Aujourd'hui, dans de nombreux champs d'applications, de plus en plus de problèmes d'ingénierie demandent d'avoir une évaluation précise et efficace de quantités d'intérêt.Très souvent, ces quantités dépendent de la solution d'une équation aux dérivées partielles (EDP) paramétrée où les paramètres -- physiques ou géométriques -- sont les entrées du modèle et les quantités d'intérêt -- valeurs moyennes -- en sont les sorties.Les techniques de réduction d'ordre, notamment la méthode des bases réduites qui est la méthode utilisée tout au long de ces travaux,permettent de répondre à ces demandes.Dans cette thèse nous nous intéressons à la mise en place d'un framework en C++, supportant le calcul parallèle, permettant d'appliquer la méthode des bases réduites à des problèmes multi-physiques non-linéaires tels queles problèmes de convection naturelle (couplage fluide-thermique), ou encore la modélisation d'aimants de type résistifs à hauts champs (nous nous limitons au couplage thermo-electrique) aboutissant à une étude sur la quantification d'incertitude.La méthode des bases réduites s'appuie naturellement sur une approximation obtenue via la discrétisation élément fini du problème à traiter. Pour cela nous utilisons la librairie de calcul Feel++, spécialisée dans la résolution d'EDPs.Nous nous intéressons également aux problèmes de type multi-échelles.La particularité de ces problèmes est de manipuler un ensemble de phénomènes mettant en jeu des échelles différentes, comme c'est le cas par exemple lorsque nous considérons un écoulement en milieu poreux.La méthode des éléments finis multi-échelles permet d'avoir le comportement "global", associé aux grandes échelles, de la solution du problème sans devoir le résoudre sur les petites échelles.Nous proposons une nouvelle construction des fonctions de base élément fini multi-échelles basée sur la méthode des bases réduites. / Today, in many fields of applications, more and more engineering problems require to have an accurate and efficient evaluation of quantities of interest.Often, these quantities depend on a partial differential equation (PDE) parameterized solution -- physical or geometrical -- are the model inputs and the quantities of interest -- average values ​​-- are the outputs.The order reduction techniques, including reduced basis method which is the method used throughout this work, can meet these demands.In this thesis, we focus on the establishment of a framework in C ++ supporting parallel computing, which applies the reduced basis method to nonlinear multiphysics problems such as problems with natural convection (fluid-thermal coupling) or the high field resistive magnet modeling (we limit ourselves to thermo-electric coupling) leading to a study on the uncertainty quantification.The reduced basis method naturally relies on an approximation obtained using the finite element discretization of the problem being treated. For this, we use the Feel ++ computation library specialized in PDE resolution.We are also interested by multiscale problems.The particularity of these problems is to manipulate a set of phenomena involving different scales, as this is the case for example when we consider a flow in porous media.The multiscale finite element method allows having a "global" behavior, linked with large scales, of the problem solution without solving it on small scales.We propose a new construction of multiscale finite element basis functions based on the reduced basis method.

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The context of this thesis is the numerical simulation of turbulent flows at moderate Reynolds numbers and the improvement of the capabilities of an in-house 3D unsteady and incompressible flow solver called SFELES to simulate such flows. In addition to this abstract, this thesis includes five other chapters. The second chapter of this thesis presents the numerical methods implemented in the two CFD solvers used as part of this work, namely SFELES and PHASTA. The third chapter concentrates on the implementation of a new library called FlexMG. This library allows the use of various types of iterative solvers preconditioned by algebraic multigrid methods, which require much less memory to solve linear systems than a direct sparse LU solver available in SFELES. Multigrid is an iterative procedure that relies on a series of increasingly coarser approximations of the original 'fine' problem. The underlying concept is the following: low wavenumber errors on fine grids become high wavenumber errors on coarser levels, which can be effectively removed by applying fixed-point methods on coarser levels. Two families of algebraic multigrid preconditioners have been implemented in FlexMG, namely smooth aggregation-type and non-nested finite element-type. Unlike pure gridless multigrid, both of these families use the information contained in the initial fine mesh. A hierarchy of coarse meshes is also needed for the non-nested finite element-type multigrid so that our approaches can be considered as hybrid. Our aggregation-type multigrid is smoothed with either a constant or a linear least square fitting function, whereas the non-nested finite element-type multigrid is already smooth by construction. All these multigrid preconditioners are tested as stand-alone solvers or coupled with a GMRES (Generalized Minimal RESidual) method. After analyzing the accuracy of the solutions obtained with our solvers on a typical test case in fluid mechanics (unsteady flow past a circular cylinder at low Reynolds number), their performance in terms of convergence rate, computational speed and memory consumption is compared with the performance of a direct sparse LU solver as a reference. Finally, the importance of using smooth interpolation operators is also underlined in this work. The fourth chapter is devoted to the study of subgrid scale models for the large eddy simulation (LES) of turbulent flows. It is well known that turbulence features a cascade process by which kinetic energy is transferred from the large turbulent scales to the smaller ones. Below a certain size, the smallest structures are dissipated into heat because of the effect of the viscous term in the Navier-Stokes equations. In the classical formulation of LES models, all the resolved scales are used to model the contribution of the unresolved scales. However, most of the energy exchanges between scales are local, which means that the energy of the unresolved scales derives mainly from the energy of the small resolved scales. In this fourth chapter, constant-coefficient-based Smagorinsky and WALE models are considered under different formulations. This includes a classical version of both the Smagorinsky and WALE models and several scale-separation formulations, where the resolved velocity field is filtered in order to separate the small turbulent scales from the large ones. From this separation of turbulent scales, the strain rate tensor and/or the eddy viscosity of the subgrid scale model is computed from the small resolved scales only. One important advantage of these scale-separation models is that the dissipation they introduce through their subgrid scale stress tensor is better controlled compared to their classical version, where all the scales are taken into account without any filtering. More precisely, the filtering operator (based on a top hat filter in this work) allows the decomposition u' = u - ubar, where u is the resolved velocity field (large and small resolved scales), ubar is the filtered velocity field (large resolved scales) and u' is the small resolved scales field. At last, two variational multiscale (VMS) methods are also considered. The philosophy of the variational multiscale methods differs significantly from the philosophy of the scale-separation models. Concretely, the discrete Navier-Stokes equations have to be projected into two disjoint spaces so that a set of equations characterizes the evolution of the large resolved scales of the flow, whereas another set governs the small resolved scales. Once the Navier-Stokes equations have been projected into these two spaces associated with the large and small scales respectively, the variational multiscale method consists in adding an eddy viscosity model to the small scales equations only, leaving the large scales equations unchanged. This projection is obvious in the case of a full spectral discretization of the Navier-Stokes equations, where the evolution of the large and small scales is governed by the equations associated with the low and high wavenumber modes respectively. This projection is more complex to achieve in the context of a finite element discretization. For that purpose, two variational multiscale concepts are examined in this work. The first projector is based on the construction of aggregates, whereas the second projector relies on the implementation of hierarchical linear basis functions. In order to gain some experience in the field of LES modeling, some of the above-mentioned models were implemented first in another code called PHASTA and presented along with SFELES in the second chapter. Finally, the relevance of our models is assessed with the large eddy simulation of a fully developed turbulent channel flow at a low Reynolds number under statistical equilibrium. In addition to the analysis of the mean eddy viscosity computed for all our LES models, comparisons in terms of shear stress, root mean square velocity fluctuation and mean velocity are performed with a fully resolved direct numerical simulation as a reference. The fifth chapter of the thesis focuses on the numerical simulation of the 3D turbulent flow over a re-entry Apollo-type capsule at low speed with SFELES. The Reynolds number based on the heat shield is set to Re=10^4 and the angle of attack is set to 180º, that is the heat shield facing the free stream. Only the final stage of the flight is considered in this work, before the splashdown or the landing, so that the incompressibility hypothesis in SFELES is still valid. Two LES models are considered in this chapter, namely a classical and a scale-separation version of the WALE model. Although the capsule geometry is axisymmetric, the flow field in its wake is not and induces unsteady forces and moments acting on the capsule. The characterization of the phenomena occurring in the wake of the capsule and the determination of their main frequencies are essential to ensure the static and dynamic stability during the final stage of the flight. Visualizations by means of 3D isosurfaces and 2D slices of the Q-criterion and the vorticity field confirm the presence of a large meandering recirculation zone characterized by a low Strouhal number, that is St≈0.15. Due to the detachment of the flow at the shoulder of the capsule, a resulting annular shear layer appears. This shear layer is then affected by some Kelvin-Helmholtz instabilities and ends up rolling up, leading to the formation of vortex rings characterized by a high frequency. This vortex shedding depends on the Reynolds number so that a Strouhal number St≈3 is detected at Re=10^4. Finally, the analysis of the force and moment coefficients reveals the existence of a lateral force perpendicular to the streamwise direction in the case of the scale-separation WALE model, which suggests that the wake of the capsule may have some preferential orientations during the vortex shedding. In the case of the classical version of the WALE model, no lateral force has been observed so far so that the mean flow is thought to be still axisymmetric after 100 units of non-dimensional physical time. Finally, the last chapter of this work recalls the main conclusions drawn from the previous chapters.

Numerical solution of differential equations having multitude of scales in the solution field is one of the most challenging research areas, but highly demanded in scientific and industrial applications. One of the natural approaches for handling such problems is to separate the scales and approximate the solution of the segregated scales with appropriate numerical method. Variational multiscale method (VMS) is a predominant method in the paradigm of scale separation schemes. In our work we have used the VMS technique to develop a numerical scheme for computations of turbulent flows in time-dependent domains. VMS allows separation of the entire range of scales in the flow field into two or three groups, thereby enabling a different numerical treatment for the different groups. In the context of computational fluid dynamics(CFD), VMS is a significant new improvement over the classical large eddy simulation (LES). VMS does away with the commutation errors arising due to filtering in LES. Further, in a three-scale VMS approach the model for the subgrid scale can be contained to only a part of the resolved scales instead of effecting the entire range of resolved scales. The projection based VMS scheme that we have developed gives a robust and efficient method for solving problems of turbulent fluid flows in deforming domains, governed by incompressible Navier {Stokes equations. In addition to the existing challenges due to turbulence, the computational complexity of the problem increases further when the considered domain is time-dependent. In this work, we have used an arbitrary Lagrangian-Eulerian (ALE) based VMS scheme to account for the domain deformation. In the proposed scheme, the large scales are represented by an additional tensor valued space. The resolved large and small scales are computed in a single unified equation, and the effect of unresolved scales is confined only to the resolved small scales, by using a projection operator. The popular Smagorinsky eddy viscosity model is used to approximate the effects of unresolved scales. The used ALE approach consists of an elastic mesh update technique. Moreover, a computationally efficient scheme is obtained by the choice of orthogonal finite element basis function for the resolved large scales, which allows to reformulate the ALE-VMS system matrix into the standard form of the NSE system matrix. Thus, any existing Navier{Stokes solver can be utilized for this scheme, with modifications. Further, the stability and error estimates of the scheme using a linear model of the NSE are also derived. Finally, the proposed scheme has been validated by a number of numerical examples over a wide range of problems.

Une méthode de couplage continu-discret a été développée pour simuler les mécanismes complexes d'endommagement de la silice soumise à un choc laser de haute puissance. Dans un premier temps, une classification des méthodes numériques existantes a été faite pour choisir celles les mieux adaptées à la simulation du comportement sous choc de la silice. Comme résultat de cette classification, deux méthodes ont été retenues: la méthode des éléments discrets (DEM) et la méthode des éléments naturels contraints (CNEM). Ces méthodes sont alors couplées en se basant sur la technique dite "Arlequin". Puis, un modèle numérique permettant de tenir compte des différents phénomènes qui caractérise le comportement de la silice sous haute pression a été développé. Pour bien caractériser les mécanismes de fissuration de la silice à l’échelle microscopique, un nouveau modèle de rupture a été développé dans ce travail. Finalement, ces deux modèles, modèle de comportement et modèle de rupture, ont été intégrés dans la méthode du couplage pour simuler d'un point de vue mécanique le choc laser sur un échantillon en silice. / A discrete-continuum coupling approach has been developed to simulate the laser-induced damage in silica glass. First, a classification of the different numerical methods has been performed to select the ones that best meet the objectives of this work. Acting upon this classification, the Discrete Element Method (DEM) and the Constrained Natural Element Method (CNEM) have been retained. Subsequently, a coupling approach between these methods has been proposed. This approach is based on the Arlequin technique. In the second part, a numerical model of the silica glass mechanical behavior has been developed to better characterize the silica glass response under highly dynamic loadings and particularly loading generated by a laser beam. To correctly characterize the silica glass cracking mechanisms, a new fracture model has been proposed in this work. Finally, all these developments have been used to simulate the laser-induced damage in silica glass.

Les parties tournantes des turbomachines aéronautiques sont composées d’une succession de roues aubagées qui permettent le transfert de l’énergie entre l’air et le rotor. Ces roues aubagées constituent des pièces particulièrement sensibles car elles doivent répondre en termes de dimensionnement à des impératifs de performances aérodynamiques, d’aéroacoustique et de tenue mécanique à la rotation,à la température et à la charge aérodynamique. Le contact avec frottement existant au niveau des attaches aube-disque joue un rôle important sur les niveaux vibratoires.Ce travail porte sur l’étude de l’usure par fretting sous chargements dynamiques dans les interfaces frottantes. En effet, les vibrations de l’aube peuvent produire des micro-glissements en pied d’aubequi peuvent entraîner un phénomène d’usure par fretting. Les connaissances sur le comportement de l’usure sous sollicitations dynamiques sont faibles. Seuls existent des outils numériques pour modéliser l’usure dans le cas de sollicitations quasi-statiques. Nous proposons dans cette thèse des méthodes pour calculer l’évolution de l’usure au cours des cycles de chargement dynamique basées sur une approche multi-échelle en temps. La réponse vibratoire de la structure est liée à une échelle de temps rapide qui est calculée par une méthode d’équilibrage harmonique, dans laquelle les déplacements et les efforts sont projetés sur la base de Fourier. Différentes approches temps-fréquence de calcul des coefficients de Fourier des forces de contact sont présentées. La cinétique d’usure est liée à une échelle lente et différentes méthodes sont proposées pour l’intégrer. La prise en compte des géométries usées dans le modèle éléments finis se fait par l’ajout d’un vecteur des profondeurs d’usure dans le terme de pénalité des lagrangiens dynamiques. Des exemples académiques valident et illustrent les méthodes proposées. Ces méthodes sont ensuite appliquées à l’étude de l’usure par fretting en pied d’aube de soufflante. L’étude numérique met en lumière le couplage entre vibration et usure par fretting aux interfaces de contact. La modification du comportement dynamique global de la roue aubagée est aussi observée. / The rotating parts of aeronautical turbomachineries are made of bladed disks which enable the transfer of energy from the air to the rotor. These bladed disks are especially critical parts because their dimensioning has to meet strict requirements in terms of aerodynamical performance, aeroacoustics and mechanical resistance to rotation, temperature and aerodynamical loads. The frictional contact at the interface between blade and disk has an important influence on the vibratory levels.This work deals with the study of fretting-wear in frictional interfaces under dynamical loading. Indeed,the blade’s vibrations can produce micro-slidings in blade’s root which may entail fretting-wear. Wear under dynamical loading is a badly known phenomenon. Numerical tools exist for quasic-static conditions only. Here,methods are proposed to quantify the evolution of wear along dynamical loadingcycles based on a time-multiscale approach. The vibratory response of the structure is linked with a fasttime scale which is calculated by a harmonic balance method : displacements and forces are expressed through Fourier series. Different frequency-time approaches are presented to compute the Fourier coefficients of contact forces. Wear kinetics is linked with a slow time scale and different methods are proposed to integrate it.Worn geometries are taken into account in the finite elements model by a wear depth vector included in the penalty term of dynamic lagrangians. Academic examples validate and illustrate the proposed methods. These methods are then used to study fretting-wear in a fan’s bladeroot. The numerical results highlight the coupling between vibration and fretting-wear in frictional interfaces.The modification of the global dynamical behaviour of the bladed disk is also observed.

L'industrie se tourne de plus en plus vers les matériaux composites. A l'échelle de la microstructure leur comportement est fortement hétérogène mais à l'échelle de la structure ceux-ci peuvent être considérés homogène. Les méthodes multi-échelles ont été développées pour résoudre les problèmes de structure avec un temps de calcul raisonnable. Ces méthodes sont validées par comparaison avec un calcul numérique où les hétérogénéités sont entièrement maillées. Dans ce travail de thèse, une structure architecturée modèle a été créée au centre d'une plaque (homogène) mince en acier inoxydable (304L). La cellule unitaire du matériau architecturé est constitué d'un carré avec un trou au centre. L'utilisation d'une caméra à très haute résolution (270 millions de pixels) permet de suivre simultanément l'évolution des déformations aux échelles microscopique et macroscopique. La variation de l'orientation de la structure architecturée modifie les sollicitations appliquées aux cellules unitaires. Les expériences réalisées ont pour but d'analyser les cinématiques de déformation des cellules unitaires sous un chargement multi-axial. La recherche des cellules ayant une cinématique périodique est réalisée. Il est ainsi montré que les cellules avec une cinématique non périodique correspondent à la zone de transition entre le matériau architecturé et le matériau homogène. La connaissance des cinématiques des cellules permet d'investiguer les changements d'échelles dans le domaine linéaire et non-linéaire. Le passage de l'échelle macroscopique à l'échelle microscopique est particulièrement étudié avec le choix des conditions aux limites. Le remplacement des cellules ayant une cinématique périodique par un milieu homogène équivalent (MHE) est traité. La géométrie de la cellule unitaire introduit des symétries dans le comportement du MHE, celui-ci devient cubique. Les caractéristiques élastiques du MHE sont obtenus par homogénéisation à partir des résultats expérimentaux. Un critère de Tsaï-Hill est identifié dans le domaine non-linéaire. Le dernier chapitre s'intéresse à la fissuration de la zone architecturée et à l'initiation de la localisation des déformations dans les cellules. Le support de la localisation est calculé à partir du champ des déformations mesuré par CIN. La cinématique de la cellule est enrichie avec une discontinuité et le saut de déplacement normal à la localisation est identifié. Une comparaison avec le saut de déplacement calculé par corrélation d'images étendue à l'échelle macroscopique est menée afin de valider la stratégie d'identification à l'échelle microscopique. / Industry employ more and more composite materials in structures todecrease the weight. At the microstructure scale behavior is strongly heterogeneous but at the structure scale behaviour may be considered homogeneous. Multiscale methods have been developed to solve the structural problems with a reasonable calculation time. These methods are validated by comparison with a numerical calculation where heterogeneities are fully meshed. In this thesis work, an ideal architectural material was created in the center of a (homogeneous) stainless steel (304L) thin plate. The unit cell architecture material consists of a square with a hole in the center. The use of a high resolution camera (270 million pixels) allows to follow simultaneously the evolution of deformation at microscopic and macroscopic scales. The orientation of the heterogeneous structure modifies the sollicitations applied to the unit cells. The experiments are designed to analyze the kinematics of deformation of the unit cells in a multi-axial loading. Unit cells with periodic kinematics are searched. It is thus shown that the cells with a non-periodic kinematic correspond to the transition zone between the homogeneous material and the architectured material. Knowledge of the kinematic cells allows to investigate the scale changings in the linear and nonlinear range. The downscaling from the macroscopic to the microscopic scale is particularly studied with the choice of boundary conditions. An equivalent homogeneous medium (MHE) is determined as a remplacement for the cells having a periodic kinematic. The geometry of the unit cell introduced symmetries in the behavior of MHE, it becomes cubic (orthotropic with material parameters). The elastic characteristics of the MHE are obtained by homogenization from the experimental results. A criterion of Tsai-Hill is identified in the non-linear domain. The last chapter is interested in cracking of the architected zone and the initiation of strain localization in cells. The support of location is calculated from the strain field measured by correlation. The kinematics of the cell is enriched with a discontinuity and the displacement jump normal to the localization is identified. A comparison with the displacement jump calculated by extended digital image correlation at the macroscopic scale is conducted to validate the identification strategy at the microscopic level.

L'objectif principal de ce travail est d'améliorer la précision et l'efficacité des modèles LES au moyen des méthodes Galerkine discontinues (DG). Deux thématiques principales ont été étudiées: les stratégies d'adaptation spatiale et les modèles LES pour les méthodes d'ordre élevé.Concernant le premier thème, dans le cadre des méthodes DG la résolution spatiale peut être efficacement adaptée en modifiant localement soit le maillage (adaptation-h) soit le degré polynômial de la solution (adaptation-p). L'adaptation automatique de la résolution nécessite l'estimation des erreurs pour analyser la qualité de la solution locale et les exigences de résolution. L'efficacité de différentes stratégies de la littérature est comparée en effectuant des simulations h- et p-adaptatives.Sur la base de cette étude comparative, des algorithmes statiques et dynamiques p-adaptatifs pour la simulation des écoulements instationnaires sont ensuite développés et analysés. Les simulations numériques réalisées montrent que les algorithmes proposés peuvent réduire le coût de calcul des simulations des écoulements transitoires et statistiquement stationnaires.Un nouvel estimateur d'erreur est ensuite proposé. Il est local, car n'exige que des informations de l'élément et de ses voisins directs, et peut être calculé en cours de simulation pour un coût limité. Il est démontré que l'algorithme statique p-adaptatif basé sur cet estimateur d'erreur peut être utilisé pour améliorer la précision des simulations LES sur des écoulements turbulents statistiquement stationnaires.Concernant le second thème, une nouvelle méthode, consistante avec la discrétisation DG, est développée pour l'analyse a-priori des modèles DG-LES à partir des données DNS. Elle permet d'identifier le transfert d'énergie idéal entre les échelles résolues et non résolues. Cette méthode est appliquée à l'analyse de l'approche VMS (Variational Multiscale). Il est démontré que pour les résolutions fines, l'approche DG-VMS est capable de reproduire le transfert d'énergie idéal. Cependant, pour les résolutions grossières, typique de la LES à nombres de Reynolds élevés, un meilleur accord peut être obtenu en utilisant un modèle mixte Smagorinsky-VMS. / The main goal of this work is to improve the accuracy and computational efficiency of Large Eddy Simulations (LES) by means of discontinuous Galerkin (DG) methods. To this end, two main research topics have been investigated: resolution adaptation strategies and LES models for high-order methods.As regards the first topic, in the framework of DG methods the spatial resolution can be efficiently adapted by modifying either the local mesh size (h-adaptation) or the degree of the polynomial representation of the solution (p-adaptation).The automatic resolution adaptation requires the definition of an error estimation strategy to analyse the local solution quality and resolution requirements.The efficiency of several strategies derived from the literature are compared by performing p- and h-adaptive simulations. Based on this comparative study a suitable error indicator for the adaptive scale-resolving simulations is selected.Both static and dynamic p-adaptive algorithms for the simulation of unsteady flows are then developed and analysed. It is demonstrated by numerical simulations that the proposed algorithms can provide a reduction of the computational cost for the simulation of both transient and statistically steady flows.A novel error estimation strategy is then introduced. It is local, requiring only information from the element and direct neighbours, and can be computed at run-time with limited overhead. It is shown that the static p-adaptive algorithm based on this error estimator can be employed to improve the accuracy for LES of statistically steady turbulent flows.As regards the second topic, a novel framework consistent with the DG discretization is developed for the a-priori analysis of DG-LES models from DNS databases. It allows to identify the ideal energy transfer mechanism between resolved and unresolved scales.This approach is applied for the analysis of the DG Variational Multiscale (VMS) approach. It is shown that, for fine resolutions, the DG-VMS approach is able to replicate the ideal energy transfer mechanism.However, for coarse resolutions, typical of LES at high Reynolds numbers, a more accurate agreement is obtained by a mixed Smagorinsky-VMS model.

Beaucoup de procédés utilisés dans l'industrie sidérurgique (coulée de lingots,coulée continue, …) peuvent générer des défauts : macro-ségrégation, mauvaises propriétés de la microstructure, défauts surfaciques. Ces problèmes peuvent être résolus par un contrôle de la température et de l’écoulement d'acier liquide. Le brassage électromagnétique (EMS) est une technique largement utilisée pour contrôler l’écoulement d'acier liquide par l’imposition d'un champ électromagnétique. Cette technique est complexe car elle couple plusieurs types de problèmes physiques:écoulement multiphasique, solidification,transfert de chaleur et induction électromagnétique à basse fréquence.En outre, l’approche expérimentale est difficile de par la dimension,l'environnement et le coût des procédés considérés. Pour ces raisons, des simulations numériques efficaces sont nécessaires pour comprendre les applications EMS et améliorer les procédés évoqués. L'objectif de cette thèse est de développer une méthodologie numérique robuste,efficace et précise pour la simulation multi-physique de l'EMS, en particulier pour le brassage dans le moule dans le cadre de la coulée continue d'acier. Cette méthodologie a été mise en oeuvre dans le code commercial THERCAST® pour être utilisé dans le cadre d’applications industrielles / Many of the processes used in thesteelmaking industry (e.g. ingot casting,continuous casting, …) can lead todefects: macro-segregation, poormicrostructure properties, surfacedefects. These issues can be solved bycontrolling the temperature and the flowof molten steel. Electromagnetic stirring(EMS) is a widely used technique to steerthe flow of liquid steel by thesuperimposition of an electro-magneticfield. This application is complex becauseit couples several physical problems:multi-phase flow, solidification, heattransfer and low frequency electromagneticinduction. In addition,experimental work is difficult because ofthe size, environment and cost of theconsidered processes. For thesereasons, efficient and effective numericalsimulations are needed to understandEMS applications and improve theaforementioned processes.The objective of this thesis is to developa robust, efficient and accurate numericalprocedure for the multi-physicssimulation of EMS, especially for in-moldstirring in the framework of continuouscasting of steel. This procedure has beenimplemented in the commercial codeTHERCAST® in order to be used forindustrial applications.

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