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Li, Siran. "Analysis of several non-linear PDEs in fluid mechanics and differential geometry." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:20866cbb-e5ab-4a6b-b9dc-88a247d15572.
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In the thesis we investigate two problems on Partial Differential Equations (PDEs) in differential geometry and fluid mechanics. First, we prove the weak L p continuity of the Gauss-Codazzi-Ricci (GCR) equations, which serve as a compatibility condition for the isometric immersions of Riemannian and semi-Riemannian manifolds. Our arguments, based on the generalised compensated compactness theorems established via functional and micro-local analytic methods, are intrinsic and global. Second, we prove the vanishing viscosity limit of an incompressible fluid in three-dimensional smooth, curved domains, with the kinematic and Navier boundary conditions. It is shown that the strong solution of the Navier-Stokes equation in H r+1 (r > 5/2) converges to the strong solution of the Euler equation with the kinematic boundary condition in H r, as the viscosity tends to zero. For the proof, we derive energy estimates using the special geometric structure of the Navier boundary conditions; in particular, the second fundamental form of the fluid boundary and the vorticity thereon play a crucial role. In these projects we emphasise the linkages between the techniques in differential geometry and mathematical hydrodynamics.
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Bocchi, Edoardo. "Compressible-incompressible transitions in fluid mechanics : waves-structures interaction and rotating fluids." Thesis, Bordeaux, 2019. http://www.theses.fr/2019BORD0279/document.
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Ce manuscrit porte sur les transitions compressible-incompressible dans les équations aux dérivées partielles de la mécanique des fluides. On s'intéresse à deux problèmes : les structures flottantes et les fluides en rotation. Dans le premier problème, l'introduction d'un objet flottant dans les vagues induit une contrainte sur le fluide et les équations gouvernant le mouvement acquièrent une structure compressible-incompressible. Dans le deuxième problème, le mouvement de fluides géophysiques compressibles est influencé par la rotation de la Terre. L'étude de la limite à rotation rapide montre que le champ vectoriel de vitesse tend vers une configuration horizontale et incompressible.Les structures flottantes constituent un exemple particulier d'interaction fluide-structure, où un solide partiellement immergé flotte à la surface du fluide. Ce problème mathématique modélise le mouvement de convertisseurs d'énergie marine. En particulier, on s'intéresse aux bouées pilonnantes, installées proche de la côte où les modèles asymptotiques en eaux peu profondes sont valables. On étudie les équations de Saint-Venant axisymétriques en dimension deux avec un objet flottant à murs verticaux se déplaçant seulement verticalement. Les hypothèses sur le solide permettent de supprimer le problème à bord libre associé avec la ligne de contact entre l'air, le fluide et le solide. Les équations pour le fluide dans le domaine extérieur au solide sont donc écrites comme un problème au bord quasi-linéaire hyperbolique. Celui-ci est couplé avec une EDO non-linéaire du second ordre qui est dérivée de l'équation de Newton pour le mouvement libre du solide. On montre le caractère bien posé localement en temps du système couplé lorsque que les données initiales satisfont des conditions de compatibilité afin de générer des solutions régulières.Ensuite on considère une configuration particulière: le retour à l'équilibre. Il s'agit de considérer un solide partiellement immergé dans un fluide initialement au repos et de le laisser retourner à sa position d'équilibre. Pour cela, on utilise un modèle hydrodynamique différent, où les équations sont linearisées dans le domaine extérieur, tandis que les effets non-linéaires sont considérés en dessous du solide. Le mouvement du solide est décrit par une équation intégro-différentielle non-linéaire du second ordre qui justifie rigoureusement l'équation de Cummins, utilisée par les ingénieurs pour les mouvements des objets flottants. L'équation que l'on dérive améliore l'approche linéaire de Cummins en tenant compte des effets non-linéaires. On montre l'existence et l'unicité globale de la solution pour des données petites en utilisant la conservation de l'énergie du système fluide-structure.Dans la deuxième partie du manuscrit, on étudie les fluides en rotation rapide. Ce problème mathématique modélise le mouvement des flots géophysiques à grandes échelles influencés par la rotation de la Terre. Le mouvement est aussi affecté par la gravité, ce qui donne lieu à une stratification de la densité dans les fluides compressibles. La rotation génère de l'anisotropie dans les flots visqueux et la viscosité turbulente verticale tend vers zéro dans la limite à rotation rapide. Notre interêt porte sur ce problème de limite singulière en tenant compte des effets gravitationnels et compressibles. On étudie les équations de Navier-Stokes-Coriolis anisotropes compressibles avec force gravitationnelle dans la bande infinie horizontale avec une condition au bord de non glissement. Celle-ci et la force de Coriolis donnent lieu à l'apparition des couches d'Ekman proche du bord. Dans ce travail on considère des données initiales bien préparées. On montre un résultat de stabilité des solutions faibles globales pour des lois de pression particulières. La dynamique limite est décrite par une équation quasi-géostrophique visqueuse en dimension deux avec un terme d'amortissement qui tient compte des couches limitesThis manuscript deals with compressible-incompressible transitions arising in partial differential equations of fluid mechanics. We investigate two problems: floating structures and rotating fluids. In the first problem, the introduction of a floating object into water waves enforces a constraint on the fluid and the governing equations turn out to have a compressible-incompressible structure. In the second problem, the motion of geophysical compressible fluids is affected by the Earth's rotation and the study of the high rotation limit shows that the velocity vector field tends to be horizontal and with an incompressibility constraint.Floating structures are a particular example of fluid-structure interaction, in which a partially immersed solid is floating at the fluid surface. This mathematical problem models the motion of wave energy converters in sea water. In particular, we focus on heaving buoys, usually implemented in the near-shore zone, where the shallow water asymptotic models describe accurately the motion of waves. We study the two-dimensional nonlinear shallow water equations in the axisymmetric configuration in the presence of a floating object with vertical side-walls moving only vertically. The assumptions on the solid permit to avoid the free boundary problem associated with the moving contact line between the air, the water and the solid. Hence, in the domain exterior to the solid the fluid equations can be written as an hyperbolic quasilinear initial boundary value problem. This couples with a nonlinear second order ODE derived from Newton's law for the free solid motion. Local in time well-posedness of the coupled system is shown provided some compatibility conditions are satisfied by the initial data in order to generate smooth solutions.Afterwards, we address a particular configuration of this fluid-structure interaction: the return to equilibrium. It consists in releasing a partially immersed solid body into a fluid initially at rest and letting it evolve towards its equilibrium position. A different hydrodynamical model is used. In the exterior domain the equations are linearized but the nonlinear effects are taken into account under the solid. The equation for the solid motion becomes a nonlinear second order integro-differential equation which rigorously justifies the Cummins equation, assumed by engineers to govern the motion of floating objects. Moreover, the equation derived improves the linear approach of Cummins by taking into account the nonlinear effects. The global existence and uniqueness of the solution is shown for small data using the conservation of the energy of the fluid-structure system.In the second part of the manuscript, highly rotating fluids are studied. This mathematical problem models the motion of geophysical flows at large scales affected by the Earth's rotation, such as massive oceanic and atmospheric currents. The motion is also influenced by the gravity, which causes a stratification of the density in compressible fluids. The rotation generates anisotropy in viscous flows and the vertical turbulent viscosity tends to zero in the high rotation limit. Our interest lies in this singular limit problem taking into account gravitational and compressible effects. We study the compressible anisotropic Navier-Stokes-Coriolis equations with gravitational force in the horizontal infinite slab with no-slip boundary condition. Both this condition and the Coriolis force cause the apparition of Ekman layers near the boundary. They are taken into account in the analysis by adding corrector terms which decay in the interior of the domain. In this work well-prepared initial data are considered. A stability result of global weak solutions is shown for power-type pressure laws. The limit dynamics is described by a two-dimensional viscous quasi-geostrophic equation with a damping term that accounts for the boundary layers
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Barker, Tobias. "Uniqueness results for viscous incompressible fluids." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:db1b3bb9-a764-406d-a186-5482827d64e8.
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First, we provide new classes of initial data, that grant short time uniqueness of the associated weak Leray-Hopf solutions of the three dimensional Navier-Stokes equations. The main novelty here is the establishment of certain continuity properties near the initial time, for weak Leray-Hopf solutions with initial data in supercritical Besov spaces. The techniques used here build upon related ideas of Calderón. Secondly, we prove local regularity up to the at part of the boundary, for certain classes of solutions to the Navier-Stokes equations, provided that the velocity field belongs to L∞(-1; 0; L3, β(B(1) ⋂ ℝ3 +)) with 3 ≤ β < ∞. What enables us to build upon the work of Escauriaza, Seregin and Šverák [27] and Seregin [100] is the establishment of new scale-invariant estimates, new estimates for the pressure near the boundary and a convenient new ϵ-regularity criterion. Third, we show that if a weak Leray-Hopf solution in ℝ3 +×]0,∞[ has a finite blow-up time T, then necessarily limt↑T||v(·, t)||L3,β(ℝ3 +) = ∞ with 3 < β < ∞. The proof hinges on a rescaling procedure from Seregin's work [106], a new stability result for singular points on the boundary, suitable a priori estimates and a Liouville type theorem for parabolic operators developed by Escauriaza, Seregin and Šverák [27]. Finally, we investigate a notion of global-in-time solutions to the Navier- Stokes equations in ℝ3, with solenoidal initial data in the critical Besov space ?-1/44,∞(ℝ3), which has certain continuity properties with respect to weak* convergence of the initial data. Such properties are motivated by the strategy used by Seregin [106] to show that if a weak Leray-Hopf solution in ℝ3×]0,∞[ has a finite blow-up time T, then necessarily limt↑T ||v(·, t)||L3(ℝ3) = ∞. We prove new decomposition results for Besov spaces, which are key in the conception and existence theory of such solutions.
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Kolumban, Jozsef. "Control issues for some fluid-solid models." Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLED012/document.
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L'analyse du comportement d'un solide ou de plusieurs solides à l'intérieur d'un fluide est un problème de longue date, que l'on peut voir décrit dans de nombreux manuels classiques d'hydrodynamique. Son étude d'un point de vue mathématique a suscité une attention croissante, en particulier au cours des 15 dernières années. Ce projet de recherche vise à mettre l'accent sur plusieurs aspects de cette analyse mathématique, en particulier sur le contrôle et les problèmes asymptotiques. Un modèle simple d'évolution fluide-solide est celui d'un seul corps rigide entouré d'un fluide incompressible parfait. Le fluide est modelé par les équations d'Euler, tandis que le solide évolue selon la loi de Newton et est influencé par la pression du fluide sur la limite. L'objectif de cette thèse de doctorat consisterait en diverses études dans cette branche et, en particulier, étudierait les questions de contrôlabilité de ce système, ainsi que des modèles de limite pour les solides minces qui convergent vers une courbe. Nous souhaitons également étudier le système de contrôle Navier-Stokes / solid d'une manière similaire au problème de contrôlabilité du système Euler / solid. Une autre direction pour ce projet de doctorat est d'obtenir une limite lorsque le solide se concentre dans une courbe. Est-il possible d'obtenir un modèle simplifié d'un objet mince évoluant dans un fluide parfait, de la même manière que des modèles simplifiés ont été obtenus pour des objets qui sont petits dans toutes les directions? Cela pourrait ouvrir la voie à des recherches futures sur la dérivation des flux de cristaux liquides comme limite du système décrivant l'interaction entre le fluide et un filet de tubes solides lorsque le diamètre des tubes converge à zéroThe analysis of the behavior of a solid or several solids inside a fluid is a long-standing problem, that one can see described in many classical textbooks of hydrodynamics. Its study from a mathematical viewpoint has attracted a growing attention, in particular in the last 15 years. This research project aims at focusing on several aspect of this mathematical analysis, in particular on control and asymptotic issues. A simple model of fluid-solid evolution is that of a single rigid body surrounded by a perfect incompressible fluid. The fluid is modeled by the Euler equations, while the solid evolves according to Newton’s law, and is influenced by the fluid’s pressure on the boundary. The goal of this PhD thesis would consist in various studies in this branch, and in particular would investigate questions of controllability of this system, as well as limit models for thin solids converging to a curve. We would also like to study the Navier-Stokes/solid control system in a similar manner to the previously discussed controllability problem for the Euler/solid system. Another direction for this PhD project is to obtain a limit when the solid concentrates into a curve. Is it possible to obtain a simplified model of a thin object evolving in a perfect fluid, in the same way as simplified models were obtained for objects that are small in all directions? This could open the way to future investigations on derivation of liquid crystal flows as the limit of the system describing the interaction between the fluid and a net of solid tubes when the diameter of the tubes is converging to zero
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Helluy, Philippe. "Simulation numérique des écoulements multiphasiques: de la théorie aux applications." Habilitation à diriger des recherches, Université du Sud Toulon Var, 2005. http://tel.archives-ouvertes.fr/tel-00657839.
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Perrin, Charlotte. "Modèles hétérogènes en mécanique des fluides : phénomènes de congestion, écoulements granulaires et mouvement collectif." Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAM023/document.
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Cette thèse est dédiée à la description et à l'analyse mathématique de phénomènes d'hétérogénéités et de congestion dans les modèles de la mécanique des fluides.On montre un lien rigoureux entre des modèles de congestion douce de type Navier-Stokes compressible qui intègrent des forces de répulsion à très courte portée entre composants élémentaires; et des modèles de congestion dure de type compressible/incompressible décrivant les transitions entre zones libres et zones congestionnées.On s'intéresse ensuite à la modélisation macroscopique de mélanges formés par des particules solides immergées dans un fluide.On apporte dans ce cadre une première réponse mathématique à la question de la transition entre les régimes de suspensions dictés par les interactions hydrodynamiques et les régimes granulaires dictés par les contacts entre les particules solides.On met par cette démarche en évidence le rôle crucial joué par les effets de mémoire dans le régime granulaire.Cette approche permet également un nouveau point de vue pour l'étude mathématique des fluides avec viscosité dépendant de la pression.On s'intéresse enfin à la modélisation microscopique et macroscopique du trafic routier.Des schémas numériques originaux sont proposés afin de reproduire des phénomènes de persistance d'embouteillagesThis thesis is dedicated to the description and the mathematical analysis of heterogeneities and congestion phenomena in fluid mechanics models.A rigorous link between soft congestion models, based on the compressible Navier--Stokes equations which take into account short--range repulsive forces between elementary components; and hard congestion models which describe the transitions between free/compressible zones and congested/incompressible zones.We are interested then in the macroscopic modelling of mixtures composed solid particles immersed in a fluid.We provide a first mathematical answer to the question of the transition between the suspension regime dictated by hydrodynamical interactions and the granular regime dictated by the contacts between the solid particles.The method highlights the crucial role played by the memory effects in the granular regime.This approach enables also a new point of view concerning fluids with pressure-dependent viscosities.We finally deal with the microscopic and the macroscopic modelling of vehicular traffic.Original numerical schemes are proposed to robustly reproduce persistent traffic jams
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Benjelloun, Saad. "Quelques problèmes d'écoulement multi-fluide : analyse mathématique, modélisation numérique et simulation." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2012. http://tel.archives-ouvertes.fr/tel-00764374.
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La présente thèse comporte trois parties indépendantes. La première partie présente une preuve d'existence de solutions faibles globales pour un modèle de sprays de type Vlasov-Navier-Stokes-incompressible avec densité variable. Ce modèle est obtenu par une limite formelle à partir d'un modèle Vlasov-Navier-Stokes-incompressible avec fragmentation, où seules deux valeurs de rayons de particules sont considérées : un rayon r1 pour les particules avant fragmentation, et un rayon r2 plus petit pour les particules obtenues par fragmentation. Le modèle asymptotique est obtenu dans la limite r2 tendant vers zéro. La démonstration s'appuie sur des techniques de régularisation et de troncature en vitesse, sur le théorème de Schauder et enfin sur une méthode de compacité de Lions-Di-Perna pour l'élimination des régularisations introduites dans le système initial. La deuxième partie concerne la modélisation de l'impact d'une vague de liquide sur une paroi. L'objectif de cette partie est d'obtenir un modèle pour la fuite du gaz environnant sur les "côtés" de la vague. Un modèle numérique est réalisé en remplaçant la vague liquide par une masse solide indéformable et un schéma VFFC-ALE est conçu pour la simulation numérique du modèle. La mise sans dimension des équations permet de montrer les nombres sans dimension qui régissent le phénomène de fuite. La vitesse moyenne de fuite est comparée à la vitesse dans le cas d'un fluide incompressible (pour lequel on a une expression exacte). Enfin, via la simulation numérique, une étude paramétrique est réalisée en fonction des nombres sans dimensions. Dans la troisième partie on présente une méthode numérique pour la simulation d'un modèle Vlasov-Boltzmann-Euler pour les sprays. Cette méthode couple le schéma VFFC à la méthode PIC (Particle In Cell). Les résultats présentés concernent l'écoulement d'un spray dans un pipeline courbe qu'on modélise par un système Vlasov-Boltzmann-Euler quasi-1D.
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Noisette, Florent. "Interactions avec la frontière pour des équations d’évolutions non-linéaires, non-locales." Electronic Thesis or Diss., Bordeaux, 2024. http://www.theses.fr/2024BORD0356.
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Ce manuscrit est découpé en deux parties et 9 chapitres. Dans la deuxième partie, j’ai mis les six résultats principaux prouvé pendant ma thèse :• Chapitre 5 : unicité des solutions d’Euler 2D avec sources et puits;• Chapitre 6 : unicité des solutions de l’équation de Camassa-Holm avec flot entrant et sortant ;• Chapitre 7 : un algorithme pour la simulation numérique de la croissance de micro-algues;• Chapitre 8 : Dérivée de forme de l’opérateur Dirichlet vers Neumann sur une variété bornée; ETcaractère bien posé d’une équation sur les protrusions céllulaires;• Chapitre 9 : régularité de l’opérateur de Dirichlet vers Neumann sur une variété Hs.Les deux premiers résultats ont été réalisés sous la tutelle de Franck Sueur au début de ma thèse, voir [ NS21 ] et [ Noi23 ] pour leur versions individuelles. Le troisième a été écrit à la suite du CEMRACS, en collaboration avec Mickaël Bestard et Léo Meyer, sous la direction de Bastien Polizzi, ainsi que Thierry Goudon et Sebastian Minjeaud, que vous trouverez aussi dans [ Ber+23 ]. Tout en étant plus éloigné du reste de mes travaux, l’algorithme sur lequel nous avons travaillé est interessant et je suis content de l’inclure ici. Les deux derniers résultats ont été écrits sous la tutelle de David Lannes, en cours de publication [ Noi24 ]. En première partie, je présente chacun des résultats, dans l’ordre. Le chapitre 1 va introduire l’équation et la littérature nécessaire pour comprendre le résultat du chapitre 5, le chapitre 2 fait de même pour le résultat du chapitre 6, et ainsi de suite jusqu’au chapitre 4, qui lui introduit à la fois les réultatats du chapitre 8 et 9The main results of my PhD thesis are :• Uniqueness of bounded vorticity solution for the 2D euler equation with sources and sinks• Uniqueness of bounded momentum solution of the CH equation with in and out-flow• An algorythm for the simulation of growth of Micro algae• shape derivative of the Dirichlet to neumann operator on a generic bounded domain• regularity of the Dirichlet to Neumann operator on a generic H^s manifold
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Doyeux, Vincent. "Modelisation et simulation de systemes multi-fluides. Application aux ecoulements sanguins." Phd thesis, Université de Grenoble, 2014. http://tel.archives-ouvertes.fr/tel-00939930.
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Dans ce travail, nous développons un cadre de calcul dédié à la simulation d'écoulements à plusieurs fluides. Nous présentons des validations et vérifications de ces méthodes sur des problèmes de capture d'interfaces et de simulations de bulles visqueuses. Nous montrons ensuite que ce cadre de calcul est adapté à la simulation d'objet rigides en écoulement. Puis, nous étendons ces méthodes à la simulation d'objets déformables simulant le comportement des globules rouges : les vésicules. Nous validons aussi ces simulations. Enfin nous appliquons les précédents modèles à des problèmes ouverts de microfluidique tels que la séparation d'une suspension dans une bifurcation microfluidique et la rhéologie en milieu confiné.
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Martin, Sébastien. "Modélisation et analyse mathématique de problèmes issus de la mécanique des fluides : applications à la tribologie et aux sciences du vivant." Habilitation à diriger des recherches, Université Paris Sud - Paris XI, 2012. http://tel.archives-ouvertes.fr/tel-00765580.
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Ce mémoire presente une synthèse de travaux de recherche consacrés à l'analyse de problèmes mathématiques issus de la mécanique des fluides. En particulier, par le mélange de modélisation, d'analyse théorique et numérique d' équations aux dérivées partielles ainsi que de calcul scientifique, les champs applicatifs de ces travaux ont porté essentiellement sur deux grandes thématiques : la mécanique des films minces et les biosciences. Cette synthèse s'articule autour de trois chapitres : 1) la lubrification hydrodynamique, 2) les lois de conservation scalaires sur un domaine borné et 3) la modélisation mathématique appliquée aux sciences du vivant qui présente, à son tour, deux axes distincts : la modélisation du système respiratoire et, en particulier, des échanges gazeux dans l'arbre bronchique et la simulation de suspensions biomimétiques actives ou passives dans un fluide de Stokes.
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Wylie, Jonathan James. "Geological fluid mechanics." Thesis, University of Cambridge, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627211.
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Dellacherie, Stéphane. "Étude et discrétisation de modèles cinétiques et de modèles fluides à bas nombre de Mach." Habilitation à diriger des recherches, Université Pierre et Marie Curie - Paris VI, 2011. http://tel.archives-ouvertes.fr/tel-00870146.
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Ce mémoire résume les travaux que nous avons réalisés de 1995 à 2010. Ces travaux ont eu pour thème l'étude et la discrétisation, d'une part, de modèles cinétiques de type Fokker-Planck ou de type Boltzmann semi-classiques et, d'autre part, de modèles fluides de type Euler ou de type Navier-Stokes à bas nombre de Mach. L'équation de Fokker-Planck étudiée modélise les collisions entre ions et électrons dans un plasma chaud, et concerne ici la fusion par confinement inertiel. Les équations de Boltzmann semi-classiques étudiées sont de deux types. Le premier type modélise la réaction de fusion thermonucléaire entre un ion deuterium et un ion tritium donnant une particule alpha et un neutron, et concerne également ici la fusion par confinement inertiel. Le deuxième type - connu sous le nom d'équations de Wang-Chang & Uhlenbeck - modélise ici les transitions d'énergie quantique dans les couches électroniques d'atomes d'uranium et de fer provoquées par les collisions entre ces mêmes atomes au sein du procédé SILVA de Séparation Isotopique par Laser sur Vapeur Atomique. Nous avons étudié les propriétés de base de ces deux types d'équations de Boltzmann semi-classiques, et, dans le cas des équations de Wang-Chang & Uhlenbeck, nous avons proposé un algorithme de couplage cinétique-fluide. L'étude de cet algorithme nous a incité à étudier la notion de relaxation dans un mélange binaire de gaz et de fluides non-miscibles, et à souligner les points communs de cette approche avec la théorie cinétique standard. L'étude de modèles moyennés pour des mélanges de fluides non-miscibles nous a amené à proposer et à discrétiser un modèle sans ondes acoustiques modélisant la déformation d'une interface entre deux fluides non-miscibles provoquée par de forts gradients thermiques à bas nombre de Mach. Puis, afin d'améliorer la précision des calculs tout en en maîtrisant le coût, nous avons également étudié la possibilité de résoudre sur un maillage dynamique de type AMR un modèle simplifié de déformation d'interface. Ces études à bas nombre de Mach nous ont également incités à analyser sur maillage cartésien le mauvais comportement à bas nombre de Mach des schémas de type Godunov appliqués au système d'Euler compressible. Enfin, nous avons justifié l'algorithme LBM dans le cas de l'équation de la chaleur.
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Duvigneau, Régis. "Conception optimale en mécanique des fluides numérique : approches hiérarchiques, robustes et isogéométriques." Habilitation à diriger des recherches, Université Nice Sophia Antipolis, 2013. http://tel.archives-ouvertes.fr/tel-00904328.
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Mes travaux de recherche concernent les méthodes pour la conception optimale en mécanique des fluides numérique. Il s'agit d'un contexte difficile, dans la mesure où l'évaluation de la fonctionnelle coût pour l'optimisation s'appuie sur la résolution des équations aux dérivées partielles régissant l'écoulement, caractérisées par de fortes non- linéarités, anisotropies et éventuellement discontinuités. Plus spécifiquement, mes travaux ont porté sur le développement de méthodes de conception hiérarchiques, pour la modélisation et la paramétrisation, dans le but d'améliorer les propriétés de convergence; sur des méthodes de conception isogéométriques, permettant l'emploi d'une base unique d'ordre élevé pour la représentation géométrique et la simulation; sur des méthodes de conception robuste, pour prendre en compte les incertitudes et les erreurs durant la procédure de conception. Ces développements ont été appliqués à divers problèmes de conception optimale, principalement en aérodynamique compressible, mais aussi en hydrodynamique, pour des modélisations allant des équations d'Euler stationnaires aux équations de Navier-Stokes instationnaires avec fermeture turbulente. Les résultats obtenus ont notamment montré l'intérêt d'introduire un niveau de modélisation supplémentaire : l'utilisation de méta-modèles de type Processus Gaussiens, associés à une recherche des paramètres de conception maximisant l'amélioration probable, conduit à une optimisation globale pour un nombre de simulations significativement réduit (de l'ordre de quelques dizaines). De plus, cette approche peut permettre de prendre en compte les incertitudes et erreurs, en introduisant la notion d'observation bruitée. Le second résultat important concerne l'emploi des méthodes d'analyse isogéométrique, qui offrent un cadre conceptuel intégrant la géométrie et l'analyse. J'ai montré que cette approche permet le développement de schémas d'ordre élevé, de méthodes hiérarchiques pour la modélisation et l'optimisation, et facilite l'analyse de sensibilité et les couplages multidisciplinaires.
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Minelli, Andrea. "Optimisation de forme aéro-acoustique d'un avion d'affaires supersonique." Phd thesis, Université Nice Sophia Antipolis, 2013. http://tel.archives-ouvertes.fr/tel-00938396.
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Ce travail porte sur le developpement de m ethodes num eriques innovantes pour la conception a ero -acoustique optimale de forme des con gurations supersoniques. Ce manuscrit pr esente tout d'abord l'analyse et le d eveloppement des approches num eriques pour la pr evision du bang sonique . Le couplage du calcul CFD tridimensionnel en champ proche prenant en compte la d ecomposition multipolaire de Fourier et la propagation atmosph erique bas ee sur un algorithme de trac e de rayons est am elior e par l'int egration d'un processus automatique d' adaptation anisotrope de maillage. La deuxi eme partie de ce travail se concentre sur l' elaboration et l'application des techniques de conception pour l'optimisation d'une con guration aile-fuselage supersonique. Un module de conception inverse, AIDA , fournit a partir d'une signature acoustique cible au sol a faible bang sonique la g eom etrie de la con- guration correspondante. Pour am eliorer a la fois les performances acoustique et a erodynamique, des techniques d'optimisation directes de forme sont utilis ees pour r esoudre des probl emes d'optimisation mono et multi- disciplinaires et une analyse d etaill ee est r ealis ee. Des strat egies innovantes bas ees sur la coop eration et les jeux comp etitifs sont en n appliqu ees au probl eme d'optimisation multidisciplinaire o rant une alternative aux algorithmes traditionnels MDO . L'hybridation de ces deux strat egies ouvre la voie a une nouvelle fa con d'explorer le front de Pareto de mani ere e cace. Celle-ci est mise en application sur un cas pratique.
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Hildyard, M. L. "The fluid mechanics of filters." Thesis, University of Leeds, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.233871.
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Figueroa, Leonardo E. "Deterministic simulation of multi-beaded models of dilute polymer solutions." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:4c3414ba-415a-4109-8e98-6c4fa24f9cdc.
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We study the convergence of a nonlinear approximation method introduced in the engineering literature for the numerical solution of a high-dimensional Fokker--Planck equation featuring in Navier--Stokes--Fokker--Planck systems that arise in kinetic models of dilute polymers. To do so, we build on the analysis carried out recently by Le~Bris, Leli\`evre and Maday (Const. Approx. 30: 621--651, 2009) in the case of Poisson's equation on a rectangular domain in $\mathbb{R}^2$, subject to a homogeneous Dirichlet boundary condition, where they exploited the connection of the approximation method with the greedy algorithms from nonlinear approximation theory explored, for example, by DeVore and Temlyakov (Adv. Comput. Math. 5:173--187, 1996). We extend the convergence analysis of the pure greedy and orthogonal greedy algorithms considered by Le~Bris, Leli\`evre and Maday to the technically more complicated situation of the elliptic Fokker--Planck equation, where the role of the Laplace operator is played out by a high-dimensional Ornstein--Uhlenbeck operator with unbounded drift, of the kind that appears in Fokker--Planck equations that arise in bead-spring chain type kinetic polymer models with finitely extensible nonlinear elastic potentials, posed on a high-dimensional Cartesian product configuration space $\mathsf{D} = D_1 \times \dotsm \times D_N$ contained in $\mathbb{R}^{N d}$, where each set $D_i$, $i=1, \dotsc, N$, is a bounded open ball in $\mathbb{R}^d$, $d = 2, 3$. We exploit detailed information on the spectral properties and elliptic regularity of the Ornstein--Uhlenbeck operator to give conditions on the true solution of the Fokker--Planck equation which guarantee certain rates of convergence of the greedy algorithms. We extend the analysis to discretized versions of the greedy algorithms.
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Goode, Peter Allan. "Momentum transfer across fluid-fluid interfaces in porous media." Thesis, Heriot-Watt University, 1991. http://hdl.handle.net/10399/847.
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Coffey, Christopher J. "The fluid mechanics of emptying boxes." Thesis, Imperial College London, 2006. http://hdl.handle.net/10044/1/11978.
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Connick, Owen. "The fluid mechanics of hybrid ventilation." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/39347.
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A low-energy ventilation system is often incorporated as one of the major energy saving measures in sustainable building design. These systems often employ a hybrid strategy in which mechanical equipment, governed by a computer controlled building management system, is used to assist or manage a naturally-driven airflow - the latter occurring due to the density difference between warm air inside and cooler air outside the room. Hybrid ventilation flows are poorly understood and the principal aim of the research was to enhance our understanding of the fluid mechanics through complementary theoretical and experimental modelling. The research begins by comparing solely natural and solely mechanical ventilation of a room. The hybrid ventilation of a room is then considered under the combined effect of naturally occurring and mechanically imposed pressure differences, in which a mechanical fan imposes a fixed airflow rate through one vent, thereby altering the natural pressure distribution. Simplified theoretical models, to describe the ventilation airflow rate through a room and the resulting mean air temperature, were developed for solely natural ventila- tion, solely mechanical ventilation and, finally, hybrid ventilation. At each stage the theoretical model was compared with results from small-scale experiments, and good agreement was demonstrated. From the theoretical investigation, the neutral pressure level emerged as a key pa- rameter in determining the characteristics of the ventilation airflow. Moreover, it was found that the airflow rate through an open vent can be controlled remotely by managing the position of the neutral pressure level, and that this can be achieved by varying the magnitude of the mechanically imposed airflow rate. Experimental investigations revealed that, as the neutral pressure level approached the plane of a vent, quasi-steady pulsing flows and bi-directional or exchange flows were observed. The complicated fluid dynamics involved in these flows provides inspiration for significant future work.
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PAULINO, RIVANIA HERMOGENES. "USING MULTIGRID TECHNIQUES ON FLUID MECHANICS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1997. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=19462@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOREste trabalho trata da solução numérica das equações de Navier-Stokes, na forma vorticidade-função corrente, via método das Diferenças Finitas e técnicas de aceleração baseadas no uso de malhas múltiplas. Embora outras opções tenham sido consideradas, a que melhor funcionou tratou o problema de forma não acoplada: a solução da equação de vorticidade foi obtida pela uso desta aceleração e a solução da equação de função corrente, uma equação puramente elíptica, foi resolvida via método das relaxações sucessivas. O código desenvolvido foi aplicado a diversos problemas, inclusive ao problema da cavidade com tampa móvel, em diversos números de Reynolds, típico no teste de simuladores em Dinâmica dos Fluidos. Foram testados um método clássico (armazenamento da correção) e o método FAZ (Full Approximation Storage). Os resultados obtidos mostram claramente os ganhos computacionais obtidos na formulação escolhida. Expressando em percentual, valores com 80 por cento de ganho foram obtidos se comparados os resultados do método multigrid com o método iterativo básico utilizado (S.O.R.), indicando o potencial do uso desta técnica para problemas mais complexo incluindo aqueles em coordenadas generalizadas.
This works deals with the numerical solution of the Navier-Stokes equations, written in the stream function-vorticity form, by the finite difference method and acceleration techniques using multiple meshes. Although other solution schemes have been investigated, best results were obtained by treating the problem in a non-coupled form: the solution for the vorticity equation was obtained by the multigrid method and the solution of the streamfunction equation, which is purely elliptic, was solved by the S.O.R. (Successive over relaxation method). The computer code was applied to several problems, including the wall driven problem considering a wide range of Reynolds numbers, which is a typical benchmark problem for testing fluid-dynamic simulations. The classical method (storage of the correction) and the methos FAS (Full Approximation Storage) have been tested. The results obtained clearly show that a very efficient computational scheme has been achieved with the multigrid method. For example, when comparing this method with the basic S.O.R. method, relative gains in the order of 80 per cent have been obtained. This indicates that the present technique has potential use in more complicated fluid dynamics problems including those involving generalized coordinates.
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Heimerdinger, Daniel John. "Fluid mechanics in a magnetoplasmadynamic thruster." Thesis, Massachusetts Institute of Technology, 1988. http://hdl.handle.net/1721.1/34030.
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Woods, Andrew W. "Geophysical fluid flows." Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.306472.
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Boutounet, Marc. "Modèles asymptotiques pour la dynamique d'un film liquide mince." Phd thesis, Ecole nationale superieure de l'aeronautique et de l'espace, 2011. http://tel.archives-ouvertes.fr/tel-00777981.
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Dans cette thèse, nous proposons de décrire la dynamique d'un film liquide mince entraîné par un écoulement gazeux. Dans une première partie, nous montrons comment écrire des modèles à une équation, sur la hauteur, ou à deux équations, sur la hauteur et le débit, à partir des équations de Navier-Stokes en utilisant la méthode des développements asymptotiques. Nous étudions alors les propriétés des systèmes ainsi obtenus. Dans la deuxième partie, nous utilisons la même méthode pour étendre les modèles aux cas des écoulements sur une topographie quelconque mais aussi aux écoulements bi-couches à surface libre et les écoulements de deux fluides entre deux plaques. La dernière partie consiste en une étude numérique d'un écoulement cisaillé à l'aide du code SLOSH et d'une application d'un des modèles trouvé dans le cas de deux fluides superposés à surfaces libres.
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Belme, Anca. "Aerodynamique Instationnaire et Methode Adjointe." Phd thesis, Université Nice Sophia Antipolis, 2011. http://tel.archives-ouvertes.fr/tel-00671181.
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Cette thèse contribue à la simulation numérique des écoulements d'un fluide compressible modélisé par les équations de Euler et Navier-Stokes: étude d'un schéma d'ordre élévé basé sur une matrice de masse, modélisation des écoulement turbulents compressibles à très haut Reynolds, développement des estimateurs et correcteurs d'erreurs a posteriori et a priori, et adaptation de maillage anisotrope pour les fonctionnelles d'observation. Concernant la prédiction des écoulements turbulents, on s'est intéressé aux modèles hybrides de type RANS/LES comportant les nouveautés suivantes: traitement des tourbillons de grande échelle utilisant la formulation VMS (Variational Multi-Scale) et du RANS employé sur la paroi sur une distance imposée via une zone de protection conçue afin d'éviter le phénomène assez commun apelé "grid induced model depletion". Le niveau de viscosité du modèle VMS-LES est de plus controllé par un procédé de double filtre dynamique. La seconde partie concerne l'adaptation de maillage anisotrope pour mieux observer une fontionnelle d'observation. Les estimations a priori sont réalises pour le modèle des équations d'Euler et Navier-Stokes en instationnaire en 2D et 3D. A partir de ces estimations on sait définir les maillages optimaux au cours du calcul instationnaire, en fonction de l'état et de l'état adjoint. Le système d'optimalité est discrétisé et résolu à l'aide d'une méthode de point fixe instationnaire global, comportant une stratégie de stockage/recalcul pour le couplage état/ état adjoint. Des applications à la propagation d'ondes de choc et d'ondes acoustiques sont présentées.
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Gart, Sean William. "Interfacial fluid dynamics inspired by natural systems." Diss., Virginia Tech, 2016. http://hdl.handle.net/10919/64459.
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Many natural systems interact with the interface between air and liquids on a daily basis. Plants like the lotus that have self-cleaning leaf surfaces and animals that intake fluids in a variety of ways are all examples of these systems. Plants and animals exploit interfacial fluid dynamics in a variety of ways to survive in numerous harsh environments. In this thesis, five studies, inspired by natural interactions with interfaces are presented.
The first study explores the influence of surface wettability in the dynamics of beams struck by water droplets. This study is inspired by raindrop-leaf interaction in nature. We characterize beam behavior after impact using a simple ODE and also find that a hydrophobic cantilever experiences reduced average torque over time than a cantilever with a hydrophilic surface.
In the second study we investigate the fluid dynamics of how dogs lap water with their tongue. Dogs lap because they have incomplete cheeks and cannot suck. When lapping, a dog's tongue pulls a liquid column from the bath, suggesting that the hydrodynamics of column formation are critical to understanding how dogs drink. We measured lapping in nineteen dogs and used the results to generate a physical model of the tongue's interaction with the air-fluid interface. These experiments help to explain how dogs exploit the fluid dynamics of the generated column. The results demonstrate that effects of acceleration govern lapping frequency, which suggests that dogs curl the tongue to create a larger liquid column. Comparing lapping in dogs and cats reveals that, despite similar morphology, these carnivores lap in different physical regimes: a high-acceleration regime for dogs and a low-acceleration regime for cats.
In the third study how bats drink on the wing is investigated. Bats are unique in nature in that they are one of the only animals that ingest fluids during non-hovering flight. This behavior has the advantage that bats can drink and maintain flight while hunting for food. We find that bats simply extend the tongue and drag it on the water surface while flying. The bats ingest water that coats the inside of the mouth and tongue after removal from a water bath. Bats also change their wing-beat pattern to avoid hitting the water.
We investigate the crown splash instability formed when a rounded rod impacts a fluid bath. The crown splash has been widely studied; however, it has not been seen in the configuration we present. When a rounded rod impacts water, it displaces fluid, and that fluid forms a lamella that climbs up the side of the rod. Depending on the speed of impact, rod size, and other fluid parameters an instability similar to a crown splash forms. In this study, we characterize the growth of the fluid lamella along with the wavelength of the instability.
Finally, we investigate the dynamics of squeezed fluids inspired by clapping wet hands. When water splashes, numerous water droplets, rather than fluid threads, are dispersed. This squeezing motion of the hands makes the fluid in between eject and eventually break into drops. In this study, the trajectory of a rim formed by fluid squeezed between two plates is measured and captured by a theoretical model. Additionally, the spacial distribution of the rim perturbation is predicted using Rayleigh-Plateau instability theory.Ph. D.
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Sakatani, Yuho. "Relativistic viscoelastic fluid mechanics and the entropic formulation of continuum mechanics." 京都大学 (Kyoto University), 2012. http://hdl.handle.net/2433/157762.
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Nugent, Charles Patrick. "Studies of fluid interfaces." Thesis, Queen's University Belfast, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.317468.
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Marshall, G. S. "Muiticomponent fluid flow computation." Thesis, Teesside University, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384659.
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Brereton, Clive. "Fluid mechanics of high velocity fluidised beds." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/28629.
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This thesis project studied a number of aspects relating to the fluid, mechanics of circulating fluidised beds. Studies of the macrostructure of a 9.3 m high x .15 m dia. riser showed a strong dependence of one important macroscopic descriptor, the density profile, upon the geometry of the gas/solids exit and the location of the solids return. It was found that abrupt exits promoted inertial solids separation from the conveying gas which generated strong internal circulation patterns and high slip velocities.
Microstructural studies, in support of the macrostructural investigation, and using a needle capacitance probe, showed how the radial density profile develops with height causing a gradual density decay. The structure, characterised by an "intermittency index," was strongly radially non-uniform at all locations in the lower regions of the column with pronounced aggregation or clustering at the highest densities. However, the cluster-like structures present at the base rapidly gave way to a more dilute core-annular type flow slightly further up the column.
This radially non-uniform structure was used to explain a number of macroscopic phenomena. These included the effects of exit type, solids return location, secondary air addition and gas mixing. The results of the various studies, drawn together, allow fast fluidisation to be defined tentatively with respect to its relationships to choking, pneumatic transport, and other fluidisation regimes.
Separate studies were performed to examine gas mixing and the transition to turbulent fluidisation. The gas residence time distribution was found to be substantially different from plug flow and could be characterised crudely by a two-zone model. The turbulent transition was found to be gradual, but nonetheless a transition, although a developed turbulent zone did not exist until well beyond transport conditions.Applied Science, Faculty of
Chemical and Biological Engineering, Department of
Graduate
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Lister, John Ronald. "Density-driven flows in geological fluid mechanics." Thesis, University of Cambridge, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328831.
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Archer, Andrew John. "Statistical mechanics of soft core fluid mixtures." Thesis, University of Bristol, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.288269.
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FOINY, DAMIEN. "COUPLED SYSTEMS IN MECHANICS: FLUID STRUCTURE INTERACTIONS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2017. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=32283@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE EXCELENCIA ACADEMICA
As interações fluido-estrutura são muito comuns na engenharia mecânica e civil porque muitas estruturas, como pontes, plataformas de petróleo, linhas de transmissão ou turbinas eólicas, estão diretamente em contato com um fluido, que pode ser o ar, no caso de vento, ou água, que irá perturbar a estrutura através de ondas. Um papel importante do engenheiro é prevenir a falha da estrutura devido às instabilidades criadas pelas interações fluidoestrutura. Este trabalho apresentará em primeiro lugar todos os conceitos básicos necessários para o estudo de problemas de interação fluido-estrutura. Assim, é realizada uma análise dimensional visando classificar os problemas de fluido-estrutura. A classificação é baseada na velocidade reduzida, e algumas conclusões sobre as conseqüências das interações fluido-estrutura podem ser feitas em termos de estabilidade ou, o que é mais interessante, de instabilidade. De fato, usando modelos simplificados, pode-se mostrar instabilidades estáticas e dinâmicas, induzidas por fluxo, que podem ser críticas para a estrutura. As partes finais do trabalho apresentarão uma estrutura não-linear específica, uma ponte suspensa. Primeiro, a formulação de um modelo simplificado unidimensional é explicada e, em seguida, através de uma discretização por elementos finitos, é realizado um estudo dinâmico. Além disso, algumas conclusões são apresentadas sobre a dinâmica das pontes suspensas. A última parte deste trabalho apresenta um método que foi uma importante fonte de publicação para nós, o método de decomposição regular.
Fluid-structure interactions are very common in mechanical and civil engineering because many structures, as bridges, offshore risers, transmission lines or wind turbines are directly in contact with a fluid, which can be air, which will be source of wind, or water, which will perturb the structure through waves. An important role of the engineer is to prevent structure failure due to instabilities created by the fluid-structure interactions. This work will first present all the basic concepts needed for the study of fluid-structure interaction problems. Thus, a dimensional analysis of those problems is performed and also all the equations governing such cases are presented. Then, thanks to the dimensional analysis made, a classification of problems, namely based on the reduced velocity, can be done and some conclusions concerning the consequences of the fluid-structure interactions can be drawn in terms of stability or, which is more interesting, instability. Indeed, using simplified models one can show static and dynamic flow-induced instabilities that may be critical for the structure. The final parts of the work will present a specific non-linear structure, a suspension bridge. First the formulation of a simplified one-dimensional model is explained and then, through a finite element discretization, a dynamical study is performed. Also, some conclusions are made concerning the dynamic of suspension bridges. The last part of this work presents a method that was an important source of publication for us, the Smooth Decomposition method.
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Smith, Andrew. "The fluid mechanics of embryonic nodal cilia." Thesis, University of Birmingham, 2013. http://etheses.bham.ac.uk//id/eprint/4626/.
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Symmetry breaking of the left-right body axis is a crucial step in development for many vertebrate species. In many this is initiated with a directional cilia-driven fluid flow in the organising structure. This work focuses on the mouse and the zebrafish organising structures, the node and Kupffer's vesicle, wherein cilia perform a tilted rotation producing an asymmetric flow. Using singularities of Stokes flow, slender body theory and the boundary integral equation, a computational model of flow in the mouse node for a range of cilia configurations simulating developmental stages is developed and run on the University of Birmingham's cluster, BlueBEAR. The results show the emergence of a directional flow as the cilia tilt increases. To model the Kupffer's vesicle the regularised boundary integral equation is used with a mesh representation of the entire domain to investigate potential cilia mechanisms that produce the observed flow as there is not a consensus. The results show that a combination of the experimental observations could be a sufficient mechanism. This model is expanded using observations of cilia with two rotation frequencies which are incorporated by allowing such cilia to ‘wobble’. This wobble accentuates the asymmetric flow in wildtype embryos and diminishes it in mutant embryos. All of these results agree well with experiment suggesting that vertebrates develop a combination of rotation mechanisms in their organising structures before an appropriate symmetry breaking flow is established.
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Pegler, Samuel Santeri. "The fluid mechanics of ice-shelf buttressing." Thesis, University of Cambridge, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.608122.
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Jarvis, Richard Allan. "Crystallization and melting in geological fluid mechanics." Thesis, University of Cambridge, 1991. https://www.repository.cam.ac.uk/handle/1810/275236.
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Vella, Dominic Joseph Robert. "The fluid mechanics of floating and sinking." Thesis, University of Cambridge, 2007. https://www.repository.cam.ac.uk/handle/1810/221845.
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This thesis is concerned with the fluid mechanics of floating and sinking. More specifically, the majority of this thesis considers the role played by surface tension in allowing dense objects to float. We first derive the conditions under which objects can float at an interface between two fluids. We obtain the conditions on density and size for various objects to float and show that being 'super-hydrophobic' does not generally help small, dense objects to float. Super-hydrophobicity does, however, dramatically reduce the energy required to remove an object from the interface. We then show that two floating objects can sink if they come into close proximity with one another. We extend this to show that a raft consisting of many interfacial objects can become arbitrarily large without sinking, providing that its density is below a critical value. Above this critical value, there is a threshold size at which sinking occurs. We then consider the surface tension dominated impact of an object onto a liquid-gas interface. We determine a similarity solution, valid shortly after impact, for the shape of the interface and study the asymptotic properties of the capillary waves generated by impact. We also show how the interfacial deformation slows down the impacting body. We use a boundary integral simulation to study the motion at later times and determine the conditions under which the object either sinks or is trapped by the surface. We find that for an object of a given weight there is a threshold impact speed above which it sinks. We study the waterlogging of a floating porous body as a model for the waterlogging of the pumice 'rafts' that often form on bodies of open water after a volcanic eruption. We study the inflow of water that is driven by capillary suction and hydrostatic pressure imbalances, and determine the time taken for this inflow to cause the object to sink. Finally, we study the effects of a natural slope on the spreading of carbon dioxide sequestered into aquifers. We use laboratory models and numerical techniques to study the spreading of the resulting gravity current. Initially the current spreads axisymmetrically, while at later times it spreads predominantly along any slope in the overlying cap rock. We show that in industrial settings the time scale over which this asymmetry develops is typically a few years. This effect may have important practical implications since the current propagates faster in the asymmetric state.
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Omnès, Florian. "Geometry optimization applied to incompressible fluid mechanics." Thesis, Sorbonne université, 2018. http://www.theses.fr/2018SORUS278.
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Cette thèse de mathématiques appliquées est consacrée à la modélisation et à l'exploration de techniques numériques d'optimisation de la forme d'objets au contact de fluides. Le premier chapitre est consacré à un algorithme d'optimisation géométrique mis en œuvre dans le logiciel optiflow, dans le cas où le bord à optimiser est associé à des conditions de non-glissement. L'implémentation est mise en ligne et accompagnée d'une notice d'utilisation. Il est ainsi possible de l'utiliser pour des applications de la vie réelle, par exemple pour l'optimisation de la géométrie d'un pipeline, de conduits de climatisation, etc. Dans le second chapitre, nous décrivons une façon de modéliser l'écoulement fluide à travers une aquaporine. Après avoir précisé et motivé le modèle fluide, nous prouvons l'existence d'une forme optimale pour le critère d'énergie dissipée par le fluide. Les conditions de bord de glissement partiel font apparaître des difficultés dans le calcul de sensibilité, nous présentons un traitement numérique spécifique pour y remédier. Enfin, plusieurs exemples numériques sont présentés et commentésThis applied mathematics thesis is dedicated to the modelling and exploration of numerical geometry optimization techniques. The first chapter is dedicated to a geometry optimization algorithm implemented in optiflow, in the case where the boundary to optimize is associated to no-slip conditions. The implementation is online and comes with a manual. It is therefore possible to use it for real-life applications such as pipeline or air conditioning, etc. In the second chapter, I describe a way to model fluid flow through an aquaporine. After making the fluid model precise, the existence of an optimal shape for the dissipated energy criterion is proven. Partial boundary conditions make appear difficulties in the sensitivity analysis of the optimization problem. A specific numerical treatment is presented to overcome this difficulty. Finally, several numerical examples are presented and commented
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Hatoum, Hoda. "Fluid Mechanics of Transcatheter Aortic Valve Replacement." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1541781379381912.
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Santavicca, Jeffery W. "Fluid mechanics tutorials in GKS supported FORTRAN." Thesis, This resource online, 1992. http://scholar.lib.vt.edu/theses/available/etd-09122009-040300/.
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Rathgen, Helmut. "Superhydrophobic surfaces from fluid mechanics to optics." Göttingen Sierke, 2008. http://d-nb.info/991741188/04.
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Ryan, Barry James Saffman P. G. "Lie-Poisson integrators in Hamiltonian fluid mechanics /." Diss., Pasadena, Calif. : California Institute of Technology, 1993. http://resolver.caltech.edu/CaltechETD:etd-10242005-152235.
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MAHMUD, MD READUL. "Fluid Mechanics in Innovative Food Processing Technology." Doctoral thesis, Politecnico di Torino, 2016. http://hdl.handle.net/11583/2641365.
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Generally, food industries employ traditional technologies and bulk devices for mixing, aeration, oxidation, emulsification and encapsulation. These processes are characterized by high energy consumption and result in high cost product, with limited diversity and usually with non-competitive quality. Moreover, the byproduct is also high. In recent years immense efforts have been dedicated to overcome these issues and major advances in food engineering have come from transfer and adaptation of knowledge from related fields such as chemical and mechanical engineering. It is well known that the majority of elements contribute to transport properties, physical and rheological behavior, texture and sensorial traits of foods are in micro-level. In this context invention at microscopic level is of critical importance to improve the existing foods quality while targeting also the development of new products.
Therefore, microfluidics has a significant role in future design, preparation and characterization of food micro-structure. The diminutive scale of the flow channels in microfluidic systems increases the surface to volume ratio and is therefore advantageous for many applications. Furthermore, high quality food products can be manufactured by means of innovative microfluidic technology characterized by less energy consumption and a continuous process in substitution to the problematic batch one.
To meet these challenges, this work is focused on main two tasks: (i) efficient micromixing, and (ii) production of microbubbles and microdroplets.
Firstly, two novel 3D split and recombine (SAR) micromixers are designed on an extensive collection of established knowledge. Mixing characteristics of two species were elucidated via experimental and numerical studies associated with microchannels at various inlet flow-rate ratios for a wide range of Reynolds numbers (1-100); at the same time, results are compared with two well-known micromixers. It was found that performances of the mixers are significantly affected by their design, inlet flow-rate ratios and Reynolds numbers. The proposed micromixers show better efficiency (more than 90%) in all examined range of Reynolds numbers than the well-known basic mixers at each desired region; the required pressure-drop is also significantly less than that of the previous mixers. Furthermore, numerical residence time distribution (RTD) was also explored, which successfully predicts the experimental results. In a word, the presented new micromixers have advantages of high efficiency, low pressure-drop, simple fabrication, easy integration and ease for mass production.
Secondly, four micro-devices are designed for the mono-dispersed droplets and bubbles generation. Two different experimental setups were used to create water droplet in silicone oil (W/O) and air bubble in silicone oil (A/O) for continuous flow rate from 10 ml/h to 230 ml/h. The mean size of droplet and bubble as well as frequency of generation can be controlled by dispersed and continuous flow rate. Besides, squeezing and dripping flow regimes are observed inside the four devices over a broad range of Capillary numbers: 0.01~0.18. Among the examined four devices, T-1 and T-2 provide smaller droplet (100 µm) and higher production rate. Furthermore, negative pressure setup provides more robust bubble generation but positive pressure yields better production rate. In addition, droplet and bubble diameter is about four times less than the microchannel dimension, therefore small droplet and bubble can be generated spending less energy.
In summary, the investigation in this dissertation reflects that both SAR micromixers and micro-devices are very efficient and can be applied to meet the growing demands of food industries. The first part of the thesis, chapters 1 to 5, addresses state of art, design, experimental technique and results of micromixers. The second part, chapters 6 to 9, presents background, construction of devices, tests and results related to the production of microdroplets and microbubbles. Finally, chapter 10 summaries the whole presented work.
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Tendani, Adrien. "Effet régularisant, controlabilité et anisotropie en mécanique des fluides." Electronic Thesis or Diss., Bordeaux, 2024. http://www.theses.fr/2024BORD0214.
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Dans cette thèse, nous nous intéressons principalement aux propriétés dissipatives de certaines EDP, notamment issues de la mécanique des fluides. Les deux grandes problématiques à travers lesquelles ces propriétés sont étudiées sont la théorie de Cauchy (effet régularisant, caractère bien posé, solution faible et unicité faible-forte) et la théorie du contrôle (contrôlabilité exacte aux trajectoires et caractérisation des états atteignables). Dans ce travail, plusieurs modèles sont étudiées : le système de Navier-Stokes- Korteweg, qui décrit un fluide compressible avec des effets de capillarité induisant de la dispersion ; le système de Navier-Stokes sous-Riemannien sur les groupes de Lie stratifiés, où le système présente des propriétés d’anisotropie liées à la structure sous- Riemannienne ; et l’équation de la chaleur semi-linéaire, pour laquelle les états atteignables sont étudiés. Les outils utilisés sont variés : analyse de Fourier (sur l’espace euclidien et les groupes de Lie), inégalités de Carleman, calcul para-différentiel anisotrope, quantification des groupes de Lie nilpotents et analyse complexeIn this thesis, we are mainly interested in the dissipative properties of certain PDEs, particularly from fluid mechanics. The two major issues through which these properties are studied are: Cauchy’s theory (regularizing effect, well-posed character, weak solution and weakstrong uniqueness) and the control theory (exact controllability of trajectories and characterization of achievable states). In this work, several models are studied: the Navier-Stokes-Korteweg system, which describes a compressible fluid with capillarity effects which inducing dispersion; the sub- Riemannian Navier-Stokes system on stratified Lie groups, where the system exhibits anisotropy properties linked to the sub-Riemannian structure; and the semi-linear heat equation, for which the achievable states are studied. The tools used are varied: Fourier analysis (on Euclidean space and Lie groups), Carleman inequalities, anisotropic para-differential calculation, quantification of nilpotent Lie groups and complex analysis
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Scotte, Anton, and Emil Zeidlitz. "Investigating the Numerical Applicability of Analogies between Quantum Mechanics and Fluid Mechanics." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-276578.
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Oswell, J. E. "Fluid loading with mean flow." Thesis, University of Cambridge, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239158.
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Liu, Ying. "Measurements of jet velocity in unstratified and stratified fluids." Thesis, Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/19474.
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Mallone, Kevin Charles. "A more robust wall model for use with the two-equation turbulence model." Thesis, University of Hertfordshire, 1995. http://hdl.handle.net/2299/14149.
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The applicability of computational fluid dynamics (CFD) modelling schemes to turbulent wall-bounded flows is a matter of concern. In the near-wall region of bounded flows, the standard high Reynolds number k-e model is not valid and requires the use of empirical wall models to mimic the behaviour of this region. A theoretical study of the physics of prevalent wall modelling techniques showed that the velocity distribution took no account of the pressure gradient. To determine the effect of this shortcoming, a typical transient three-dimensional flow was analysed using current CFD methods and the results compared with experimental flow measurements. Consideration of these results showed that the 'traditional' wall model was unable to replicate observed flow features in the near-wall region: further analysis of the computational results confirmed that these poor flow predictions arose from the inability of the model to consider local pressure gradient effects. Consequently, a strong case was made for a more robust wall model for use in conjunction with the standard high Reynolds number k-e model. A number of boundary layer analyses were reviewed and Coles' law of the wake (1956) presented as a viable candidate for the development of a new wall modelling scheme. In theory, Coles' law (1956) provides a description of bounded flows under arbitrary pressure gradients up to the point of near-separation and may be extended to the study of reversed flows. A generic algorithm for Coles' law was prepared and used to study the fundamental test cases of U-bend and backward facing step flows. In a comparison between documented experimentation, 'conventional' CFD modelling and Coles' law models of these flows, the Coles' law model was shown to provide a viable alternative to 'traditional' schemes. Consequently, the Coles' law model of the near-wall region, being valid for pressure-driven flows, offers an extension to the range of flows for which the standard high Reynolds number k-e model may be used.
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Pêgo, João Pedro Gomes Moreira. "Advanced fluid mechanics studies of ship propulsion systems." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=983754853.
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Chikatamarla, Shyam S. "Hierarchy of lattice Boltzmann models for fluid mechanics /." Zürich : ETH, 2008. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=17893.
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Wake, Amanda Kathleen. "Modeling Fluid Mechanics in Individual Human Carotid Arteries." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/7562.
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In the interest of furthering the understanding of hemodynamics, this study has developed a method for modeling fluid mechanics behavior in individual human carotid arteries. A computational model was constructed from magnetic resonance (MR) data of a phantom carotid bifurcation model, and relevant flow conditions were simulated. Results were verified by comparison with previous in vitro experiments. The methodology was extended to create subject-specific carotid artery models from geometry data and fluid flow boundary conditions which were determined from MR and phase contrast MR (PCMR) scans of human subjects. The influence of subject-specific boundary conditions on the flow field was investigated by comparing a model based on measured velocity boundary conditions to a model based on the assumption of idealized velocity boundary conditions.
It is shown that subject-specific velocity boundary conditions in combination with a subject-specific geometry and flow waveform influence fluid flow phenomena associated with plaque development. Comparing a model with idealized Womersley flow boundary conditions to a model with subject-specific velocity boundary conditions demonstrated the importance of employing inlet and flow division data obtained from individual subjects in order to predict accurate, clinically relevant, fluid flow phenomena such as low wall shear stress areas and negative axial velocity regions. This study also illustrates the influence of the bifurcation geometry, especially the flow divider position, with respect to the velocity distribution of the common carotid artery on the development of flow characteristics. Overall it is concluded that accurate geometry and velocity measurements are essential for modeling fluid mechanics in individual human carotid arteries for the purpose of understanding atherosclerosis in the carotid artery bifurcation.