5 degrees of freedom, each leading to a separate equation. Furthermore, regions of large p, T and σ′ gradients require small-scale discretization for accurate solutions, greatly increasing the number of equations. When the rock mass surrounding the reservoir region is included, it is represented by many elements or nodes. These factors mean that accurate analysis of realistic 3-D problems is challenging, and will so remain as we seek to solve larger and larger coupled problems involving nonlinear responses. To overcome the first challenge, the displacement discontinuity method is introduced wherein a large-scale 3-D case is divided into a reservoir region where Δp, ΔT and non-linear effects are critical and analyzed using FEM, and an outside region in which the reservoir is encased where Δp and ΔT effects are inconsequential and the rock may be treated as elastic, analyzed with a 3D displacement discontinuity formulation. This scheme leads to a tremendous reduction in the degrees of freedom, yet allows for reasonably rigorous incorporation of the reactions of the surrounding rock. The second challenge arises from some forms of numerical instability. There are actually two types of sharp gradients implied in the transient advection-diffusion problem: one is caused by the high Peclet numbers, the other by the sharp gradient which appears during the small time steps due to the transient solution. The way to eliminate the spurious oscillations is different when the sharp gradients are induced by the transient evolution than when they are produced by the advective terms, and existing literature focuses mainly on eliminating the spurious spatial temperature oscillations caused by advection-dominated flow. To overcome the second challenge, numerical instability sources are addressed by introducing a new stabilized finite element method, the subgrid scale/gradient subgrid scale (SGS/GSGS) method.

There are two big challenges which restrict the extensive application of fully coupled geomechanics-reservoir modeling. The first challenge is computational effort. Consider a 3-D simulation combining pressure and heat diffusion, elastoplastic mechanical response, and saturation changes; each node has at least 5 degrees of freedom, each leading to a separate equation. Furthermore, regions of large p, T and σ′ gradients require small-scale discretization for accurate solutions, greatly increasing the number of equations. When the rock mass surrounding the reservoir region is included, it is represented by many elements or nodes. These factors mean that accurate analysis of realistic 3-D problems is challenging, and will so remain as we seek to solve larger and larger coupled problems involving nonlinear responses. To overcome the first challenge, the displacement discontinuity method is introduced wherein a large-scale 3-D case is divided into a reservoir region where Δp, ΔT and non-linear effects are critical and analyzed using FEM, and an outside region in which the reservoir is encased where Δp and ΔT effects are inconsequential and the rock may be treated as elastic, analyzed with a 3D displacement discontinuity formulation. This scheme leads to a tremendous reduction in the degrees of freedom, yet allows for reasonably rigorous incorporation of the reactions of the surrounding rock. The second challenge arises from some forms of numerical instability. There are actually two types of sharp gradients implied in the transient advection-diffusion problem: one is caused by the high Peclet numbers, the other by the sharp gradient which appears during the small time steps due to the transient solution. The way to eliminate the spurious oscillations is different when the sharp gradients are induced by the transient evolution than when they are produced by the advective terms, and existing literature focuses mainly on eliminating the spurious spatial temperature oscillations caused by advection-dominated flow. To overcome the second challenge, numerical instability sources are addressed by introducing a new stabilized finite element method, the subgrid scale/gradient subgrid scale (SGS/GSGS) method.

No description available.

Les procédés de trempe sont largement répandus dans l'industrie en particulier dans le domaine de l'automobile, du nucléaire et de l'aérospatiale car ils ont un impact direct sur la microstructure, les propriétés mécaniques et les contraintes résiduelles de pièces critiques. La trempe est un processus fortement non-linéaire à cause des couplages forts entre la mécanique des fluides, les transferts thermiques aux différentes interfaces, les transformations de phase du solide et l'ébullition du milieu de trempe. Malgré les progrès effectués par la simulation numérique, ce procédé reste extrêmement difficile à modéliser.Dans ce travail, nous proposons le développement d'outils numériques permettant la simulation réaliste de ce procédé à l'échelle industrielle. La mécanique des fluides est simulée en utilisant une méthode d'Elements Finis stabilisés permettant de considérer des écoulements à haut nombre de Reynolds. Les transferts thermiques sont calculés directement sans l'utilisation de coefficients de transferts empiriques, en utilisant le couplage fort entre le fluide et le solide. Nous avons développé un modèle de changement de phase pour l'eau permettant de considérer les différents régimes d'ébullition. Une formulation unifiée des équations de Navier-Stokes, considérant une phase compressible et une phase incompressible a été développée afin de prendre en compte plus précisément la dynamique de la vapeur et de l'eau. Une procédure dynamique d'adaptation anisotrope de maillage, permettant une description plus fine des interfaces et une prise en compte plus précise des caractéristiques des écoulements est utilisée.Des exemples numériques exigeants ainsi qu'une validation expérimentale permettent d'évaluer la précision et la robustesse des outils proposés.Les outils développés permettent ainsi l'optimisation du mode opératoire du procédé, des ressources consommées et servent ainsi d'outils prospectifs pour la conception de produits. / Quenching processes of metals are widely adopted procedures in the industry, in particular automotive, nuclear and aerospace industries, since they have direct impacts on changing mechanical properties, controlling microstructure and releasing residual stresses of critical parts. Quenching is a highly nonlinear process because of the strong coupling between the fluid mechanics, heat transfer at the interface solid-fluid, phase transformation in the metal and boiling. In spite of the maturity and the popularity of numerical formulations, several involved mechanisms are still not well resolved.Therefore we propose a Direct Numerical Simulation of quenching processes at the industrial scale dealing with these phenomena. The fluid mechanics is simulated using a Finite Element Method adapted for high convective flows allowing the use of high stirring velocity in the quenching bath. Heat transfers are computed directly without the use of heat transfer coefficients but using the strong coupling between the fluid and the solid. We use a phase change model for the water that models all boiling regimes. A unified formulation of the Navier-Stokes equations, taking into account a compressible gas and an incompressible liquid is developed to model more accurately the vapor-water dynamics. A dynamic mesh adaptation procedure is used, increasing the resolution in the description of the interfaces and capturing more accurately the features of the flows.We assess the behavior and the accuracy of the proposed formulation in the simulation of time-dependent challenging numerical examples and experimental results.These recent developments enable the optimization of the process in terms of operating conditions, resources consumed and products conception.

L'Interaction Fluide-Structure (IFS) décrit une classe très générale de problème physique, ce qui explique la nécessité de développer une méthode numérique capable de simuler le problème FSI. Pour cette raison, un solveur IFS est développé qui peut traiter un écoulement de fluide incompressible en interaction avec des structures différente: élastique ou rigide. Dans cet aspect, le solveur peut couvrir une large gamme d'applications.La méthode proposée est développée dans le cadre d'une formulation monolithique dans un contexte Eulérien. Cette méthode consiste à considérer un seul maillage et résoudre un seul système d'équations avec des propriétés matérielles différentes. La fonction distance permet de définir la position et l'interface de tous les objets à l'intérieur du domaine et de fournir les propriétés physiques pour chaque sous-domaine. L'adaptation de maillage anisotrope basé sur la variation de la fonction distance est ensuite appliquée pour assurer une capture précise des discontinuités à l'interface fluide-solide.La formulation monolithique est assurée par l'ajout d'un tenseur supplémentaire dans les équations de Navier-Stokes. Ce tenseur provient de la présence de la structure dans le fluide. Le système est résolu en utilisant une méthode élément fini et stabilisé suivant la formulation variationnelle multiéchelle. Cette formulation consiste à décomposer les champs de vitesse et pression en grande et petite échelles. La particularité de l'approche proposée réside dans l'enrichissement du tenseur de l'extra contraint.La première application est la simulation IFS avec un corps rigide. Le corps rigide est décrit en imposant une valeur nul du tenseur des déformations, et le mouvement est obtenu par la résolution du mouvement de corps rigide. Nous évaluons le comportement et la précision de la formulation proposée dans la simulation des exemples 2D et 3D. Les résultats sont comparés avec la littérature et montrent que la méthode développée est stable et précise.La seconde application est la simulation IFS avec un corps élastique. Dans ce cas, une équation supplémentaire est ajoutée au système précédent qui permet de résoudre le champ de déplacement. Et la contrainte de rigidité est remplacée par la loi de comportement du corps élastique. La déformation et le mouvement du corps élastique sont réalisés en résolvant l'équation de convection de la Level-Set. Nous illustrons la flexibilité de la formulation proposée par des exemples 2D. / Numerical simulations of fluid-structure interaction (FSI) are of first interest in numerous industrial problems: aeronautics, heat treatments, aerodynamic, bioengineering... Because of the high complexity of such problems, analytical study is in general not sufficient to understand and solve them. FSI simulations are then nowadays the focus of numerous investigations, and various approaches are proposed to treat them. We propose in this thesis a novel monolithic approach to deal with the interaction between an incompressible fluid flow and rigid/ elastic material. This method consists in considering a single grid and solving one set of equations with different material properties. A distance function enables to define the position and the interface of any objects with complex shapes inside the volume and to provide heterogeneous physical properties for each subdomain. Different anisotropic mesh adaptation algorithms based on the variations of the distance function or on using error estimators are used to ensure an accurate capture of the discontinuities at the fluid-solid interface. The monolithic formulation is insured by adding an extra-stress tensor in the Navier-Stokes equations coming from the presence of the structure in the fluid. The system is then solved using a finite element Variational MultiScale (VMS) method, which consists of decomposition, for both the velocity and the pressure fields, into coarse/resolved scales and fine/unresolved scales. The distinctive feature of the proposed approach resides in the efficient enrichment of the extra constraint. In the first part of the thesis, we use the proposed approach to assess its accuracy and ability to deal with fluid-rigid interaction. The rigid body is prescribed under the constraint of imposing the nullity of the strain tensor, and its movement is achieved by solving the rigid body motion. Several test case, in 2D and 3D with simple and complex geometries are presented. Results are compared with existing ones in the literature showing good stability and accuracy on unstructured and adapted meshes. In the second, we present different routes and an extension of the approach to deal with elastic body. In this case, an additional equation is added to the previous system to solve the displacement field. And the rigidity constraint is replaced with a corresponding behaviour law of the material. The elastic deformation and motion are captured using a convected level-set method. We present several 2D numerical tests, which is considered as classical benchmarks in the literature, and discuss their results.

Aujourd'hui, avec l'amélioration des puissances de calcul informatique, la simulation numérique est devenue un outil essentiel pour la prédiction des phénomènes physiques et l'optimisation des procédés industriels. La modélisation de ces phénomènes pose des difficultés scientifiques car leur résolution implique des temps de calcul très longs malgré l'utilisation d'importantes ressources informatiques.Dans cette thèse, on s'intéresse à la résolution de problèmes complexes couplant écoulements et transferts thermiques. Les problèmes physiques étant fortement anisotropes, il est nécessaire d'avoir un maillage avec une résolution très élevée pour obtenir un bon niveau de précision. Cela implique de longs temps de calcul. Ainsi il faut trouver un compromis entre précision et efficacité. Le développement de méthodes d'adaptation en temps et en espace est motivé par la volonté de faire des applications réelles et de limiter les inconvénients inhérents aux méthodes de résolution non adaptatives en terme de précision et d'efficacité. La résolution de problèmes multi-échelles instationnaires sur un maillage uniforme avec un nombre de degrés de liberté limité est souvent incapable de capturer les petites échelles, nécessite des temps de calcul longs et peut aboutir à des résultats incorrects. Ces difficultés ont motivé le développement de méthodes de raffinement local avec une meilleure précision aux endroits adéquats. L'adaptation en temps et en espace peut donc être considérée comme une composante essentielle de ces méthodes.L'approche choisie dans cette thèse consiste en l'utilisation de méthodes éléments finis stabilisées et le développement d'outils d'adaptation espace-temps pour améliorer la précision et l'efficacité des simulations numériques.Le développement de la méthode adaptative est basé sur un estimateur d'erreur sur les arrêtes du maillage afin de localiser les régions du domaine de calcul présentant de forts gradients ainsi que les couches limites. Ensuite une métrique décrivant la taille de maille en chaque noeud dans les différentes directions est calculée. Afin d'améliorer l'efficacité des calculs la construction de cette métrique prend en compte un nombre fixe de noeuds et aboutit à une répartition et une orientation optimale des éléments du maillage. Cette approche est étendue à une formulation espace-temps où les maillages et les pas de temps optimaux sont prédits sur des intervalles de temps en vue de contrôler l'erreur d'interpolation sur la domaine de calcul. / Nowadays, with the increase in computational power, numerical modeling has become an intrinsic tool for predicting physical phenomena and developing engineering designs. The modeling of these phenomena poses scientific complexities the resolution of which requires considerable computational resources and long lasting calculations.In this thesis, we are interested in the resolution of complex long time and large scale heat transfer and fluid flow problems. When the physical phenomena exhibit sharp anisotropic features, a good level of accuracy requires a high mesh resolution, hence hindering the efficiency of the simulation. Therefore a compromise between accuracy and efficiency shall be adopted. The development of space and time adaptive adaptation techniques was motivated by the desire to devise realistic configurations and to limit the shortcomings of the traditional non-adaptive resolutions in terms of lack of solution's accuracy and computational efficiency. Indeed, the resolution of unsteady problems with multi-scale features on a prescribed uniform mesh with a limited number of degrees of freedom often fails to capture the fine scale physical features, have excessive computational cost and might produce incorrect results. These difficulties brought forth investigations towards generating meshes with local refinements where higher resolution was needed. Space and time adaptations can thus be regarded as essential ingredients in this recipe.The approach followed in this work consists in applying stabilized finite element methods and the development of space and time adaptive tools to enhance the accuracy and efficiency of the numerical simulations.The derivation process starts with an edge-based error estimation for locating the regions, in the computational domain, presenting sharp gradients, inner and boundary layers. This is followed by the construction of nodal metric tensors that prescribe, at each node in the spatial mesh, mesh sizes and the directions along which these sizes are to be imposed. In order to improve the efficiency of computations, this construction takes into account a fixed number of nodes and generates an optimal distribution and orientation of the mesh elements. The approach is extended to a space-time adaptation framework, whereby optimal meshes and time-step sizes for slabs of time are constructed in the view of controlling the global interpolation error over the computation domain.