Le taux de déformation des matériaux est élevé pendant le soudage / formage à grande vitesse, le découpage, le sertissage, etc. Les propriétés des matériaux sous déformation à grande vitesse ne suivent pas la même loi que dans le cas de chargement quasi statiques. La caractérisation des matériaux à taux de déformation important est assez difficile et nécessite des équipements sophistiqués. Grâce au développement de la technologie de formage électromagnétique, le test d'expansion d'anneau électromagnétique présente un grand potentiel à utiliser pour caractériser les matériaux à haute vitesse de déformation. Pendant le test d’expansion de l’anneau électromagnétique, la pièce à usiner peut atteindre une vitesse d’expansion de l’ordre de 100m/s et une vitesse de déformation de 104 s-1. Par conséquent, ce test peut être utilisé pour prédire les paramètres du matériau, tels que la dureté et la ductilité à déformation à grande vitesse. Pour d’atteindre cet objectif, un modèle approprié décrivant le processus est nécessaire. Ce modèle doit contenir un couplage électromagnétique-mécanique-thermique pour bien décrire le problème multi-physique. Il existe deux méthodes principales de modélisation dans la littérature, viz. Les méthodes semi-analytiques et les méthodes des éléments finis (parfois combinées avec la méthode des éléments limitants). Les méthodes semi-analytiques nécessitent un temps de calcul court mais offrent une faible précision par rapport aux méthodes des éléments finis. Cependant, en raison de la complexité du couplage multi-physique, l’erreur de calcul est difficile à estimer. De plus, les déformations hétérogènes ainsi que les états de contrainte compliqués peuvent influencer l’identification. Dans ce sens, cette thèse s’est principalement concentrée sur les méthodes d’analyse et de modélisation du test d’expansion d’anneau électromagnétique, incluant les comportements locaux et les phénomènes dynamiques à l’aide des outils expérimentaux et numériques. Par ailleurs, cette thèse comprend aussi le développement d’un méthode semi-analytique permettant le couplage multi-physique, ce qui a été validé par un modèle numérique idéal et par des tests expérimentaux. Les résultats expérimentaux ont été obtenus à l’aide d’une caméra à grande vitesse et du vélocimétrie photovoltaïque Doppler (PDV) pour différents cas tests. Ils ont été utilisés pour déterminer les paramètres du processus et du matériau à l’aide des modèles numériques. Les modèles adaptés pour analyser les états de contrainte et de déformation durant le test d’expansion d’anneau montrent que ce dernier n’est pas un test de traction uniaxial pur comme revendiqué par les chercheurs. En outre, le phénomène de vibration qui se produise de la récupération élastique a été étudié par simulations multi-physiques et par systèmes PDV. Cette étude de récupération élastique permet de mieux comprendre les paramètres influençant du test, ce qui pourrait être utilisé pour contrôler le rebond dans d’autres processus électromagnétique. La méthode de modélisation semi-analytique pour le test d’expansion de l’anneau électromagnétique, qui comprend quatre parties de calcul (partie mécanique, thermique, force de Lorentz et courant de Foucault), a été analysée à l’aide de simulations numériques. Les résultats obtenus ressemblent étroitement aux résultats obtenus par un test idéal et un test expérimental. L’analyse d’erreur des différents aspects physiques permet d’améliorer la précision de calcul semi-analytique, ce qui pourrait être utilisé comme outil supplémentaire d’obtention rapide des paramètres de contrôle dans les tests. Il pourrait aussi être utilisé pour l’identification des paramètres des matériels à déformation à grande vitesse. / High stain rate material deformations are prevalent during high speed impacts, high speed forming/welding, cutting, crimping, blast etc. Characteristics of materials under high strain rate deformation do not follow the same as it occurs under the quasi-static loading conditions. However, characterization of materials under high strain rate deformation is always challenging and it requires sophisticated equipment. Thanks to the development in electromagnetic forming technology, the electromagnetic ring expansion test shows a great potential to be used to characterize materials under high strain rate conditions. During the electromagnetic ring expansion test, the workpiece can reach deformation velocities in the order of 100 m/s and a strain rate of up to 104 s-1. Consequently, this test can be used to predict the material parameters such as the strain rate hardening and ductility under extremely high strain rates (strain rates in the order of 103 – 104 s-1). In order to achieve this goal, an appropriate model is required to describe the process. The model should contain an electromagnetic-mechanical-thermal coupling to obtain the accurate multi-physics nature of the problem. There exist two main modeling methods in literature, viz., the semi-analytical methods and finite element methods (sometime combined with boundary element method). Normally, the semi-analytical methods require short calculation time while it provides lower accuracy in comparison with finite element methods. However, due to the complexity of multi-physics coupling, the calculation error is difficult to be analyzed. Moreover, errors in calculation and identification assumptions may also result from heterogeneous deformations or localized specific phenomena (such as local necking at multi points or electric current localization, skin effect, edge effect of Lorentz force etc.) that could influence identification work as well as stress and strain states. Therefore, this thesis mainly focused on the analysis and modeling methods of ring expansion test including local behaviors and dynamic phenomena with the help of experimental and numerical tools. Moreover, this thesis also includes a development of a semi-analytical method with multi-physics coupling capabilities, which has been validated using a theoretical model and experimental frameworks. Experimental measurements were obtained using high-speed cameras and photonic Doppler velocimetry (PDV) for various test cases are used together with numerical models to investigate the process and material parameters. The models used to analyze the stress and stain states during a ring expansion test show that the ring expansion test is not a pure uniaxial tensile test as claimed by researchers. Besides, another potential process behavior, the vibration phenomena that occurs during the elastic recovery was investigated using multi-physics simulations and PDV systems. This investigation of the elastic recovery helps to understand the potential influencing parameters of the test those are applicable and could be used to control the springback phenomenon during other electromagnetic forming processes. The semi-analytical modeling method for ring expansion test including four calculation parts (mechanical part, eddy current, Lorentz force calculation, thermal part) were analyzed with the help of numerical simulations. The results obtained from analytical work closely resemble with the numerical simulations for both theoretical model and an experimental case study. The error analysis of various physical aspects allows improving the accuracy of semi-analytical calculation that could be used as an additional platform to obtain rapid calculation of the test conditions. This semi-analytical method could be extended in the future to identify material parameters under high strain rate deformations.

La mécanique computationnelle est un outil incontournable pour le monde de l’ingénierie mécanique. Motivé par un désir de réalisme et soumis à un perpétuel gigantisme, les modèles numériques doivent aujourd’hui inclure des phénomènes physiques de plus en plus complexes. Par conséquence, d’importantes capacités calculatoires sont requises afin de traiter des problèmes à la fois non-linéaires mais aussi de grande taille. Pour atteindre cet objectif, il convient de développer les stations de calculs mais aussi les méthodes algorithmiques utilisées afin de résoudre efficacement ces types de problèmes. Récemment, les méthodes de réduction de modèle se révèlent comme d’excellentes options au développement d’algorithmes de résolution performants. Le problème du contact frottant entre solides élastiques est particulièrement bien connu pour sa complexité et dont les temps de calcul peuvent devenir prohibitifs. En effet, les lois qui le régissent sont très hautement non-linéaires (non différentiables). Dans ce mémoire, nous nous proposons d’appliquer différentes méthodes de réduction de modèle (a posteriori et a priori) à ce type de problème afin de développer des méthodes de calculs accélérées dans le cadre de la méthode des éléments finis. Tout d’abord, en se plaçant dans le cadre des petites perturbations en évolution quasistatique, la réductibilité de diverses solutions impliquant du contact frottant est mise en évidence via leur décomposition en valeur singulière. De plus, leur contenu à échelle séparée est exhibé. La méthode non-incrémentale et non-linéaire à large incrément de temps (LATIN) est par la suite présentée. Dans un second temps et à partir des observations faites précédemment, une méthode LATIN accélérée est proposée en s’inspirant des méthodes multigrilles non-linéaires de type “full approximation scheme” (FAS). Cette méthode s’apparente en partie aux méthodes de réduction de modèle de type a posteriori. De plus, une stratégie de calcul de modes à partir d’un modèle de substitution est proposée. Par la suite, la décomposition propre généralisée (PGD) est utilisée afin de développer une méthode de résolution non-linéaire efficace reposant fondamentalement sur une approche de réduction de modèle de type a priori. Enfin, quelques extensions sont proposées telle que la résolution de problème faisant intervenir des études paramétriques, ou encore la prise en charge de non-linéarités supplémentaires telle que la plasticité. / Computational mechanics is an essential tool for mechanical engineering purposes. Nowadays, numerical models have to take into account complex physical phenomenons to be even more realistic and become larger and larger. As a consequence, more and more computing capacities are required in order to tackle not only non-linear problems but also large scale problems. For that purpose, both computers and numerical methods have to be developed in order to solve them efficiently. In the last decades, model reduction methods show great abilities to assign such challenges. The frictional contact problem between elastic solids is particularly well-known for its difficulty. Because its governing laws are highly non-linear (non-smooth), prohibitive computational time can occur. In this dissertation, model reduction methods (both a posteriori and a priori approaches) are deployed in order to implement efficient numerical methods to solve frictional contact problem in the finite element framework. First, small perturbations hypothesis with a quasi-static evolution are assumed. Then, reducibility of some frictional solutions is emphasized and discussed using the singular value decomposition. In addition, a scale separability phenomenon is enlightened. Then, the non-linear large time increment method (LATIN) is introduced. Secondly, an accelerated LATIN method is suggested by drawing an analogy between previous scale separability observations and the non-linear multigrid full approximation scheme (FAS). This accelerated non-linear solver relies essentially on the a posteriori model reduction approach. A precomputation strategy for modes relying on surrogate models is also suggested. Next, the proper generalized decomposition (PGD) is used to implement a non-linear solver relying fundamentally on an a priori model reduction method. Finally, some extensions are given to assign parametric studies and to take into account an additional non-linearity such as elastoplastic constitutive laws.

L’instabilité des cavités souterraines (mines, carrières, tunnels,…) peut induire les mouvements de terrains d’amplitude suffisante pour endommager les bâtiments et les infrastructures en surface. Les méthodes traditionnelles, utilisées dans les pratiques d’ingénieur pour prévoir les déformations dans les structures, sont basées sur les caractéristiques des mouvements de terrain en condition de terrain vierge sans prendre en compte l’effet de la présence des structures en surface. L’objectif de cette thèse est de prédire les déformations des ouvrages en tenant compte de l’influence de l’interaction sol-structure, d’une part ; et d’évaluer la performance d’une solution de protection (tranchée périphérique), d’autre part. Cela a été achevé par la réalisation d’études paramétriques utilisant deux approches complémentaires : une approche expérimentale à l’aide d’un modèle réduit physique 3D sous gravité normale et une modélisation numérique 3D par la méthode des éléments finis. En particulier l’effet d’un certain nombre de paramètres géométriques et mécaniques a pu être investigué dans l’étude de l’interaction sol-structure : la position de la structure par rapport à la cuvette d’affaissement, le poids de la structure et la raideur relative entre le sol et la structure. Concernant l’étude de l’efficacité de tranchées périphériques, l’effet de la position de la structure, de la position de la tranchée vis-à-vis de la structure et de la rigidité de la tranchée a été analysé. Les résultats obtenus ont abouti à une meilleure compréhension du problème d’interaction sol-structure et ont montré l’importance de cet effet qui doit être pris en compte dans l’évaluation de la vulnérabilité du bâti. Le transfert des mouvements du sol à la structure est faible (moins de 2,5%), dans le cas modélisé : structure rigide et interface glissante. Les différents résultats ont permis par ailleurs de mettre en évidence l’efficacité de la tranchée périphérique pour réduire les sollicitations affectant les structures. La tranchée doit être remplie avec un matériau très déformable et surtout placée à une distance de l’ordre d’un mètre de la structure. / The instability of underground cavities due to mining or tunneling activities can induce surface ground movements which damage overlying buildings and infrastructures. The conventional design methods, used in engineering practices to assess the structure’s deformations, are based on greendfield ground movements without taking into account the effect of the surface structure. The objective of this thesis is to predict the building deformations by taking the in-fluence of the soil-structure interaction into consideration, and to evaluate the performance of a mitigation technique (peripheral trench). This has been achieved by performing parametric studies using both the experimental approach by means of a 3D small-scale physical model under earth gravity condition and the 3D finite element numerical modeling. In particular the effect of building position, building weight, and relative stiffness of building and underlying soil has been investigated in the soil-structure interaction study. Concerning the trench effectiveness analysis, the effect of building position, trench position relatively to the building, and the trench stiffness has been investigated. The results of these investigations have led to a better understanding of the soil-structure interaction problem and have pointed out the importance of this effect which should be taken into account for building damage assessment. The transfer of ground movements to the buildings is low (less than 2.5%) for the modeled case: stiff structure and sliding contact. In addition, the results have proved the effectiveness of the peripheral trench to reduce the ground movements affecting the buildings. The trench should be filled with a very deformable material and located at a distance of around one meter from the building.

Cette thèse vise à étudier le comportement de revêtement articulé du tunnel en développant une nouvelle approche numérique à la Méthode de Réaction Hyperstatique (HRM) et la production des modèles numériques en deux dimensions et trois dimensions à l'aide de la méthode des différences finies (FDM). L'étude a été traitée d'abord sous charges statiques, puis effectuée sous charges dynamiques. Tout d'abord, une étude bibliographique a été effectuée. Une nouvelle approche numérique appliquée à la méthode HRM a ensuite été développée. En même temps, un modèle numérique en deux dimensions est programmé sur les conditions de charge statique dans le but d'évaluer l'influence des joints, en termes de la distribution et des caractéristiques des joints, sur le comportement du revêtement articulé de tunnel. Après cela, des modèles complets en trois dimensions d'un seul tunnel, de deux tunnels horizontaux et de deux tunnels empilés, dans lesquels le système des joints est simulé, ont été développés. Ces modèles en trois dimensions permettent d'étudier le comportement non seulement du revêtement du tunnel, mais encore le déplacement du sol entourant le tunnel lors de l’excavation. Un modèle numérique en trois dimensions simplifié a ensuite été réalisé afin de valider la nouvelle approche numérique appliquée à la méthode HRM.Dans la dernière partie de ce mémoire, la performance du revêtement articulé du tunnel sous chargements dynamiques est prise en compte par l’analyse quasi-statique et dynamique complète en utilisant le modèle numérique en deux dimensions (FDM). Un modèle HRM a également été développé prenant en compte des charges quasi-statiques. Les différences de comportement de tunnel sous chargements statiques et sismiques sont mises en évidence et expliquées. / This PhD thesis has the aim to study the behaviour of segmental tunnel lining by developing a new numerical approach to the Hyperstatic Reaction Method (HRM) and producing two-dimensional (2D) and three-dimensional (3D) numerical models using the finite difference method (FDM). The study first deals with under static loads, and then performs under dynamic loads. Firstly, a literature review has been conducted. A new numerical approach applied to the HRM has then been developed. At the same time, a 2D numerical model is programmed regarding static loading conditions in order to evaluate the influence of the segmental joints, in terms of both joint distribution and joint stiffness characteristics, on the tunnel lining behaviour. After that, full 3D models of a single tunnel, twin horizontal tunnels and twin tunnels stacked over each other, excavated in close proximity in which the joint pattern is simulated, have been developed. These 3D models allow one to investigate the behaviour of not only the tunnel lining but also the displacement of the ground surrounding the tunnel during the tunnel excavation. A simplified 3D numerical model has then been produced in order to validate the new numerical approach applied to the HRM. In the last part of the manuscript, the performance of the segmental tunnel lining exposed to dynamic loading is taken into consideration through quasi-static and full dynamic analyses using 2D numerical models (FDM). A new HRM model has also been developed considering quasi-static loads. The differences of the tunnel behaviour under static and seismic loadings are highlighted.

L'imagerie photoacoustique (IPA) des tissus biologiques permet de combiner les avantages des imageries optique et ultrasonore. Le principal contraste endogène pour l’IPA provient des vaisseaux sanguins en raison de la forte absorption de l'hémoglobine par rapport aux tissus environnants. De plus, les vaisseaux sanguins sont à peu près cylindriques et la concentration d'hémoglobine peut être supposée uniforme à l'intérieur des veines. Comme première contribution, nous avons développé dans cette thèse un modèle analytique de fluence optique pour plusieurs inhomogénéités cylindriques parallèles incorporées dans un milieu turbide. Les modèles analytiques n’existent que pour les cas simples. Pour traiter des situations plus complexes, comme les tissus biologiques, les méthodes numériques sont nécessaires. La deuxième contribution de cette thèse consiste à développer un solveur multigrilles de l'équation de diffusion optique et donc de proposer une méthode numérique efficace pour résoudre la fluence optique. Enfin, notre troisième contribution concerne la reconstruction de la tomographie quantitative photoacoustique (TQPA). Basée sur les modèles efficaces présentées dans les première et seconde contributions, nous avons proposé une méthode de reconstruction basée sur le modèle direct analytique pour les cas simples et une méthode d'inversion basée sur multigrille pour les cas plus réalistes. Les avantages de la méthode d'inversion basée sur multigrille sont présentés à la fois en terme de temps de calcul et de vitesse de convergence. Une validation expérimentale est présentée dans le dernier chapitre de cette thèse, prouvant la validité et l'analyse des performances des méthodes développées. / Photoacoustic imaging (PAI) of biological tissues tries to combine the advantages of optical and acoustical imaging. The main endogenous contrast for PAI is derived from blood vessels due to the strong absorption of hemoglobin compared to the background tissues. Furthermore, blood vessels are roughly cylindrical and hemoglobin concentration can be assumed to be uniform inside the vessel. Therefore, the blood vessels can be considered as “cylindrical inhomogeneities”. As a first contribution, we have developed in this thesis an analytical model of optical fluence for multiple parallel cylindrical inhomogeneities embedded in an otherwise homogeneous turbid medium. Analytical models only exist for simple cases. To deal with more complex situations like biological tissues, numerical methods are required. The second contribution of this thesis is to develop a multigrid solver of optical diffusion equation and therefore to propose an efficient numerical method to resolve the optical fluence. Finally, our third contribution is concerned with quantitative PA tomography (QPAT) reconstruction. Based on the efficient models presented in the first and second contributions, we have proposed an analytic-based reconstruction method for simple cases and a multigrid-based inversion scheme for more realistic cases. The advantages of multigrid-based inversion scheme are shown in both computation and convergence speed. An experimental validation is presented in the last chapter of this thesis, proving the validity and analyzing the performances of the developed methods.

Plusieurs machines actuellement utilisées, moteurs à combustion interne en automobile ou centrales thermiques dans l’énergie, rejettent de grandes quantités de chaleur. Généralement cette chaleur est dissipée dans l’atmosphère et son énergie perdue. Nous nous sommes donc intéressés aux moteurs à apport de chaleur externe dont l’énergie primaire est de l’énergie thermique, et plus particulièrement aux moteurs Stirling. L’une de ses principales caractéristiques est d’utiliser de la chaleur produite extérieurement comme source d’énergie. Ceci lui permet d’être multi-carburant et même d’utiliser de l’énergie thermique naturelle.L’étude menée comporte deux parties. Tout d’abord un modèle numérique zéro dimension, trois zones en temps fini a été développé. Il prend en compte les échanges thermiques aux parois et les pertes de charge, mais ne préjuge ni des dimensions moteur, ni des conditions de fonctionnement. Ceci lui permet de rester flexible pour s’adapter à l’architecture spécifique du moteur à simuler. Ensuite nous avons réalisé des mesures expérimentales sur deux moteurs de taille et puissance différentes (quelques watts et 1 kW). Ces résultats ont permis de valider le modèle. Au final nous avons obtenu un modèle numérique traduisant l’influence de paramètres dimensionnels et fonctionnels sur la puissance du moteur Stirling.Un outil d’aide à la conception de moteur Stirling a été développé en ajoutant au modèle un algorithme d’optimisation. Il permet une ébauche des caractéristiques d’un moteur Stirling. En fonction de l’application souhaitée et des contraintes s’y appliquant, il agit sur les caractéristiques choisies par l’utilisateur pour maximiser les performances. / Several machines currently used, internal combustion engines for the car industry or thermal power plants in energy, exhaust a considerable amount of heat. Generally this heat is dispersed in the atmosphere and its energy lost. So we took a special interest in external heat engines which primary energy is heat energy, and more particularly in Stirling engines. One of its main characteristics is the used of energy from heat produced externally like energy source. This allows Stirling engines to be multi-fuel and even to use natural heat energy.The study carried out is made up of two parts. First, a three zones zero dimensional finite-time thermodynamic model has been developed. It takes into account the heat transfer from the walls and the pressure drop, but does not prejudge the dimensions of the engine nor the conditions of its functioning. It is thus able to remain flexible and to adjust to the specific architecture of the engine that should be simulated. Afterwards, we have realized a series of experimental measures thanks to two engines different in size and power (a few Watt and 1 kW). These results allowed us to validate the model. In the end, we got a numerical model representing the influence of dimensional and functional parameters on the power of a Stirling engine.Eventually, a tool to assist in designing Stirling engines was developed adding an optimization algorithm to the model. It allows to sketch out a preliminary draft of the characteristics of a Stirling engine. Depending on the desired application and on the constraints exerted on the engine, the tool created will act on the characteristics of the engine chosen by the user to maximize its performances.

The purpose of this thesis is to construct a numerically solvable quantum mechanical model describing the dynamics of the indirect mechanism of the dissociative recombination process of a molecular cation by electron impact. The model also describes vibrational excitation of a molecular cation by electron impact. The solution of this model is carried out by implementing a combination of finite elements, discrete variable representation and exterior complex scaling methods. This is then specifically applied to the dissociative recombination and vibrational excitation of H$_2^+$ by an incoming electron. The results can be used to test the accuracy of approximative methods and the programs expanded to cover the cases of other diatomics. Powered by TCPDF (www.tcpdf.org)

L’objectif premier de ce travail est l’étude puis la modélisation numérique 3D du fonctionnement hydrogéologique et salin actuel d’une partie de l’aquifère superficiel de la Moyenne Camargue afin de l’utiliser, dans un second temps, pour la prévision qualitative des modifications induites par le changement climatique. La caractérisation de l’aquifère a été mené selon deux approches : une étude structurale, en utilisant des sondages à la tarière et différentes techniques géophysiques (ERT, ES et cartographie EM), et une étude hydrogéologique, intégrée par plusieurs campagnes de pompages, suivi piézométrique et des prélèvements de l’eau souterraine. Cette méthodologie a servi pour caractériser la géométrie de l’aquifère superficiel ainsi que son fonctionnement actuel et les processus qui l’affectent. Divers phénomènes environnementaux ont été identifiés, tels que : un lessivage du sol grâce à l’action de l’irrigation, un endoréisme observé dans les zones basses produit par l’effet de l’évaporation, et la reproduction des fluctuations de l’étang de Vaccarès dans la piézométrie, jusqu’au moins 30 m de la rive. Le modèle numérique construit à partir des observations du terrain reproduit les principaux processus observés. Il met en évidence un possible flux sortant vers le Vaccarès et le rôle important du marais dans l’hydrodynamique et le comportement hydrosalin du système. Les résultats du modèle face aux différents scénarios de prédiction montrent une intrusion d’eau du Vaccarès et, donc, une salinisation du système induit par la remontée du niveau marin, ainsi que la présence de l’irrigation et le marais comme facteurs essentiels dans la neutralisation de cette salinisation. / The main objective in this investigation is to construct a representative 3D numerical groundwater flow model of a local superficial aquifer in the Medium Camargue plain to simulate the actual hydrogeological and salt behavior. The 3D model will be used, in a second time, to simulate modifications of the system behavior provide by climate changes. The characterization of the aquifer was carried out by two approaches: a structural survey, using auger drilling technique and some geophysics techniques (EM mapping ERT, ES and), and a hydrogeological survey composed by several pumping tests, piezometric monitoring and groundwater samples. The methodological approach used allowed characterizing the geometry, behavior of the system and the process governing performance of the superficial aquifer. Several environmental phenomena were been identified, such as: a soil’s leaching; an endorheic phenomenon at the lower elevation areas; and the reproduction of the Vaccares pond’s fluctuations at the water table, until 30 m from shore. The numerical model, which has been constructed through field observations, reproduces principal process of the aquifer. This model highlights a possible outflow from the aquifer to the Vaccares pond and the important role of marsh in the hydrodynamic and hydrosaline behavior of the system. The results of the prediction scenarios tested with the numerical model highlights a possible intrusion from Vaccares water and, therefore, a salinization of the system produced by increase of sea level rise. The important presence of the irrigation and the marsh to neutralize a future salinization has been exposed.

Geothermal energy is the energy naturally present inside the earth crust. When a large volume of hot water and steam is trapped in subsurface porous and permeable rock structure and a convective circulating current is set up, it forms a geothermal reservoir. A geothermal system can be defined as - convective water in the upper crust of earth, which transfers heat from a heat source (in the reservoir) to a heat sink, usually the free surface. A geothermal system is made up of three main elements: a heat source, a reservoir and a fluid, which is the carrier that transfers the heat. As an alternative source of energy geothermal energy has been under attention of the researchers for quite some time. The reason behind this is the existence of several benefits like clean and renewable source of energy which has considerable environmental advantage, with no chemical pollutants or wastes are generated due to geothermal emissions, and the reliability of the power resource. Hence research has been directed in several directions like exploration of geothermal resources, modeling the characteristics of different types of geothermal reservoirs and technologies to extract energy from them. The target of these models has been the prediction of the production of the hot water and steam and thus the estimation of the electricity generating potential of a geothermal reservoir in future years. In a geothermal power plant reinjection of the heat depleted water extracted from the geothermal reservoir has been a common practice for quite some time. This started for safe wastewater disposal and later on the technology was employed to obtain higher efficiency of heat and energy extraction. In most of the cases a very small fraction of the thermal energy present in the reservoir can be recovered without the reinjection of geothermal fluid. Also maintaining the reservoir pressure is essential which gradually reduces due to continuous extraction of reservoir fluid without reinjection, especially for reservoirs with low permeabilities. Although reinjection of cold-water has several benefits, the possibility of premature breakthrough of the cold-water front, from injection well zone to production well zone, reduces the efficiency of the reservoir operation drastically. Hence for maintaining the reservoir efficiency and longer life of the reservoir, the injectionproduction well scheme is to be properly designed and injection and extraction rates are to be properly fixed. Modeling of flow and heat transport in a geothermal reservoir due to reinjection of coldwater has been attempted by several researchers analytically, numerically and experimentally. The analytical models which exist in this field deal mostly with a single injection well model injecting cold-water into a confined homogeneous porous-fractured geothermal reservoir. Often the thermal conductivity is neglected in the analytical study considering it to be negligible which is not always so, as proved in this study. Moreover heterogeneity in the reservoir is also a major factor which has not been considered in any such analytical study. In the field of numerical modeling there also exists a need of a general coupled three-dimensional thermo-hydrogeological model including all the modes of heat transport (advection and conduction), the heat loss to the confining rocks, the regional groundwater flow and the geothermal gradient. No study existing so far reported such a numerical model including those mentioned above. The present study is concerned about modeling the non-isothermal flow and heat transport in a geothermal reservoir due to reinjection of heat depleted water into a geothermal reservoir. Analytical and numerical models are developed here for the transient temperature distributions and advancement of the thermal front in a geothermal reservoir which is generated due to the cold-water injection. First homogeneous geothermal aquifers are considered and later heterogeneities of different kinds are brought into picture. Threedimensional numerical models are developed using a software code DuMux which solves flow and heat transport problems in porous media and can handle both single and multiphase flows. The results derived by the numerical models have been validated using the results from the analytical models derived in this study. Chapter 1 of the thesis gives a brief introduction about different types of geothermal reservoirs, followed by discussion on the governing differential equations, the conceptual model of a geothermal reservoir system, the efficiency of geothermal reservoirs, the modeling and simulation concepts (models construction, boundary conditions, model calibration etc.). Some problems related with geothermal reservoirs and geothermal power is also discussed. The scenario of India in the context having a huge geothermal power potential is described and different potential geothermal sites have been pointed out. In Chapter 2, the concept of reinjection of the heat depleted (cold) water into the geothermal reservoir is introduced. Starting with a brief history of the geothermal reinjection, the chapter describes the purpose and the need of reinjection of geothermal fluid giving examples of different geothermal fields over the world where reinjection has been in practice and benefitted by that. The chapter further discusses on the problems and obstacles faced by the geothermal projects resulting from the geothermal reinjection, most important of which is the thermal-breakthrough and cooling of production wells. Lastly the problem of this thesis is discussed which is to model the transient temperature distribution and the movement of the cold-water thermal front generated due to the reinjection. The need of this modeling is elaborated which represents the motivation of taking up the problem of the thesis. Chapter 3 describes an analytical model developed for the transient temperature in a porous geothermal reservoir due to injection of cold-water. The reservoir is composed of a confined aquifer, sandwiched between rocks of different thermo-geological properties. The heat transport processes considered are advection, longitudinal conduction in the geothermal aquifer, and the conductive heat transfer to the underlying and overlying rocks of different geological properties. The one-dimensional heat transfer equation has been solved using the Laplace transform with the assumption of constant density and thermal properties of both rock and fluid. Two simple solutions are derived afterwards, first neglecting the longitudinal conductive heat transport and then heat transport to confining rocks. The analytical solutions represent the transient temperature distribution in the geothermal aquifer and the confining rocks and model the movement of the cold-water thermal front in them. The results show that the heat transport to the confining rocks plays an influential role in the transient heat transport here. The influence of some parameters, e.g. the volumetric injection rate, the longitudinal thermal conductivity and the porosity of the porous media, on the transient heat transport phenomenon is judged by observing the variation of the transient temperature distribution with different values of the parameters. The effects of injection rate and thermal conductivity have been found to be high on the results. Chapter 4 represents another analytical model for transient temperature distribution in a heterogeneous geothermal reservoir underlain and overlain by impermeable rocks due to injection of cold-water. The heterogeneity of the porous medium is expressed by the spatial variation of the flow velocity and the longitudinal effective thermal conductivity of the medium. Simpler solutions are also derived afterwards first neglecting the longitudinal conduction, then the heat loss to the confining rocks depending on the situation where the contribution of them to the transient heat transport phenomenon in the porous media is negligible. Solution for a homogeneous aquifer with constant values of the rock and fluid parameters is also derived with an aim to compare the results with that of the heterogeneous one. The effect of heat loss to the confining rocks in this case is also determined and the influence of some of the parameters involved, on the transient heat transport phenomenon is assessed by observing the variation of the results with different magnitudes of those parameters. Results show that the heterogeneity plays a major role in controlling the cold-water thermal front movement. The transient temperature distribution in the geothermal reservoir depends on the type of heterogeneity. The heat loss to the confining rocks of the geothermal aquifer also has influence on the heat transport phenomenon. In Chapter 5 another analytical model is derived for a heterogeneous reservoir where the heterogeneous geothermal aquifer considered is a confined aquifer consisted of homogeneous layers of finite length and overlain and underlain by impermeable rock media. All the different layers in the aquifer and the overlying and underlying rocks are of different thermo-hydrogeological properties. Results show that the advancement of the cold-water thermal front is highly influenced by the layered heterogeneity of the aquifer. As the cold-water thermal front encounters layers of different thermo-hydrogeological properties the movement of it changes accordingly. The analytical solution derived here has been compared with a numerical model developed by the multiphysics software code COMSOL which shows excellent agreement with each other. Lastly it is shown that approximation of the properties of a geothermal aquifer by taking mean of the properties of all the layers present will lead to erroneous estimation of the temperature distribution. Chapter 6 represents a coupled three-dimensional thermo-hydrogeological numerical model for transient temperature distribution in a confined porous geothermal aquifer due to cold-water injection. This 3D numerical model is developed for solving more practical problems which eliminate the assumptions taken into account in analytical models. The numerical modeling is performed using a software code DuMux as mentioned before. Besides modeling the three-dimensional transient temperature distribution in the model domain, the chapter investigates the regional groundwater flow has been found to be a very important parameter to consider. The movement of the thermal front accelerates or decelerates depending on the direction of the flow. Influence of a few parameters involved in the study on the transient heat transport phenomenon in the geothermal reservoir domain, namely the injection rate, the permeability of the confining rocks and the thermal conductivity of the geothermal aquifer is also evaluated in this chapter. The models have been validated using analytical solutions derived in this thesis. The results are in very good agreement with each other. In Chapter 7 the main conclusions drawn from the study have been enlisted and the scope of further research is also pointed out.

We propose a hypothesis and a numerical model for the formation of branching plagioclase textures visible at both macroscopic (∼cm to ∼m) and microscopic scale within melagabbro of the Isle of Rum, Scotland, based on macroscopic, microscopic observations and relevant geological history. The plagioclase crystals are typically linked as twins and form meshes of planar stellate structures (m-scale) with a large range in geometrical organization from patchy to radiating. Evidence of macroscopic crystal aggregation and alignment is attributed to interfacial free energy minimization at the microscopic scale during growth. Accordingly, a binary immiscible Lattice Boltzmann model was developed to simulate diffusion of simplified plagioclase in the melt phase. Isothermal phase transitions modelled via first order chemical reactions are subsequently coupled with stochastic dynamics at the crystal growth front to simulate energy minimization processes including twinning during crystallization in an igneous environment. The solid phase and the liquid phase are coupled with a temporal flexibility that sets the overall ratio between the rate of diffusion and chemical enrichment in the liquid state and the rate of crystallization. The parameter space of the model is explored extensively, followed by a reasonable transcription of physical parameters and an estimation of other parameters to construct realistic simulation scenarios yielding synthetic plagioclase stellates. The results are presented, analyzed and discussed. They appear to be in reasonable qualitative agreement with observations, and several aspects of the natural stellates such as the stellate spacing and long continuous stretches of plagioclase with epitaxial junctions seem to be in reasonable quantitative agreement with observations.