Este trabalho investiga o processo de apreensão do princípio de conservação da energia mecânica por alunos em diferentes momentos da instrução formal. O trabalho é justificado pelos relatos existentes acerca da complexidade que envolve o conceito de energia, o princípio de conservação da energia, degradação e conversão relacionadas aos materiais didáticos, à sua estrutura epistemológica racional e, principalmente, à sua aprendizagem. Consideramos, para isso, duas dimensões que julgamos centrais para essa discussão: a primeira refere-se ao desenvolvimento histórico-epistemológico do conceito e, a segunda, ao seu desenvolvimento em nível individual ou cognitivo. Para a primeira dimensão resgatamos pontos chaves do desenvolvimento histórico do princípio de conservação da energia, sua relação com a conservação da vis viva e os diferentes desenvolvimentos do teorema trabalho-energia, sendo um realizado por Lazare Carnot e, outro, por Lagrange. Consoante a isso apresentamos, orbitando à primeira dimensão, de que maneira o conceito de energia mecânica é tratado em alguns manuais de ensino universitário e uma síntese dos trabalhos voltados para o conceito de energia na área de Ensino de Ciências. Para a segunda dimensão pesquisamos os conhecimentos mobilizados por estudantes de diferentes níveis privilegiando duas metodologias: a primeira num estudo coletivo, que chamamos de preliminar e, outra, em nível do indivíduo, aprofundado. A intenção do estudo preliminar foi a de verificar e confirmar que alunos que se encontram em momentos mais avançados de ensino tendem a mobilizar e articular conceitos com maior pertinência do que aqueles que se encontram em momentos anteriores. Foram aplicados 158 questionários e analisados à luz de categorias existentes na literatura da área, possibilitando a aproximação com os dados relatados em pesquisas longitudinais. A partir dessa análise e da literatura, foi possível elencar 8 situações na perspectiva de aprofundarmos o entendimento de como ocorre, de maneira explícita ou implícita, o processo de aprendizagem de 6 sujeitos para os conceitos-chaves levantados durante a ação da resolução das situações com mediação do investigador. As mediações foram gravadas em vídeo e áudio e integralmente transcritas para análise. O referencial teórico adotado para a investigação da conceitualização é a Teoria dos Campos Conceituais de Gérard Vergnaud. A análise das condutas dos sujeitos-em-ação nos permitiu inferir, por exemplo, que os sujeitos-em-ação reconhecem a conservação da energia mecânica e até mesmo, implicitamente, a expressão matemática do teorema trabalho-energia capaz de representar essa conservação na sua forma integral. Por outro lado, os dados analisados no estudo aprofundado sugerem que a dinâmica newtoniana parece atuar como obstáculo epistemológico para a aprendizagem da conservação da energia mecânica. / This work investigates the learning process of the conservation of mechanical energy by students in different levels of formal education. The work is justified by researches involving the concept of energy, the principle of the conservation and degradation of energy and transforming process related to the instructional materials. Furthermore, the complexity of rational epistemological structure of those concepts and its learning. In this case, two dimensions are considered as main points: the first one refers to the development of historical-epistemological concept and the second one to the individual cognitive development. For the first dimension, we accomplished the key points of the historical development of the principle of conservation of energy, its relation with the vis viva conservation and different developments of the work-energy theorem which were made by Lazare Carnot and other by Lagrange. According to that, we present the concept of the mechanical energy within some university books and a synthesis of works devoting the concept of the mechanical energy within the Science Learning studies. For the second dimension, we made a research about knowledge utilized by the pupils of different levels specializing in two methodologies: first about collective research called pre-study and the second one about individual research called detailed study. The aim of pre-study was to verify and confirm that high school and undergraduate students tends to mobilize and articulate concepts with better form in accordance with their level; those studies are called cross-grade or longitudinal studies. We applied and categorized 158 questionnaires which had been possible to approximate data related in longitudinal researches. After that, according to the literature, it was possible to organize 8 situations to carefully investigate how do the learning process occur, explicitly or implicitly, in 6 students about key concepts that have been appeared during the act of the resolution of the situations with mediation of the researcher. The mediations were recorded in video and audio and fully transcribed to our analysis. The framework adopted to investigate the conceptualization was the Theory of Conceptual Fields developed by the French cognitivist Gérard Vergnaud. The conduct analyses of the subjects action allowed us to infer, for example, that students recognized the conservation of the mechanical energy during the action of the students and implicitly they recognized the mathematical function that express this conservation in integral form. Moreover, the data suggests that the Newtonian dynamics acts as epistemological obstacle to the learning of the conservation of the mechanical energy.

La chronologie des recherches théoriques et numériques exposées dans cet ouvrage est étroitement liée à notre attachement à lexpérimental et aux préoccupations pratiques des grands projets de constructions hydrauliques. Les applications variées qui sont envisagées quotidiennement au HACH (Hydrodynamique Appliquée et Constructions Hydrauliques Secteur Mécanique des Solides, des Fluides et des Structures - Département ArGEnCo Université de Liège), dont plusieurs exemples sont présentés, ont permis didentifier aussi bien des pistes damélioration des modèles numériques existants au sein de la suite WOLF(suite logicielle intégrée développée par le HACH pour la modélisation et loptimisation des écoulements à surface libre), que des besoins en nouvelles potentialités de représentation. Cest de là que sont nés la plupart des développements détaillés ici, avec comme objectif principal laugmentation des capacités des logiciels du HACH pour laide à la gestion et au design douvrages hydrauliques. Le dimensionnement de structures hydrauliques, tout comme la majeure partie des problèmes touchant à lhydrodynamique des écoulements à surface libre rencontrés dans la pratique, nécessite des études à grande et petite échelles, à laide de modèles adaptés localement aux phénomènes représentés, et donc variables au sein dune même étude selon le point particulier examiné. Dautre part, loptimisation de la forme ou du fonctionnement douvrages hydrauliques requiert des outils de calibration robustes permettant une approche objective. Ces derniers doivent de plus être couplés à des logiciels de simulation dont la représentativité et les temps de calcul sont en accord avec les exigences de loptimisation. Ces deux constats principaux posent le cadre des recherches entreprises et sont à la base de la définition des objectifs du travail. Les premiers chapitres de développements sattachent à décrire le cadre numérique de la suite logicielle WOLF, et plus particulièrement des codes 1D et 2D. La rationalisation des temps de calcul des simulations filaires à grande échelle est améliorée à ce stade par limplémentation au sein du logiciel unidimensionnel dun schéma dintégration temporelle implicite, en parallèle du schéma explicite existant. De même, certaines améliorations sont déjà apportées au logiciel WOLF2D. Elles concernent lextension automatique du domaine de calcul en fonction des mailles immergées émergées, le traitement des termes sources de pente de fond et de frottement en accord avec une approche énergétique, la conservation volumique du modèle ainsi que la réorganisation de la filière de résolution des équations de façon à permettre une totale latitude dans le choix du modèle de calcul utilisé. Lenrichissement des potentialités de modélisation des outils de la suite WOLF est ensuite poursuivi par létablissement, limplémentation et lapplication à des cas théoriques et pratiques, dun modèle de turbulence adapté aux caractéristiques spécifiques de la simulation des écoulements intégrée sur la hauteur deau. Afin de dépasser les limitations, tant informatiques que de discrétisation, inhérentes à lutilisation dune taille de maille unique sur un domaine de simulation bidimensionnel, des développements sont entrepris pour permettre de mener les calculs bidimensionnels sur un maillage structuré cartésien constitué de plusieurs zones à la taille de maille différente. Dans le même ordre didée, des développements sont réalisés pour permettre lutilisation de lensemble des outils de modélisation disponibles au sein du logiciel WOLF2D de façon simultanée et automatique au sein dune même simulation. Létape ultime de ces développements est réalisée en couplant les modèles uni- et bidimensionnel au sein dune simulation unique. Une fois toutes ces étapes de développement des modèles hydrodynamiques franchies, un logiciel adapté de calage automatique de paramètres est mis au point. Utilisable avec nimporte quel code de la suite WOLF, il permet la calibration de lensemble des paramètres physiques présents au sein des logiciels hydrodynamiques, ainsi que la résolution de tout problème doptimisation ou de calibration à laide des mêmes modèles. La parallélisation de ce logiciel basé sur la méthode des Algorithmes Génétiques ouvre la porte à des applications denvergure, dont le dimensionnement hydraulique douvrages sur base de simulations bidimensionnelles découlements turbulents à surface libre sur maillage multibloc. A chaque étape, la validation des développements est réalisée de façon rigoureuse par la confrontation des résultats numériques à ceux de cas test, théoriques et expérimentaux, originaux ou proposés dans la littérature. De nombreux exemples dapplications pratiques illustrent l'ensemble des potentialités de modélisation développées et prouvent leur applicabilité et leur efficacité face aux problèmes pratiques rencontrés par les ingénieurs hydrauliciens./ The chronology of the theoretical and numerical researches outlined in this text is closely linked to our attachment to the physical modelling and to the practical concerns related to important hydraulic projects. The various applications carried out daily in the HACH (Applied Hydrodynamics and Hydraulic Constructions - Solid, Fluid and Structures Mechanics ArGEnCo Department University of Liege), several of the being presented here, enabled to identify the ways to improve the existing numerical models of WOLF (integrated software package developed by the HACH for free surface flows modelling), as well as needs in new representation potentialities. The most of the developments described in this text were born from there, with as main objective to increase the capacities of the HACHs models to help to the management and the design of hydraulic constructions. The hydraulic structures design, and the main part of the practical problems related to free surface flows hydrodynamics, requires both large and small scales studies, with reliable models locally suited to the represented phenomena, and thus variable in a single study depending on the particular point examined. On another hand, the shape and working optimization of hydraulic structures requires robust calibration tools allowing an objective approach. The latter have to be linked to simulation software with modelling capacities and computation times in agreement with the optimization requirements. Both these assessments specify the framework of the researches of this thesis and are at the roots of the definition of the objectives of this work. The first chapters of developments aim to describe the numerical framework of the WOLF package, and more particularly the 1D and 2D models. The rationalization of the computation times for large scale one-dimensional simulations is improved at this stage by implementing in the 1D solver an implicit time integration scheme in parallel to the existing explicit one. Similarly, some improvements have been brought to the solver WOLF2D. They concern the automatic extension of the computation domain regarding the wet and dry cells, the treatment of the slope and roughness source terms with an energetic approach, the water volume conservation as well as the reorganization of the equations resolution scheme in order to be totally free in the choice of the mathematical model to solve. The enrichment of the modelling potentialities of the WOLF software is then pursued by setting, implementing and applying an original turbulence model suited to the specific characteristics of the depth integrated flow modelling. In order to get over the computer and modelling limitations inherent in the use of a single mesh size to model a 2D domain, developments have been carried out to allow the realisation of two-dimensional computations on a structured Cartesian grid composed of several areas with different mesh sizes. In the same way, developments have been carried out to use the whole of the mathematical models available in WOLF2D simultaneously and automatically in a single simulation. The ultimate step of these developments consisted in linking the 1D and the 2D models in a single computation. Following all these steps of developments of hydrodynamic models, a suitable tool for parameters automatic calibration has been set up. Usable with any solver of the WOLF package, it allows the calibration of the whole of the physical parameters present in the hydrodynamic solvers, as well as the resolution of any calibration or optimization problem with these models. The final parallelisation of this Genetic Algorithms based tool opens the door to complex applications, such as the hydraulic design of structures on the basis of two-dimensional simulations of free surface turbulent flows on multiblock grid. At each step, the validation of the developments is rigorously performed through the comparison of the numerical results with those from test cases, theoretical or experimental, original or from the literature. Several practical applications examples illustrate the whole of the developed modelling potentialities and prove their applicability and efficiency facing the most of practical problems encountered by hydraulic engineers.

Este trabalho investiga o processo de apreensão do princípio de conservação da energia mecânica por alunos em diferentes momentos da instrução formal. O trabalho é justificado pelos relatos existentes acerca da complexidade que envolve o conceito de energia, o princípio de conservação da energia, degradação e conversão relacionadas aos materiais didáticos, à sua estrutura epistemológica racional e, principalmente, à sua aprendizagem. Consideramos, para isso, duas dimensões que julgamos centrais para essa discussão: a primeira refere-se ao desenvolvimento histórico-epistemológico do conceito e, a segunda, ao seu desenvolvimento em nível individual ou cognitivo. Para a primeira dimensão resgatamos pontos chaves do desenvolvimento histórico do princípio de conservação da energia, sua relação com a conservação da vis viva e os diferentes desenvolvimentos do teorema trabalho-energia, sendo um realizado por Lazare Carnot e, outro, por Lagrange. Consoante a isso apresentamos, orbitando à primeira dimensão, de que maneira o conceito de energia mecânica é tratado em alguns manuais de ensino universitário e uma síntese dos trabalhos voltados para o conceito de energia na área de Ensino de Ciências. Para a segunda dimensão pesquisamos os conhecimentos mobilizados por estudantes de diferentes níveis privilegiando duas metodologias: a primeira num estudo coletivo, que chamamos de preliminar e, outra, em nível do indivíduo, aprofundado. A intenção do estudo preliminar foi a de verificar e confirmar que alunos que se encontram em momentos mais avançados de ensino tendem a mobilizar e articular conceitos com maior pertinência do que aqueles que se encontram em momentos anteriores. Foram aplicados 158 questionários e analisados à luz de categorias existentes na literatura da área, possibilitando a aproximação com os dados relatados em pesquisas longitudinais. A partir dessa análise e da literatura, foi possível elencar 8 situações na perspectiva de aprofundarmos o entendimento de como ocorre, de maneira explícita ou implícita, o processo de aprendizagem de 6 sujeitos para os conceitos-chaves levantados durante a ação da resolução das situações com mediação do investigador. As mediações foram gravadas em vídeo e áudio e integralmente transcritas para análise. O referencial teórico adotado para a investigação da conceitualização é a Teoria dos Campos Conceituais de Gérard Vergnaud. A análise das condutas dos sujeitos-em-ação nos permitiu inferir, por exemplo, que os sujeitos-em-ação reconhecem a conservação da energia mecânica e até mesmo, implicitamente, a expressão matemática do teorema trabalho-energia capaz de representar essa conservação na sua forma integral. Por outro lado, os dados analisados no estudo aprofundado sugerem que a dinâmica newtoniana parece atuar como obstáculo epistemológico para a aprendizagem da conservação da energia mecânica. / This work investigates the learning process of the conservation of mechanical energy by students in different levels of formal education. The work is justified by researches involving the concept of energy, the principle of the conservation and degradation of energy and transforming process related to the instructional materials. Furthermore, the complexity of rational epistemological structure of those concepts and its learning. In this case, two dimensions are considered as main points: the first one refers to the development of historical-epistemological concept and the second one to the individual cognitive development. For the first dimension, we accomplished the key points of the historical development of the principle of conservation of energy, its relation with the vis viva conservation and different developments of the work-energy theorem which were made by Lazare Carnot and other by Lagrange. According to that, we present the concept of the mechanical energy within some university books and a synthesis of works devoting the concept of the mechanical energy within the Science Learning studies. For the second dimension, we made a research about knowledge utilized by the pupils of different levels specializing in two methodologies: first about collective research called pre-study and the second one about individual research called detailed study. The aim of pre-study was to verify and confirm that high school and undergraduate students tends to mobilize and articulate concepts with better form in accordance with their level; those studies are called cross-grade or longitudinal studies. We applied and categorized 158 questionnaires which had been possible to approximate data related in longitudinal researches. After that, according to the literature, it was possible to organize 8 situations to carefully investigate how do the learning process occur, explicitly or implicitly, in 6 students about key concepts that have been appeared during the act of the resolution of the situations with mediation of the researcher. The mediations were recorded in video and audio and fully transcribed to our analysis. The framework adopted to investigate the conceptualization was the Theory of Conceptual Fields developed by the French cognitivist Gérard Vergnaud. The conduct analyses of the subjects action allowed us to infer, for example, that students recognized the conservation of the mechanical energy during the action of the students and implicitly they recognized the mathematical function that express this conservation in integral form. Moreover, the data suggests that the Newtonian dynamics acts as epistemological obstacle to the learning of the conservation of the mechanical energy.