En acoustique sous marine, les ´etudes sur les zones en eau peu profondes sontredevenues strat´egiques. Cette th`ese porte sur l’ ´etude de la s´eparation et la d´etectionde trajet dans le cadre des eaux peu profondes tomographie acoustique oc´eanique. Dansune premi´ere ´etape de notre travail, nous avons donn´e un bref aperc¸u sur les techniquesexistantes de traitement acoustique sous-marine afin de trouver la difficult´e toujoursconfront´es `a ce type de m´ethodes. Par cons´equent, nous avons fait une conclusion qu’ilest encore n´e cessaire d’am´eliorer la r´esolution de s´eparation afin de fournir des informationsplus utiles pour l’ ´etape inverse de la tomographie acoustique oc´eanique.Ainsi, une enquˆete sur les mthodes haute r´esolution est effecut´ee. Enfin, nous avonspropos´e une m´ethode `a haute r´esolution appel´ee lissage MUSICAL (MUSIC Active largeband), qui combine le lissage de fr´equence spatiale avec l’algorithme MUSICAL, pourune s´eparation efficace de trajet coh´erentes ou totalement corr´el´es. Cependant, cettem´ethode est bas´ee sur la connaissance a priori du nombre de trajet. Ainsi, nous introduisonsun test (exponential fitting test) (EFT) `a l’aide de courte longueur des ´echantillonspour d´eterminer le nombre de trajets. Ces deux m´ethodes sont appliqu´ees `a la fois desdonn´ees synth´etiques et les donn´ees r´eelles acquises dans un r´eservoir `a petite ´echelle.Leurs performances sont compar´ees avec les m´ethodes conventionnelles pertinentes. / As the studies on shallow-water acoustics became an active field again, this dissertationfocuses on studying the separation and detection of raypaths in the context of shallowwaterocean acoustic tomography. As a first step of our work, we have given a briefreview on the existing array processing techniques in underwater acoustics so as to findthe difficulties still faced by these methods. Consequently, we made a conclusion thatit is still necessary to improve the separation resolution in order to provide more usefulinformation for the inverse step of ocean acoustic tomography. Thus, a survey on highresolutionmethod is provided to discover the technique which can be extended to separatethe raypaths in our application background. Finally, we proposed a high-resolutionmethod called smoothing-MUSICAL (MUSIC Actif Large band), which combines thespatial-frequency smoothing with MUSICAL algorithm, for efficient separation of coherentor fully correlated raypaths. However, this method is based on the prior knowledgeof the number of raypaths. Thus, we introduce an exponential fitting test (EFT)using short-length samples to determine the number of raypaths. These two methodsare both applied to synthetic data and real data acquired in a tank at small scale. Theirperformances are compared with the relevant conventional methods respectively.

Lors d’une opération de forage, un certain nombre d’événements imprévus par rapport à l’écoulement du fluide de forage dans le puits, peuvent se produire assez rapidement. Des exemples de tels événements sont les afflux de pétrole ("kick") ainsi que les pertes de boue dans la formation. Un "kick" qui augmente en intensité peut entraîner, par ce que l’on nomme, un "blowout" (par exemple l’incident Deepwater Horizon en 2010). Les pertes et les gains sont habituellement détectés en contrôlant l’équilibre de la boue de forage dans le puits, en particulier en contrôlant le débit sortant du puits et en le comparant au débit entrant induit par les pompes. La plupart des méthodes de surveillance, de l’écoulement du puits en cours de forage, est d’utiliser un simple "paddle" (capteur qui mesure la hauteur du fluide de forage avec l’inclinaison d’une pagaie) dans la ligne d’écoulement de retour, ou d’utiliser un débitmètre de Coriolis (débitmètre connu pour sa précision, mais coûteux et nécessite une installation complexe en ajoutant un "by-pass"). Il y a un besoin évident d’un nouveau débitmètre précis, mais facile à installer et peu coûteux. Le canal Venturi a été utilisé comme débitmètre pendant des années dans l’industrie des eaux. Il apparaît comme une solution peu chère mais précise pour mesurer des débits importants. Beaucoup de personnes ont travaillé sur cette solution pour améliorer sa précision et élargir son champ d’application. Ils ont développé des modèles, sur la base d’un processus d’étalonnage, permettant de relier la hauteur en amont au débit. Cela signifie que les modèles actuels, comme ISO NORM 4359 [1], peuvent être uniquement utilisés pour l’écoulement d’eau et pour une géométrie bien spécifique. Comme nous le savons, les boues ont des comportement non- Newtonien, et donc ces modèles établis ne peuvent pas être utilisés avec ce type de fluides. Pour notre application, la forme trapézoïdale apparaît comme un bon compromis entre la précision et la portée des mesures de débit. Ainsi, nous avons développé un modèle capable de calculer le débit en prenant en compte les propriétés du fluide ainsi que les paramètres géométriques du canal. Ce modèle a été simplifié sous forme 1D en utilisant la théorie des eaux peux profondes, et a été complété par un modèle de friction tenant en compte de la variation des propriétés des fluides et de la géométrie du canal. Ce modèle a été validé par une série d’expériences avec les deux types de fluides: Newtonien et non-Newtonien, où nous avons mesuré le débit et la hauteur de l’écoulement à différents endroits le long du canal Venturi. Nous avons également réalisé des simulations 3D, en simulant des écoulements Newtoniens et non- Newtonien le long du canal. Pour généraliser cette étude, cette démarche a été étendue à une autre forme de Venturi plus adapté à un certain design de plate-forme pétrolière. Les corrélations et les modèles développés et validés expérimentalement au cours de cette étude peuvent être utilisés pour étendre l’utilisation des canaux Venturi à tous les fluides Newtonien mais aussi non-Newtonien. Il est maintenant l’occasion pour les industries de proposer une solution, peu chère mais précise pour mesurer les débits dans des canaux ouverts et pour tous types de fluides. / During a drilling operation, a certain number of unexpected events, related to the flow of drilling fluid in the well, may happen rather quickly. Examples of such events are formation fluid influx (kick) and mud loss to the formation. An uncontrolled kick that increases in intensity may result in what is known as a blowout (e.g. the Deepwater Horizon incident in 2010). Influxes and kicks are traditionally detected by monitoring the drilling mud balance in the well, in particular, by monitoring the flow out the well and comparing it to the incoming flow induced by the pumps. Most methods of monitoring the flow out of the well while drilling consists in using a simple paddle (sensor that measures the height of drilling fluid with the inclination of a paddle) in the return flow line, or in using a Coriolis flow meter (flow meter known for its accuracy but expensive and requires a complex installation by adding a bypass). There is a clear need of a new accurate flow meter, but easy to install and inexpensive. The Venturi flume has been used as flow meter for years in water industry. It appears as a cheap but accurate solution to measure large flow rates. Many people have worked on this solution to improve its accuracy and to expand its scope. They have developed models, based on a calibration process, to relate the upstream height to the flow rate. This means that current models, as ISO NORM 4359 [1], can be used only for water flow and specific geometry. As known, muds have non-Newtonian behavior and water models cannot be used with this kind of fluids. For our application, trapezoidal shape appears as a good compromise between accuracy and range of flow rate measurements. Thus, we built a model able to compute the flow rate with taking into account fluid properties and geometrical parameters. This model is simplified in 1D form by using the Shallow Water theory, and completed by a friction model taking into account the variation of fluid properties and geometry along the open channel. It have been validated by series of experiments with both Newtonian and non-Newtonian fluids, where we measured the flow rate and heights of the flow at different locations along the trapezoidal Venturi flume. It have been also completed by 3D CFD which has been simulated both Newtonian and non-Newtonian flows along the flume. To generalized this study, the work was extended to another shape of Venturi more suited to some rig design. The correlations and models developed and experimentally validated during this research can be used to extend the use of Venturi flume flow meters for any fluids : Newtonian and non- Newtonian. It is an opportunity for industries to propose a cheap but accurate solution to measure flow rates in open channels with any kind of fluids.

Submitted by Eduarda Figueiredo (eduarda.ffigueiredo@ufpe.br) on 2015-03-12T15:30:43Z No. of bitstreams: 2 Leite_FS-Tese2012-DOCEAN-tt.pdf: 7355705 bytes, checksum: cdd11be57564224083c3a2b8946fb3de (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) / Made available in DSpace on 2015-03-12T15:30:44Z (GMT). No. of bitstreams: 2 Leite_FS-Tese2012-DOCEAN-tt.pdf: 7355705 bytes, checksum: cdd11be57564224083c3a2b8946fb3de (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Previous issue date: 2012-09-26 / FACEPE / A exploração de óleo e gás vem apresentando um rápido crescimento em regiões de baixa latitude, mesmo assim pouquíssimos experimentos e modelagens envolvendo vazamento de gás têm sido publicados pela comunidade científica. Este estudo foi desenvolvido de modo a aumentar o conhecimento a respeito do comportamento da pluma de gás durante um vazamento acidental em águas rasas. Os métodos usados e os resultados obtidos são apresentados neste estudo, assim como um modelo para simular o transporte e a dispersão de uma pluma de gás liberada em águas rasas. Primeiramente, experimentos de campo foram realizados através da simulação de um vazamento de gás natural a aproximadamente 30 m de profundidade na costa nordeste do Brasil. Quatro cenários distintos, com variadas condições de forçantes geofísicas, foram associados a diferentes fluxos de gás (de 3000 a 9000 L.h-1) e períodos sazonais (verão e inverno). Num segundo estágio, a análise de dispersão da pluma de gás foi realizada com os dados obtidos in situ. O modelo usou um volume de controle lagrangiano para discretização e simulou a evolução da pluma de gás associando a termodinâmica e o impacto desta na hidrodinâmica da pluma de gás. De acordo com os dados coletados, o transporte predominante da corrente ocorreu para sulsudoeste (nordeste) durante o verão (inverno). A diferença no diâmetro da pluma ocorreu principalmente na camada mais próxima à superfície. A pluma de gás deslocou-se para sul-sudoeste no verão e para nordestenorte durante o inverno. Os fluxos de gás liberados no assoalho oceânico pareceram não afetar a hidrodinâmica local. O movimento da pluma foi sempre influenciado pelas forçantes de maré e meteorológica, nesta ordem. Os resultados de modelagem indicaram que, à medida que a pluma sobe na coluna de água, a mesma é deslocada horizontalmente na direção da corrente predominante. A situação extrema estabeleceu um raio crítico (máximo deslocamento horizontal) da fonte de gás de 35,2 m. A comparação entre os dados medidos e os calculados mostrou que o modelo representou satisfatoriamente as principais características da liberação de gás, tais como o deslocamento, o diâmetro e o tempo de ascensão da pluma. Apesar das plumas apresentarem a largura média da mesma ordem de magnitude entre as medições e os cálculos, melhorias podem aumentar o desempenho do modelo durante o desenvolvimento inicial das plumas. Dados importantes e únicos foram coletados durante os vazamentos de gás, os quais contribuíram para a caracterização do comportamento de diferentes fluxos em diferentes períodos. Os experimentos forneceram uma base de dados para um modelo computacional que foi capaz de reproduzir o transporte e a dispersão de uma pluma de gás no ambiente marinho. O modelo foi capaz de prever o transporte e destino do gás liberado no ambiente. O mesmo pode, portanto, ser usado como uma ferramenta para planos de contingência de vazamentos acidentais de gás no oceano. / Underwater oil and gas exploration has been growing fast in low latitude regions, even though very few experimental data acquisition and modeling involving gas release in tropical and shallow waters have been published by the scientific community. This study was developed to increase the knowledge concerning the gas behavior during a subsurface blowout in shallow waters. The methods used and the results obtained from this study are presented, as well as a model to simulate the transport and dispersion of a subsurface gas plume released from shallow waters. At first, field experiments were carried out by simulating a subsurface blowout with natural gas at approximately 30 m depth in the Northeast Brazilian coast. Four distinct scenarios with varied conditions of geophysical forcing were associated with different fluxes (from 3000 to 9000 L.h-1) and seasonal periods (summer and winter). As a second stage, the analysis of the gas plume dispersion was accomplished with the data obtained from the above campaigns. The model used a Lagrangian control volume for discretization and simulated the gas plume evolution, associating thermodynamics and the impact of the thermodynamics on the hydrodynamics of the gas plume. The predominant transport occurred toward the south-southwest (northeast) during the summer (winter) period. The difference in the plume width occurred mainly in the upper surface layer. The gas plume displaced toward the south-southwest (northeast-north) during the summer (winter) period. The gas flow releases seemed not to affect the local hydrodynamics. The plume movement was always influenced by the tidal and meteorological forcings, in that order. The simulation results indicated that, as the gas plume rose in the water column, the same plume was horizontally displaced toward current predominant direction. The extreme situation provided a critical radius (maximum horizontal displacement) from the gas release source of 35.2 m. The comparison between the measured and the calculated data showed that the model satisfactorily represented the main features of the gas release, such as the displacement, diameter and ascending time of the plume. Although the mean plume widths have the same order of magnitude between the measurements and the calculations, improvements may enhance the model’s performance during the earlier plume development. Important and unique data were collected during these subsurface releases, which contributed to the characterization of the behavior of different blowouts in different seasons. The experiments provided a baseline for a computational model capable of reproducing gas plume transport and dispersion in the marine environment. The model was able to predict the gas release transport and fate in the environment. Thus it can be used as a tool for contingency planning of an accidental underwater gas release.

Os métodos geofísicos constituem um conjunto de várias ferramentas de investigação, com características específicas e com aplicação, em especial, no estudo de áreas submersas, tendo em vista a inacessibilidade as estes ambientes pelos métodos convencionais. Entretanto, sua aplicação nem sempre traz os resultados esperados e assim, o objetivo principal deste estudo é discutir e avaliar a aplicabilidade dos métodos geofísicos, com ênfase nos métodos sísmicos, em estudos de áreas submersas rasas: plataforma continental interna, áreas costeiras, rios, lagos e reservatórios. O estabelecimento de critérios que auxiliem a escolha do método geofísico mais adequado para a melhor solução ao problema geológico ou geotécnico colocado, visa, entre outros aspectos, contribuir para a mitigação dos problemas, principalmente ambientais, causados pela atividade antrópica concentrada nestes ambientes e ampliar o conhecimento geológico básico, propiciando deste modo intervenções sustentadas nestes complexos ambientes. / Geophysical methods consist of a series of investigation tools with specific features that are critical to the study of water-covered areas, since these environments cannot be reached with conventional methods. However, sometimes these applications fail to provide the expected results. The objective of this study is to discuss and assess the applicability of geophysical methods by focusing on seismic methods in studies conducted in shallow water-covered areas: inner continental shelves, coastal areas, rivers, lakes and reservoirs. Criteria to help to select the most appropriate geophysical method to solve geological or geotechnical issues must be established to minimize problems, particularly environmental problems caused by concentrated anthropic activity, and to expand basic geological knowledge to allow for sustained interventions in these complex environments. This study is based on extensive bibliographic research and on several projects developed by IPT (Institute for Technological Research of São Paulo State) and by IOUSP (Oceanography Institute of the University of São Paulo), in addition to partnerships with private companies and other institutes in Brazil that address this field of knowledge. The focus on shallow waters was driven by the lack of systematic data and the demand for geological and geotechnical knowledge in these areas, due to the concentration, in these sectors, of the main economic activities of our current society: projects to build or reassess port dimensions, installation of moles, ducts, marinas, bridges, tunnels, fishing activities, beach regeneration, mineral prospecting, waterways, dredging, installation of reservoirs for water storage or flood containment, and reservoir silting. In any of these topics, basic geological knowledge of the bottom and subbottom of water-covered areas is essential to ensure the venture’s success. Considering this, geophysical methods, particularly seismic ones, are investigation tools that effectively contribute to generate new information, and are the only set of tools available to quickly and objectively provide enough data to improve the geological understanding of the area under investigation. The result of this study includes a discussion on the feasibility of the methodologies recommended, based on an extensive survey conducted in 2005/2006 on the availability of geophysical equipment in research institutes and private companies in Brazil.

Originally developed in the 1970s for the optimal control of systems governed by partial differential equations, the adjoint method has found several successful applications, e.g. in meteorology with large-scale 3D or 4D atmospheric data assimilation schemes, for carbon cycle data assimilation in biogeochemistry and climate research, or in oceanographic modelling with efficient adjoint codes of ocean general circulation models.<p><p>Despite the variety of applications in these research fields, adjoint methods have only very recently drawn attention from the ocean acoustics community. In ocean acoustic tomography and geoacoustic inversion, where the inverse problem is to recover unknown acoustic properties of the water column and the seabed from acoustic transmission data, the solution approaches are typically based on travel time inversion or standard matched-field processing in combination with metaheuristics for global optimization. <p><p>In order to complement the adjoint schemes already in use in meteorology and oceanography with an ocean acoustic component, this thesis is concerned with the development of the adjoint of a full-field acoustic propagation model for shallow water environments. <p><p>In view of the increasing importance of global ocean observing systems such as the European Seas Observatory Network, the Arctic Ocean Observing System and Maritime Rapid Environmental Assessment (MREA) systems for defence and security applications, the adjoint of an ocean acoustic propagation model can become an integral part of a coupled oceanographic and acoustic data assimilation scheme in the future. <p><p>Given the acoustic pressure field measured on a vertical hydrophone array and a modelled replica field that is calculated for a specific parametrization of the environment, the developed adjoint model backpropagates the mismatch (residual) between the measured and predicted field from the receiver array towards the source.<p><p>The backpropagated error field is then converted into an estimate of the exact gradient of the objective function with respect to any of the relevant physical parameters of the environment including the sound speed structure in the water column and densities, compressional/shear sound speeds, and attenuations of the sediment layers and the sub-bottom halfspace. The resulting environmental gradients can be used in combination with gradient descent methods such as conjugate gradient, or Newton-type optimization methods tolocate the error surface minimum via a series of iterations. This is particularly attractive for monitoring slowly varying environments, where the gradient information can be used to track the environmental parameters continuously over time and space.<p><p>In shallow water environments, where an accurate treatment of the acoustic interaction with the bottom is of outmost importance for a correct prediction of the sound field, and field data are often recorded on non-fully populated arrays, there is an inherent need for observation over a broad range of frequencies. For this purpose, the adjoint-based approach is generalized for a joint optimization across multiple frequencies and special attention is devoted to regularization methods that incorporate additional information about the desired solution in order to stabilize the optimization process.<p><p>Starting with an analytical formulation of the multiple-frequency adjoint approach for parabolic-type approximations, the adjoint method is progressively tailored in the course of the thesis towards a realistic wide-angle parabolic equation propagation model and the treatment of fully nonlocal impedance boundary conditions. A semi-automatic adjoint generation via modular graph approach enables the direct inversion of both the geoacoustic parameters embedded in the discrete nonlocal boundary condition and the acoustic properties of the water column. Several case studies based on environmental data obtained in Mediterranean shallow waters are used in the thesis to assess the capabilities of adjoint-based acoustic inversion for different experimental configurations, particularly taking into account sparse array geometries and partial depth coverage of the water column. The numerical implementation of the approach is found to be robust, provided that the initial guesses are not too far from the desired solution, and accurate, and converges in a small number of iterations. During the multi-frequency optimization process, the evolution of the control parameters displays a parameter hierarchy which clearly relates to the relative sensitivity of the acoustic pressure field to the physical parameters. <p><p>The actual validation of the adjoint-generated environmental gradients for acoustic monitoring of a shallow water environment is based on acoustic and oceanographic data from the Yellow Shark '94 and the MREA '07 sea trials, conducted in the Tyrrhenian Sea, south of the island of Elba.<p> <p>Starting from an initial guess of the environmental control parameters, either obtained through acoustic inversion with global search or supported by archival in-situ data, the adjoint method provides an efficient means to adjust local changes with a couple of iterations and monitor the environmental properties over a series of inversions. <p><p>In this thesis the adjoint-based approach is used, e.g. to fine-tune up to eight bottom geoacoustic parameters of a shallow-water environment and to track the time-varying sound speed profile in the water column. <p><p>In the same way the approach can be extended to track the spatial water column and bottom structure using a mobile network of sparse arrays.<p><p>Work is currently being focused on the inclusion of the adjoint approach into hybrid optimization schemes or ensemble predictions, as an essential building block in a combined ocean acoustic data assimilation framework and the subsequent validation of the acoustic monitoring capabilities with long-term experimental data in shallow water environments. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

L’évaluation du débit en réseaux hydrauliques à surface libre est une problématique actuelle sur le plan scientifique, à forts enjeux technologiques, économiques et écologiques. Dans cette thèse, de nouvelles méthodologies d’instrumentation, basées sur une synergie entre mesures non intrusives de hauteur d’eau et modélisation numérique ont été développées. Celles-ci s’appliquent d’une part à des collecteurs dont le fonctionnement hydraulique est complexe et, d’autre part, à des ouvrages non-standard (Venturi, déversoirs d’orage). Ce travail de thèse multidisciplinaire vise une meilleure compréhension de l’écoulement pour en déduire des relations Q=f(hi) plus robustes, spécifiques à chaque site et associées à leurs incertitudes; mais également l’identification de possibles modifications du site de mesure afin d’améliorer l’estimation du débit. Au final, l’applicabilité des méthodologies développées a été éprouvée au travers de plusieurs études sur sites réels. / The evaluation of the flow rate in free surface water systems is a current scientific problem, related to high technological, economical and ecological issues. In this study, new methods of instrumentation based on a synergy between non-intrusive water level measurements and numerical modeling have been developed. These methods are applied first to sewer pipes with complex hydraulic conditions then to non-standard hydraulic structures (Venturi flumes, Combined Sewer Overflows). This multidisciplinary work aims at a better understanding of the flow to identify more robust site-specific Q=f(hi) relationships related to their uncertainties. It also aims at the identification of possible modification of the measurement site in order to improve the flow rate evaluation. Finally, the applicability of the developed methodologies has been tested through several real site studies.

Cette thèse porte sur l'approximation numérique des équations de Saint-Venant et de quelques problèmes qui leur sont reliés. Dans la première partie, nous analysons les propriétés mathématiques et les applications des schémas numériques sur grilles décalées. La robustesse de ces schémas est prouvée sur des applications telles que les équations de Saint-Venant dans un domaine en rotation, en vue des écoulements géostrophiques, ainsi que l'extension de ces équations au cas visqueux. Dans la seconde partie, nous présentons des modèles basés sur les équations de Saint-Venant. Nous commençons par étudier le couplage avec l'équation d'Exner, qui porte sur le transport des sédiments. Nous observons des propriétés de convergence numérique vers la solution exacte dans un cas de solution analytique, et nous constatons un bon accord avec des données expérimentales dans le cas de la rupture de barrage avec fond érodable. Nous continuons par l'étude d'un schéma numérique, basé sur une méthode de volumes finis colocalisés (HLLC) pour l'approximation du modèle de Richard-Gavrilyuk. Ce modèle étend les équations de Saint-Venant au cas des écoulements avec cisaillement. Des tests numériques montrent la validité du schéma / This thesis is devoted to the numerical approximation of the shallow water equations and of some related models. In the first part, we analyze the mathematical properties and the applications of the staggered grid scheme. The robustness of this scheme is validated on various applications such as the rotating shallow water equations for geostrophic flows model and viscous shallow water equations. In the second part, we consider some related models. Firstly focusing on the coupling between the Exner equation and the shallow water equations, modelling bedload sediment transport, we observe in a particular case the numerical convergence of the scheme to the exact solution, as well as a good agreement with the experimental data in the dam-break with erodible bottom test. Secondly, we present a numerical scheme based on the finite volume collocated scheme (HLLC) in order to approximate the Richard-Gavrilyuk model. This model is an extension of the shallow water model, fit for modelling the shear shallow water flows. Some numerical tests provide a validation of the scheme

In this thesis we study the properties of exoplanetary atmospheres. The first part describes methods for searching exoplanets, statistics of discovered exoplanets and the sampling factors. The second part describes the properties of chosen planets and moons in the Solar system (Venus, Mars and Titan) and also possible properties of the exoplanetary atmospheres that are only briefly understood. The third part describes the atmospheric models which incorporate a full 3D model of the atmosphere, and a shallow- water model. We also show the results of exoplanetary atmospheric models published in the scientific journals. This part also describes the icosahedral geodetic grid that is advantageous for the global climatic models, and also discretisation on sphere and the application of the operators (gradient, divergence, vorticity) on geodetic grid. The last part is about creating program for global shallow water model in divergence-vorticity variables with forcing system with using icosahedral geodetic grid - we describe technical properties connected with model creating, parameters which the model uses during time integration, geographic system for results display and we show results for various kinds of extrasolar planets and planets in the Solar system. We used several numerical tests for testing model...

On étudie dans le cadre de la thèse une famille de schémas numériques permettant de résoudre les équations de Saint-Venant. Ces schémas utilisent une décomposition d'opérateur de type Lagrange-projection afin de séparer les ondes de gravité et les ondes de transport. Un traitement implicite du système acoustique (relié aux ondes de gravité) permet aux schémas de rester stable avec de grands pas de temps. La correction des flux de pression rend possible l'obtention d'une solution approchée précise quel que soit le régime d'écoulement vis-à-vis du nombre de Froude. Une attention toute particulière est portée sur le traitement du terme source qui permet la prise en compte de l'influence de la topographie. On obtient notamment la propriété dite équilibre permettant de conserver exactement certains états stationnaires, appelés état du "lac au repos". Des versions 1D et 2D sur maillages non-structurés de ces méthodes ont été étudiées et implémentées dans un cadre volumes finis. Enfin, une extension vers des méthodes ordres élevés Galerkin discontinue a été proposée en 1D avec des limiteurs classiques ainsi que combinée avec une boucle MOOD de limitation a posteriori. / In this thesis we study a family of numerical schemes solving the shallow water equations system. These schemes use a Lagrange-projection like splitting operator technique in order to separate the gravity waves and the transport waves. An implicit-explicit treatment of the acoustic system (linked to the gravity waves) allows the schemes to stay stable with large time step. The correction of the pressure fluxes enables the obtain of a precise approximation solution whatever the regime flow is with respect to the Froude number. A particular attention has been paid over the source term treatment which permits to take the topography into account. We especially obtain the so-called well-balanced property giving the exact conservation of some steady states, namely the "lake at rest" state. 1D and 2D versions of this methods have been studied and implemented in the finite volumes framework. Finally, a high order discontinuous Galerkin extension has been proposed in 1D with classical limiters along with a combined MOOD loop a posteriori limiting strategy.

No description available.