Cette thèse porte sur la simulation numérique de modèles couplés pour l'écoulement et le transport dans les milieux poreux. Nous présentons une nouvelle méthode de couplage entre les réactions chimiques et le transport en utilisant une méthode de Newton-Krylov, et nous étudions également un modèle d'écoulement en milieu fracturé qui traite l'intersection des fractures par une méthode de décomposition de domaine. <br /> Ce travail est divisé en trois parties : la première partie contient une analyse de différents schémas numériques pour la discrétisation des problèmes d'advection-diffusion, notamment par une technique de séparation d'opérateurs, ainsi que leur mise en oeuvre informatique, dans un code industriel.<br /> La deuxième partie, qui est la contribution majeure de cette thèse, est consacrée à la modélisation et à l'implémentation d'une méthode de couplage globale pour le transport réactif. Le système couplé transport-chimie est décrit, après discrétisation en temps, par un système d'équations non linéaires. La taille du système sous-jacent, à savoir le nombre de points de grille multiplié par le nombre d'espèces chimiques, interdit la résolution du système linéaire par une méthode directe. Pour remédier à cette difficulté, nous utilisons une méthode de Newton-Krylov qui évite de former et de factoriser la matrice Jacobienne. <br /> Dans la dernière partie, nous présentons un modèle d'écoulement dans un milieu fracturé tridimensionnel, basé sur une méthode de décomposition de domaine, et qui traite l'intersection des fractures. Nous démontrons l'existence et l'unicité de la solution, et nous validons le modèle par des tests numériques.

Ce mémoire d'Habilitation à Diriger des Recherches regroupe certains travaux réalisés dans le cadre de deux applications à l'IFP : TACITE (écoulements polyphasiques dans les conduites pétrolières) et IFP-C3D (écoulements réactifs dans les moteurs à combustion). Bien que ces deux applications présentent des caractéristiques très différentes, les techniques mathématiques mises en oeuvres sont semblables, voire complémentaires.<br /><br />Dans la première partie, on montre dans quelle mesure les méthodes dites de "relaxation" permettent de rendre plus robustes les simulations numériques de TACITE. La relaxation garantit en effet la positivité de certaines de certaines variables physiquement importantes, alors que le système de départ n'est pas toujours hyperbolique en raison de la complexité des lois de fermeture utilisées. On montre aussi dans quelle mesure les méthodes dites de "multi-résolution" et de "pas de temps locaux" permettent de rendre plus rapides ces simulations, le tout dans un contexte d'intégration temporelle mixte, c'est-à-dire implicite par rapport aux ondes acoustiques rapides et explicite par rapport aux ondes cinématiques lentes.<br /><br />Dans la deuxième partie, on examine certains modèles alternatifs à celui de la première partie. L'intérêt de ces modèles de rechange est d'être plus opérationnels sur certaines configurations spécifiques, au sens où ils facilitent l'analyse mathématique, en tant que système dynamique, d'un phénomène crucial appelé "severe-slugging". Ils suggèrent également des lois de commande judicieuses pour éliminer le severe-slugging via une boucle rétroactive dont l'effacité est prouvée sur le papier et sur maquette expérimentale.<br /><br />Dans la troisième partie, on propose un schéma d'advection multi-dimenstionnelle pour la phase convective de IFP-C3D. La particularité de ce schéma, conçu à partir des schémas de type Iserles-Roe en 1-D, est une très grande précision associée à un principe de monotonie. Compact en espace et à plusieurs niveaux en temps, il permet de bien traiter le transport des variables situées aux noeuds du maillage, en combinaison avec une procédure de réparation de la masse inspirée de Shashkov.

Ce mémoire présente différentes contributions de la micromécanique à l'étude de la formulation des lois de transport et du couplage poromécanique dans les milieux poreux. On y aborde, en particulier, la problématique du gonflement d'origine physico-chimique susceptible de se développer dans les géomatériaux. La première partie est consacrée à la problématique de la modélisation micromécanique du transport. On s'intéresse, en premier lieu, au transport diffusif macroscopique à partir duquel on propose des estimations de la tortuosité en exploitant l'analogie avec les problèmes mécaniques usuels. On s'attache ensuite à estimer l'influence d'une microfissuration sur les propriétés du transport macroscopique. Finalement, on étudie la question du transport de la vapeur d'eau dans l'air pour lequel on montre que la prise en compte du gradient de pression du mélange gazeux dans l'expression du flux de masse macroscopique est essentielle. Après avoir exposé dans la deuxième partie la capacité de l'approche micromécanique à établir les équations d'état de la poroélasticité en intégrant le comportement des constituants à l'échelle microscopique, on s'intéresse dans les deux dernières parties de ce mémoire au couplage fluide/solide dans des situations où une interaction physico-chimique se superpose à l'interaction mécanique traitée classiquement. On s'intéresse tout d'abord à la modélisation micromécanique du gonflement osmotique de géomatériaux composés au moins en partie d'argile. Elle aboutit à la décomposition de l'élasticité macroscopique en deux contributions respectivement de nature mécanique et physico-chimique. Une validation expérimentale est proposée dans le cadre de l'étude du gonflement osmotique d'argilites en phase transitoire. Enfin, le phénomène de l'alcali-réaction et ses conséquences sur le comportement macroscopique d'un béton est abordé dans le cadre du gonflement libre. L'accent a été mis sur le rôle de la fraction volumique et de la morphologie du domaine envahi par le gel.

L'objet principal de cette thèse est d'étudier divers aspects de l'évolution d'un champ scalaire ou vectoriel, transporté par un champ de vitesse dont la statistique est donnée indépendamment du champ advecté. Ce faisant, on est amené également à étudier les courbes intégrales du champ de vitesse, appelées trajectoires Lagrangiennes. Après une introduction synthétique, plusieurs modèles et problèmes sont abordés. Notre modèle principal - baptisé après R. H. Kraichnan - suppose des champs de vitesse gaussiens delta-corrélés en temps. Sont étudiés les cas où la structure spatiale du champ de vitesse est soit lisse soit brownien fractionnaire (multidimensionnel). Un modèle où le champ de vitesse est corrélé en temps est également abordé. Parmi les problèmes étudiés sont les secteurs anisotropes de la quantité advectée, l'apparition d'intermittence spatiale, ou encore différents passages à la limite dans la statistique du champ de vitesse.

The classical Fickian model for solute transport in porous media cannot correctly predict the spreading (the dispersion) of contaminant plumes in a heterogeneous subsoil unless its structure is completely characterized. Although the required precision is outside the reach of current field characterization methods, the classical Fickian model remains the most widely used model among practitioners. Two approaches can be adopted to solve the effect of physical heterogeneity on transport. First, upscaling methods allow one to compute “apparent” scale-dependent parameters to be used in the classical Fickian model. In the second approach, upscaled (non-Fickian) transport equations with scale-independent parameters are used. This research aims at comparing upscaling methods for Fickian transport parameters with non-Fickian upscaled transport equations, and evaluate their capabilities to predict solute transport in heterogeneous media. The models were tested using simplified numerical examples (perfectly stratified aquifers and bidimensional heterogeneous media). Hypothetical lognormal permeability fields were investigated, for different values of variance, correlation length and anisotropy ratio. Examples exhibiting discrete and multimodal permeability distributions were also investigated using both numerical examples and a physical laboratory experiment. It was found that non-Fickian transport equations involving fractional derivatives have higher upscaling capabilities regarding the prediction of contaminant plume migration and spreading, although their key parameters can only be inferred from inverse modelling of test data.

This thesis presents an axisymmetric numerical model to simulate interfacial flows near a sharp corner, where contact line pinning occurs. The method has been used to analyze drop imbibition into a capillary. To evaluate the performance of the numerical method, for a liquid drop initially placed partially within a capillary, a thermodynamic model has also been developed, to predict equilibrium states. The first part of this thesis presents an axisymmetric VoF algorithm to simulate interfacial flows near a sharp corner. (1) A new method to exactly calculate the normals and curvatures of any circle with a radius as small as the grid size is presented. This method is a hybrid least squares height function technique which fits a discretized osculating circle to a curve, from which interface normals and curvature can be evaluated. (2) A novel technique for applying the contact angle boundary condition has been devised, based on the definition of an osculating circle near a solid phase. (3) A new flux volume construction technique is presented, which can be applied to any split advection scheme. Unlike the traditional approach where the flux volumes are assumed rectangular, the new flux volumes can be either trapezoidal or triangular. The new technique improves the accuracy and consistency of the advection scheme. (4) Explicit PLIC reconstruction expressions for axisymmetric coordinates have been derived. (5) Finally, a numerical treatment of VoF for contact line motion near a sharp corner is presented, base on the idea of contact line pinning and an edge contact angle. The second part of the thesis is on the imbibition of a drop into an open capillary. A thermodynamic analysis based on minimization of an interfacial surface energy function is presented to predict equilibrium configurations of drops. Based on the drop size compared to the hole size, the equilibrium contact angle, and the geometry of the capillary, the drop can be totally imbibed by the capillary, or may not wet the capillary at all. The thesis concludes with application of the numerical scheme to the same problem, to examine the dynamics of wetting or dewetting of a capillary. All of the simulations yield results that correspond to the equilibrium states predicted by the thermodynamic analysis, but offer additional insight on contact line motion and interface deformation near the capillary edge.

This thesis presents an axisymmetric numerical model to simulate interfacial flows near a sharp corner, where contact line pinning occurs. The method has been used to analyze drop imbibition into a capillary. To evaluate the performance of the numerical method, for a liquid drop initially placed partially within a capillary, a thermodynamic model has also been developed, to predict equilibrium states. The first part of this thesis presents an axisymmetric VoF algorithm to simulate interfacial flows near a sharp corner. (1) A new method to exactly calculate the normals and curvatures of any circle with a radius as small as the grid size is presented. This method is a hybrid least squares height function technique which fits a discretized osculating circle to a curve, from which interface normals and curvature can be evaluated. (2) A novel technique for applying the contact angle boundary condition has been devised, based on the definition of an osculating circle near a solid phase. (3) A new flux volume construction technique is presented, which can be applied to any split advection scheme. Unlike the traditional approach where the flux volumes are assumed rectangular, the new flux volumes can be either trapezoidal or triangular. The new technique improves the accuracy and consistency of the advection scheme. (4) Explicit PLIC reconstruction expressions for axisymmetric coordinates have been derived. (5) Finally, a numerical treatment of VoF for contact line motion near a sharp corner is presented, base on the idea of contact line pinning and an edge contact angle. The second part of the thesis is on the imbibition of a drop into an open capillary. A thermodynamic analysis based on minimization of an interfacial surface energy function is presented to predict equilibrium configurations of drops. Based on the drop size compared to the hole size, the equilibrium contact angle, and the geometry of the capillary, the drop can be totally imbibed by the capillary, or may not wet the capillary at all. The thesis concludes with application of the numerical scheme to the same problem, to examine the dynamics of wetting or dewetting of a capillary. All of the simulations yield results that correspond to the equilibrium states predicted by the thermodynamic analysis, but offer additional insight on contact line motion and interface deformation near the capillary edge.

This dissertation discusses the predictability of the atmosphere-ocean climate system on interannual and decadal timescales. We investigate the extent to which the atmospheric internal variability (weather noise) can cause climate prediction to lose skill; and we also look for the oceanic processes that contribute to the climate predictability via interaction with the atmosphere. First, we develop a framework for assessing the predictability of a linear stochastic system. Based on the information of deterministic dynamics and noise forcing, various predictability measures are defined and new predictability-analysis tools are introduced. For the sake of computational efficiency, we also discuss the formulation of a low-order model within the context of four reduction methods: modal, EOF, most predictable pattern, and balanced truncation. Subsequently, predictabilities of two specific physical systems are investigated within such framework. The first is a mixed layer model of SST with focus on the effect of oceanic advection.Analytical solution of a one-dimensional model shows that even though advection can give rise to a pair of low-frequency normal modes, no enhancement in the predictability is found in terms of domain averaged error variance. However, a Predictable Component Analysis (PrCA) shows that advection can play a role in redistributing the predictable variance. This analytical result is further tested in a more realistic two-dimensional North Atlantic model with observed mean currents. The second is a linear coupled model of tropical Atlantic atmosphere-ocean system. Eigen-analysis reveals that the system has two types of coupled modes: a decadal meridional mode and an interannual equatorial mode. The meridional mode, which manifests itself as a dipole pattern in SST, is controlled by thermodynamic feedback between wind, latent heat flux, and SST, and modified by ocean heat transport. The equatorial mode, which manifests itself as an SST anomaly in the eastern equatorial basin, is dominated by dynamic feedback between wind, thermocline, upwelling, and SST. The relative strength of thermodynamic vs dynamic feedbacks determines the behavior of the coupled system, and enables the tropical Atlantic variability to be more predictable than the passive-ocean scenario.

Our understanding of tephra depositional processes is significantly improved by high-resolution ground-penetrating radar (GPR) data collected at Cerro Negro volcano, Nicaragua. The data reveal three depositional regimes: (1) a near-vent region on the cone itself, where 10 GPR radargrams collected on the western flank show quantifiable differences between facies formed from low energy normal Strombolian and higher energy violent Strombolian processes, indicating imaging of scoria cone deposits may be useful in distinguishing eruptive style in older cones where the proximal to distal tephra blanket has eroded away; (2) a proximal zone in which horizons identified in crosswind profiles collected at distances of 700 and 1,000 m from the vent exhibit Gaussian distributions with a high degree of statistical confidence, with tephra thickness decreasing exponentially downwind from the cone base (350 m) to ~ 1,200 m from the vent, and where particles fall from a height of less than ~2 km; and (3) a medial zone, in which particles fall from ~4 to 7 km and the deposit is thicker than expected based on thinning trends observed in the proximal zone of the deposit, indicating a transition from sedimentation dominated by fallout from plume margins to that dominated by fallout from the buoyant eruption cloud. Horizons identified in a crosswind profile at 1600 m from vent exhibit Gaussian distributions, again with high degrees of statistical confidence. True diffusion coefficients are calculated from Gaussian fits of crosswind profiles and do not show any statistical variation between zones (2) and (3). Data display thinning trends that agree with the morphology predicted by the advection-diffusion equation to a high degree of statistical confidence, validating the use of this class of models in tephra forecasting. One such model, the Tephra2 model, is reformulated for student use. A strategy is presented for utilizing this research-caliber model to introduce university undergraduates to key concepts in model literacy, encouraging students to develop a deeper understanding of the applicability and limitations of hazard models generally. For this purpose, the Tephra2 numerical model is implemented on the VHub.org website, a venture in cyberinfrastructure that brings together volcanological models and educational materials, and provides students with the ability to explore and execute sophisticated numerical models like Tephra2.

January of 2010 brought record-breaking cold temperatures to Florida. Such freeze events can upset vulnerable populations of marine life and other species that rely on stable water temperatures. Sea turtles are one group of species that are particularly susceptible to abrupt drops in water temperature. When water temperatures drop below 10°C, a mass hypothermic stunning, or cold-stunning, event for sea turtles can be expected, with many debilitated turtles washing onshore with a very limited time window to be rehabilitated (Foley et al. 2007). The species of sea turtle that appears to cold-stun with the most frequency is the green turtle, especially juveniles. The green turtle represented the vast majority of marine turtles that were rescued during the 2010 cold-stun event. Therefore, accurate weather pattern recognition of marine cold snaps, or freezes, can alert sea turtle rescue groups and rehabilitation facilities in advance of any event, improving their readiness and response times, and ultimately preventing population declines. The proposed research fills this need by providing a qualitative analysis of select years for comparable atmospheric processes that could result in moderate to severe hypothermic stunning events. The 2010 event, along with other significant events, were examined using in situ air temperature, water temperature and wind data near two locations in Florida where hypothermic stunning events occurred: St. Joseph Bay and Mosquito Lagoon. These atmospheric parameters were represented graphically, depicting how each variable contributed to shaping an event. Cold stunning events were found to be primarily driven by frigid air temperatures and a subsequent decrease in water temperatures. Differences between the two event classifications, moderate and severe, are contingent upon the duration of the cold spell, not necessarily how quickly the water temperature dropped below the 10°C threshold value. Results suggest that repeated, quick exposure to cold air temperatures may influence the severity of a hypothermic stunning event. This research could be utilized in the formation of a forecasting model or strategy to efficiently alert the Florida Sea Turtle Stranding and Salvage Network (STSSN) to a potential sharp drop in water temperatures and, consequently, many debilitated sea turtles.