University, Diss., 1995--Paderborn.

Berlin, Freie Universiẗat, Diss., 1998. / Dateiformat: zip, Dateien im PDF-Format.

Reproduction de : Thèse doctorat : Mathématiques appliquées : Pau : 2008. / Titre provenant de l'écran titre. Bibliographie.

Göttingen, Univ., Diss., 2000. / Computerdatei im Fernzugriff.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1973. / Vita. Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Este trabalho apresenta novas soluções exatas para a equação de Helmholtz bidimensional transiente, as quais são obtidas através de Split, simetrias de Lie e transformações de Bäcklund. O objetivo do trabalho proposto é obter um procedimento sistemático que permita gerar soluções que descrevam escoamentos tridimensionais, usando grupos de Lie já disponíveis na literatura especializada para o sistema contendo as equações de Navier-Stokes tridimensionais e a equação da continuidade para escoamentos incompressíveis em geometria cartesiana. A principal dificuldade em obter soluções tridimensionais usando grupos de Lie reside na necessidade de se conhecer previamente ao menos uma solução bidimensional transiente que satisfaça as condições de não-deslizamento e não-penetração na interface sólida, bem como a prescrição de escoamento potencial distante do corpo submerso. As soluções para as equações de Navier-Stokes bidimensionais são obtidas resolvendo a equação de Helmholtz para a função corrente. Algumas das soluções foram empregadas para simular escoamentos viscosos em torno de cilindros, reproduzindo características qualitativas do escoamento transversal, e gerando resultados com razoável concordância em relação aos dados experimentais. / This work presents new exact solutions to the unsteady two-dimensional Helmholtz equation, which were obtained by split, Lie Symmetries and Bäcklund transformations. The aim of the proposed work is to obtain a systematic procedure that allows to generate exact solutions which describe three-dimensional flows, using a Lie symmetry group yet available in specialized literature for the system containing the three-dimensional Navier-Stokes equations and the continuity equation for incompressible flows in cartesian geometry. The major difficult in obtaining the three-dimensional solutions using the Lie group relies on the need of knowing beforehand at least one two-dimensional unsteady solution which satisfies the no slip and no penetration conditions at the solid interface, as well as the prescriptions of potential flows far from the immersed body. The two-dimensional solutions for the Navier-Stokes equations are obtained by solving the Helmholtz equation for the stream function . Some of the solutio ns were employed to simulate viscous flows around cylinders, reproducing qualitative features of the crossflow, and generating results which are in reasonable agreement with experimental data.

Este trabalho apresenta novas soluções exatas para a equação de Helmholtz bidimensional transiente, as quais são obtidas através de Split, simetrias de Lie e transformações de Bäcklund. O objetivo do trabalho proposto é obter um procedimento sistemático que permita gerar soluções que descrevam escoamentos tridimensionais, usando grupos de Lie já disponíveis na literatura especializada para o sistema contendo as equações de Navier-Stokes tridimensionais e a equação da continuidade para escoamentos incompressíveis em geometria cartesiana. A principal dificuldade em obter soluções tridimensionais usando grupos de Lie reside na necessidade de se conhecer previamente ao menos uma solução bidimensional transiente que satisfaça as condições de não-deslizamento e não-penetração na interface sólida, bem como a prescrição de escoamento potencial distante do corpo submerso. As soluções para as equações de Navier-Stokes bidimensionais são obtidas resolvendo a equação de Helmholtz para a função corrente. Algumas das soluções foram empregadas para simular escoamentos viscosos em torno de cilindros, reproduzindo características qualitativas do escoamento transversal, e gerando resultados com razoável concordância em relação aos dados experimentais. / This work presents new exact solutions to the unsteady two-dimensional Helmholtz equation, which were obtained by split, Lie Symmetries and Bäcklund transformations. The aim of the proposed work is to obtain a systematic procedure that allows to generate exact solutions which describe three-dimensional flows, using a Lie symmetry group yet available in specialized literature for the system containing the three-dimensional Navier-Stokes equations and the continuity equation for incompressible flows in cartesian geometry. The major difficult in obtaining the three-dimensional solutions using the Lie group relies on the need of knowing beforehand at least one two-dimensional unsteady solution which satisfies the no slip and no penetration conditions at the solid interface, as well as the prescriptions of potential flows far from the immersed body. The two-dimensional solutions for the Navier-Stokes equations are obtained by solving the Helmholtz equation for the stream function . Some of the solutio ns were employed to simulate viscous flows around cylinders, reproducing qualitative features of the crossflow, and generating results which are in reasonable agreement with experimental data.

Este trabalho apresenta novas soluções exatas para a equação de Helmholtz bidimensional transiente, as quais são obtidas através de Split, simetrias de Lie e transformações de Bäcklund. O objetivo do trabalho proposto é obter um procedimento sistemático que permita gerar soluções que descrevam escoamentos tridimensionais, usando grupos de Lie já disponíveis na literatura especializada para o sistema contendo as equações de Navier-Stokes tridimensionais e a equação da continuidade para escoamentos incompressíveis em geometria cartesiana. A principal dificuldade em obter soluções tridimensionais usando grupos de Lie reside na necessidade de se conhecer previamente ao menos uma solução bidimensional transiente que satisfaça as condições de não-deslizamento e não-penetração na interface sólida, bem como a prescrição de escoamento potencial distante do corpo submerso. As soluções para as equações de Navier-Stokes bidimensionais são obtidas resolvendo a equação de Helmholtz para a função corrente. Algumas das soluções foram empregadas para simular escoamentos viscosos em torno de cilindros, reproduzindo características qualitativas do escoamento transversal, e gerando resultados com razoável concordância em relação aos dados experimentais. / This work presents new exact solutions to the unsteady two-dimensional Helmholtz equation, which were obtained by split, Lie Symmetries and Bäcklund transformations. The aim of the proposed work is to obtain a systematic procedure that allows to generate exact solutions which describe three-dimensional flows, using a Lie symmetry group yet available in specialized literature for the system containing the three-dimensional Navier-Stokes equations and the continuity equation for incompressible flows in cartesian geometry. The major difficult in obtaining the three-dimensional solutions using the Lie group relies on the need of knowing beforehand at least one two-dimensional unsteady solution which satisfies the no slip and no penetration conditions at the solid interface, as well as the prescriptions of potential flows far from the immersed body. The two-dimensional solutions for the Navier-Stokes equations are obtained by solving the Helmholtz equation for the stream function . Some of the solutio ns were employed to simulate viscous flows around cylinders, reproducing qualitative features of the crossflow, and generating results which are in reasonable agreement with experimental data.

Cette thèse a trait au Contrôle Non Destructif par courants de Foucault. L'objet est de développer de nouvelles méthodes de calcul de la variation d'impédance d'une bobine émettrice placée au-dessus d'’une plaque conductrice contenant ou non des fissures. Les approches standards les plus robustes nécessitent le maillage par éléments finis volumiques, ce qui peut entraîner des coûts de calculs et de stockage élevés. Dans ces travaux, une géométrie idéalisée, donc simplifiée, est considérée permettant d’envisager une résolution du problème en choisissant de l'appréhender comme un problème de transmission sur l'’interface entre le conducteur et l'’air ambiant contenant la bobine. Dans le cas d'’un conducteur non fissuré, une méthode d'approximation de la variation d'impédance d'une bobine placée à la surface de la plaque est développée. Sa mise en œuvre nécessite uniquement l'’inversion de systèmes linéaires creux, diminuant ainsi le coût de calcul et de stockage. Dans le cas d'un conducteur contenant une fissure, la fissure est prise en compte à l'aide d'’une densité fictive de courant. Une fois le problème ainsi formulé, la difficulté revient au calcul de la charge fictive. Une méthode de calcul de la charge fictive de courant dans le cas de conducteurs ayant une conductivité élevée est proposée. Cette méthode s'appuie sur des développements asymptotiques pour des nombres d'onde grands / This thesis is about Non Destructive Testing by eddy currents. The goal is to develop new methods to compute the impedance variation of emitting coil placed over a conductive plate, possibly containing cracks. Standard methods require volume finite element meshes. This usually implies a computation cost and data storage high. In this thesis, we consider a solution to the problem by choosing to see is as a transmission problem on the interface between the conducting plate and the air containing the coil. When the conductor has no crack, we develop an approximate method to compute the impedance variation of a coil placed on the conductive plate. Applying this method only requires inverting sparse linear systems, this reduces the computation cost and the data storage requirements. If the plate containing a crack, the crack modeled as fictive current charge. After formulating the problem this way, the difficult part is to compute the fictive charge. We offer a method to compute it when the conducting plate has a high conductivity. It is based on asymptotic developments for high wave numbers

Ce travail présente le développement de spectromètres photoacoustiques pour la mesure de traces de gaz avec des résonateurs de Helmholtz différentiels.La cuve représente le coeur de l'instrument, le laser qui la traverse va créer une onde de pression stationnaire qui sera mesurée par des microphones. Le signal photoacoustique est fonction de la concentration du gaz et la manière dont il sera amplifié va dépendre en grande partie de la géométrie de la cuve. Une méthode aux éléments finis est utilisée pour exprimer cette caractéristique selon les modes et les fréquences propres calculées de la cuve. Les paramètres clés de la cuve sont ainsi calculés, comme la fréquence de résonance, le facteur de qualité et la constante de la cuve. Contrairement à d'autres méthodes de spectroscopie infrarouge, la sensibilité des spectromètres photoacoustiques augmente alors que la cuve se miniaturise. Cette particularité est vérifiée expérimentalement avec un bon accord avec la simulation. La modélisation prouve une nouvelle fois être suffisamment robuste pour être utilisée dans un processus d'ingénierie du spectromètre. Cet outil va en effet permettre d'optimiser les dimensions du résonateur selon les besoins de l'application, soit en privilégiant le maximum de signal, la plus haute fréquence de travail ou encore le plus faible encombrement. De nombreuses cuves ont été développés avec l'aide de la simulation, l'écart observé avec les paramètres expérimentaux est de l'ordre de 15 %. Enfin, les applications actuelles en mesure de traces de gaz demandent de mesurer la concentration d'au moins deux gaz, de façon simultanée, avec des niveaux de détection proche du ppb. Un mode de résonance de Helmholtz particulier est trouvé afin de proposer une mesure multi-gaz. Enfin, la sensibilité est augmentée grâce à un système multi-passages. / This work presents the conception of a photoacoustic spectrometer dedicated to trace gas measurements using a differential Helmholtz resonator. The main component of the instrument is the cell, where a standing wave is produced by a laser excitation and is measured with microphones. The photoacoustic signal is proportional to the gas concentration and the cell shape mainly affects its amplification. A finite element method is used to find this characteristic by calculating the cell eigenmodes and eigenfrequencies.Key parameters of the cell are then calculated, including cell frequency, quality factor and cell constant. Unlike other infrared spectroscopy methods, sensitivity of photoacoustic spectrometers increases by miniaturization process. This particular phenomenon is experimentally verified and is in good agreement with the simulation.Modelization proves again its robustness to be used on an engineering process of the spectrometer. This tool allows to optimize resonator dimensions according to the application, favouring maximum signal, higher working frequency or reduced size. Many cells designed with the help of the simulation are presented, where the observed error with experiments is of the order of 15 %. Finally, today's trace gas applications need the measurement of at least two concentrations, simultaneously with detection limits down to the ppb level. A novel Helmholtz resonance mode is then found to allow multi-gas sensing.Finally, sensitivity is increased by multi-pass systems.