Dissertations / Theses on the topic 'Perfect Fluids'
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Rowlingson, Robert R. "A class of perfect fluids in general relativity." Thesis, Aston University, 1990. http://publications.aston.ac.uk/12060/.
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This thesis is concerned with exact solutions of Einstein's field equations of general relativity, in particular, when the source of the gravitational field is a perfect fluid with a purely electric Weyl tensor. General relativity, cosmology and computer algebra are discussed briefly. A mathematical introduction to Riemannian geometry and the tetrad formalism is then given. This is followed by a review of some previous results and known solutions concerning purely electric perfect fluids. In addition, some orthonormal and null tetrad equations of the Ricci and Bianchi identities are displayed in a form suitable for investigating these space-times. Conformally flat perfect fluids are characterised by the vanishing of the Weyl tensor and form a sub-class of the purely electric fields in which all solutions are known (Stephani 1967). The number of Killing vectors in these space-times is investigated and results presented for the non-expanding space-times. The existence of stationary fields that may also admit 0, 1 or 3 spacelike Killing vectors is demonstrated. Shear-free fluids in the class under consideration are shown to be either non-expanding or irrotational (Collins 1984) using both orthonormal and null tetrads. A discrepancy between Collins (1984) and Wolf (1986) is resolved by explicitly solving the field equations to prove that the only purely electric, shear-free, geodesic but rotating perfect fluid is the Godel (1949) solution. The irrotational fluids with shear are then studied and solutions due to Szafron (1977) and Allnutt (1982) are characterised. The metric is simplified in several cases where new solutions may be found. The geodesic space-times in this class and all Bianchi type 1 perfect fluid metrics are shown to have a metric expressible in a diagonal form. The position of spherically symmetric and Bianchi type 1 space-times in relation to the general case is also illustrated.
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Daher, Ivo Martins. "Soluções das equações de campo de Einstein para fluidos perfeitos estáticos com simetria esférica." Universidade do Estado do Rio de Janeiro, 2008. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=1012.
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Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorNesta dissertação, procuramos soluções exatas das equações de campo de Einstein em Relatividade Geral que descrevem um fluido perfeito em um espaço-tempo estático com simetria esférica. A técnica utilizada para encontrar essas soluções é o algoritmo de Kovacic, que pode ser aplicado a equações diferenciais ordinárias lineares e homogêneas de segunda ordem com coeficientes racionais. Esse algoritmo é capaz de nos dar soluções fechadas em termos de funções liouvillianas, se tal equação tiver esse tipo de solução. Para esse fim, vários sistemas de coordenadas foram investigados até encontrar o que fosse mais adequado à aplicação do algoritmo. Impondo que a função da métrica 11 g seja racional, ficamos com uma equação diferencial linear e homogênea de segunda ordem que tem coeficientes racionais. Nesse trabalho, as formas arbitradas foram: g11=-A/4x x-z1/x-Z1, g11=-A/4x x-z1/(x-Z1)(x-Z2), g11=-A/4x (x-z1) (x-z2)/x-Z1 e g11= -A/4x (x-z1) (x-z2)/ 4x(x-Z1) (x-Z2) onde x é uma coordenada espacial da métrica e Α, z1 , z2 , Z1 e Z2 são parâmetros dos modelos. Depois de obter soluções analíticas, verificamos se elas satisfazem determinadas condições físicas e, então, poderiam ser utilizadas como modelos de estrelas de nêutrons sem rotação (estrelas de alta densidade).
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Sandin, Patrik. "The asymptotic states of perfect fluid cosmological models." Licentiate thesis, Karlstad : Faculty of Technology and Science, Physics, Karlstads universitet, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-4713.
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Radford, James E. Burdick Joel Wakeman. "Symmetry, reduction and swimming in a perfect fluid /." Diss., Pasadena, Calif. : California Institute of Technology, 2003. http://resolver.caltech.edu/CaltechETD:etd-06042003-181857.
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Kitchingham, David William. "Generating techniques in vacuum and stiff perfect fluid cosmologies." Thesis, Queen Mary, University of London, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.337947.
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Mitsuda, Eiji, and Akira Tomimatsu. "Breakdown of self-similar evolution in homogeneous perfect fluid collapse." American Physical Society, 2006. http://hdl.handle.net/2237/8842.
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Messenger, Paul Henry. "Rotating perfect fluid bodies in Einstein's general theory of relativity." Thesis, University of South Wales, 2005. https://pure.southwales.ac.uk/en/studentthesis/rotating-perfect-fluid-bodies-in-einsteins-general-theory-of-relativity(127bc15d-ff0d-4f8e-80fe-351c24273697).html.
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The study of rotating astrophysical bodies is of great importance in understanding the structure and development of the Universe. Rotating bodies, are not only of great interest in their own right, for example pulsars, but they have also been targeted as prime possible sources of gravitational waves, currently a topic of great interest. The ability of general relativity to describe the laws and phenomena of the Universe is unparalleled, but however there has been little success in the description of rotating astrophysical bodies. This is not due to a lack of interest, but rather the sheer complexity of the mathematics. The problem of the complexity may be eased by the adoption of a perturbation technique, in that a spherically symmetric non-rotating fluid sphere described by Einstein's equations is endowed with rotation, albeit slowly, and the result is expressed and analysed using Taylor's series. A further consideration is that of the exterior gravitational field, which must be asymptotically flat. It has been shown from experiment that, in line with the prediction of general relativity, a rotating body does indeed drag space-time around with it. This leads to the conclusion that the exterior gravity field must not only be asymptotically flat, but must also rotate. The only vacuum solution to satisfy these conditions is the Kerr metric. This work seeks to show that an internal rotating perfect fluid source may be matched to the rotating exterior Kerr metric using a perturbation technique up to and including second order parameters in angular velocity. The equations derived, are used as a starting point in the construction of such a perfect fluid solution, and it is shown how the method may be adapted for computer implementation.
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Dorostkar, Ali. "Applications of the perfectly matched layers in a discontinuous fluid media." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-176541.
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In this thesis we study the applications of the PML in a multi-layered media. The PML is constructed for the scalar wave equation and the convergence and stability of the continuous problem is studied using the normal mode analysis. A high order accurate semi-discrete problem is constructed by approximating the spatial derivatives with high order finite difference operators satisfying the summation-by-parts properties. To have a stable semi-discrete approximation of the problem, we impose boundary conditions as well as interface conditions using the simultaneous approximation term technique. In order to gain accuracy, a transformed interface condition is constructed for the PML. The semi-discrete problem is approximated using second order accurate central difference scheme. To achieve higher order accuracy we modify the time marching scheme to eliminate truncation errors. Numerical experiments are presented showing that using the proposed transformed interface conditions, higher order of accuracy and convergence are achieved.
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Hajj-Boutros, Joseph. "Détermination des nouvelles solutions exactes d’Einstein dans le cas intérieur." Paris 6, 1987. http://www.theses.fr/1987PA066421.
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Ensemble de travaux réalisé dans le cadre de la théorie de la relativité générale. La métrique de l'espace-temps adoptée est à symétrie bien précise pour simplifier dans la mesure du possible les équations du champ d’Einstein. Dans le cadre de la symétrie sphérique statique et non statique, nous avons obtenu de nouvelles solutions des équations du champ (cas intérieur). Dans le cas de la symétrie plane, nous avons pu engendrer plusieurs nouvelles solutions statiques et non statiques. Nous avons mis au point de nouvelles solutions du type cosmologique. L'espace-temps utilise étant essentiellement homogène, nous avons pu étudier le caractère non isotropique de la singularité initiale. Les conditions physiques ont été respectées. Dans le cas des solutions cosmologiques nous avons pu construire un modèle rendant compte de l'évolution possible de notre univers depuis son état initial radiatif et singulier jusqu'à son état actuel. Nous avons trouvé une solution globalement régulière dans le cadre de la symétrie cylindrique. La technique du calcul utilise a consisté dans la plupart des cas à linéariser les équations du champ.
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Loeschcke, Christian [Verfasser]. "On the relaxation of a variational principle for the motion of a vortex sheet in perfect fluid / Christian Loeschcke." Bonn : Universitäts- und Landesbibliothek Bonn, 2013. http://d-nb.info/1044868945/34.
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Reho, Riccardo. "Il tensore energia-impulso per un fluido perfetto in relatività ristretta e generale." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/14520/.
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Con questo lavoro si vuole discutere la connessione esistente tra l' equazione di continuità e l'equazione del moto di un fluido perfetto in Relatività Ristretta e Generale.
Dapprima forniremo una breve introduzione sulle basi della Relatività Ristretta , introducendo il tensore energia-impulso ed analizzando in maniera specifica tale tensore per un fluido perfetto, ricavandone le equazioni del moto.
Forniremo un secondo esempio di tensore Energia-Impulso per la materia incoerente.
Conclusa questa argomentazione ci concentreremo sulla Relatività Generale, analizzandone i principi che sono alla base e privilegiando tra questi il Principio di Covarianza Generale come linea guida per le argomentazioni logiche.
In maniera analoga a quanto fatto per la Relatività Ristretta riprenderemo la discussione per il tensore energia-impulso per un fluido perfetto dal punto di vista della Relatività Generale , soffermandoci nel caso di equilibrio idrostatico.
Sempre nel contesto della Relatività Generale verrà in ultima analisi discusso il concetto di fluido incoerente e moto geodetico.
L'ultimo capitolo è dedicato ad una appendice matematica nel quale vengono ricordati alcuni risultati dell'analisi tensoriali utili nel seguire i calcoli effettuati.
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Carigi, Giulia. "Modello iperbolico del fluido perfetto barotropico e il problema dell'instabilita gravitazionale secondo Jeans." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2013. http://amslaurea.unibo.it/5923/.
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In questa tesi proponiamo una rivisitazione del classico criterio di Jeans per l'instabilità gravitazionale di una nube di gas autogravitante, tenendo conto anche degli effetti viscosi e della presenza di una forza di Coriolis.
Si dimostra che l'aggiunta di tali presenze, pur non alterando la soglia critica di Jeans, è generalmente stabilizzante.
Infine si evidenzia un'interessante analogia, per modellamento matematico, tecniche e terminologie, fra il collasso gravitazionale e quello chemiotattico
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Косторний, Сергій Дмитрович, Сергей Дмитриевич Косторной, Serhii Dmytrovych Kostornyi, and М. В. Хилько. "Модель течения идеальной жидкости, учитывающая особенности граничных условий реальной жидкости." Thesis, Сумский государственный университет, 2013. http://essuir.sumdu.edu.ua/handle/123456789/31453.
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При проектировании гидравлических машин (ГМ) турбин и насосов выбор геометрических размеров и формы проточной части (ПЧ) с учетом взаимного влияния всех элементов ПЧ для получения высоких энергетических и динамических характеристик представляет собой сложную научно-техническую задачу. Она решается, в основном, на основании опыта и интуиции конструктора с использованием упрощенных математических моделей течения рабочей жидкости в ПЧ, одна из которых приводится в данной работе.
При цитировании документа, используйте ссылку http://essuir.sumdu.edu.ua/handle/123456789/31453
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Bhuddi, Ajit. "Approche ondulatoire pour la description numérique du comportement vibroacoustique large bande des conduites avec fluide interne." Thesis, Tours, 2015. http://www.theses.fr/2015TOUR4046/document.
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Dans ce travail, une méthode basée sur les éléments finis ondulatoires - Wave Finite Elements (WFE) - est proposée en vue de prédire le rayonnement acoustique de conduites axisyrnétriques de longueur finie, comportant un fluide interne, et immergées dans un fluide acoustique de dimensions infinies. La condition de rayonnement de Sommerfeld est prise en compte en entourant le fluide extérieur d'un perfectly matched layer (PML), c'est-à-dire une couche d'éléments absorbants dans laquelle les ondes acoustiques incidentes sont progressivement amorties. Dans le cadre de l'approche WFE, la conduite, le fluide qu'elle contient, le fluide extérieur et le PML constituent un guide d'ondes multiphysique qui est discrétisé par un maillage éléments finis périodique, et peut être ainsi modélisé comme un assemblage de sous-systèmes identiques de faible longueur. Une base d'ondes se propageant le long de la conduite, calculée à partir du modèle éléments finis d'un sous-système, est utilisée afin de prédire le comportement vibroacoustique de guides d'ondes de longueur finie à moindre coût. Des simulations numériques sont réalisées pour des cas de conduites de structure homogène ou multi-couches. La précision et l'efficacité de la méthode WFE sont clairement établies en comparaison avec la méthode des éléments finis conventionnelleIn this work, a wave finite element (WFE) method is proposed to predict the sound radiation of finite axisymmetric fluid-filled pipes immersed in an external acoustic fluid of infinite extent, The Sommerfeld radiation condition is taken into account by means of a perfectly matched layer (PML) around the external fluid. Within the WFE framework, the fluid-filled pipe, the surrounding fluid and the PML constitute a multiphysics waveguide that is discretized by means of a periodic finite element mesh, and is treated as an assembly of identical subsystems of small length. Wave modes are computed from the FE model of a multi-physics subsystem and used as a representation basis to assess the vibroacoustic behavior of the finite waveguide at a low computational cost. Numerical experiments are carried out in the cases of axisymmetric pipes of either homogeneous or multi-layered crosssections, The accuracy and efficiency of the proposed approach are dearly highlighted in comparison with the conventional FE method
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Damamme, Gilles. "Contribution à la théorie hydrodynamique de l'onde de détonation dans les explosifs condensés." Poitiers, 1987. http://www.theses.fr/1987POIT2034.
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Etude des proprietes hydrodynamiques des ondes de detonation utilisant trois niveaux successifs de modelisation. Dans l'hypothese d'une zone de reactions infiniment mince, on s'interesse a l'acceleration d'une onde de detonation convergente. Lorsque la zone de reaction est tres petite et que l'onde de detonation est stable et suivie d'une detente, on montre qu'elle est regie par une relation celerite-courbure. On propose un modele de zone de reactions ainsi qu'une modelisation de l'amorcage par choc de la detonation faisant intervenir des discontinuites partiellement reactives
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Luppé, Francine. "Contribution a l'etude de l'onde de scholte-stoneley a differentes interfaces fluide parfait/solide elastique." Paris 7, 1987. http://www.theses.fr/1987PA077222.
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Holgersson, David. "Lanczos potentialer i kosmologiska rumtider." Thesis, Linköping University, Department of Mathematics, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-2582.
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We derive the equation linking the Weyl tensor with its Lanczos potential, called the Weyl-Lanczos equation, in 1+3 covariant formalism for perfect fluid Bianchi type I spacetime and find an explicit expression for a Lanczos potential of the Weyl tensor in these spacetimes. To achieve this, we first need to derive the covariant decomposition of the Lanczos potential in this formalism. We also study an example by Novello and Velloso and derive their Lanczos potential in shear-free, irrotational perfect fluid spacetimes from a particular ansatz in 1+3 covariant formalism. The existence of the Lanczos potential is in some ways analogous to the vector potential in electromagnetic theory. Therefore, we also derive the electromagnetic potential equation in 1+3 covariant formalism for a general spacetime. We give a short description of the necessary tools for these calculations and the cosmological formalism we are using.
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Radermacher, Katharina Maria. "Strong Cosmic Censorship and Cosmic No-Hair in spacetimes with symmetries." Doctoral thesis, KTH, Matematik (Avd.), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-220400.
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This thesis consists of three articles investigating the asymptotic behaviour of cosmological spacetimes with symmetries arising in Mathematical General Relativity. In Paper A and B, we consider spacetimes with Bianchi symmetry and where the matter model is that of a perfect fluid. We investigate the behaviour of such spacetimes close to the initial singularity ('Big Bang'). In Paper A, we prove that the Strong Cosmic Censorship conjecture holds in non-exceptional Bianchi class B spacetimes. Using expansion-normalised variables, we further show detailed asymptotic estimates. In Paper B, we prove similar estimates in the case of stiff fluids. In Paper C, we consider T2-symmetric spacetimes satisfying the Einstein equations for a non-linear scalar field. To given initial data, we show global existence and uniqueness of solutions to the corresponding differential equations for all future times. In the special case of a constant potential, a setting which is equivalent to a linear scalar field on a background with a positive cosmological constant, we investigate in detail the asymptotic behaviour towards the future. We prove that the Cosmic No-Hair conjecture holds for solutions satisfying an additional a priori estimate, an estimate which we show to hold in T3-Gowdy symmetry.Denna avhandling består av tre artiklar som undersöker det asymptotiska beteendet hos kosmologiska rumstider med symmetrier som uppstår i Matematisk Allmän Relativitetsteori. I Artikel A och B studerar vi rumstider med Bianchi symmetri och där materiemodellen är en ideal fluid. Vi undersöker beteendet av sådana rumstider nära ursprungssingulariteten ('Big Bang'). I Artikel A bevisar vi att den Starka Kosmiska Censur-förmodan håller för icke-exceptionella Bianchi klass B-rumstider. Med hjälp av expansions-normaliserade variabler visar vi detaljerade asymptotiska uppskattningar. I Artikel B visar vi liknande uppskattningar för stela fluider. I Artikel C betraktar vi T2-symmetriska rumstider som uppfyller Einsteins ekvationer för ett icke-linjärt skalärfält. För givna begynnelsedata visar vi global existens och entydighet av lösningar till motsvarande differentialekvationer för all framtid. I det speciella fallet med en konstant potential, en situation som motsvarar ett linjärt skalärfält på en bakgrund med en positiv kosmologisk konstant, undersöker vi i detalj det asymptotiska beteendet mot framtiden. Vi visar att den Kosmiska Inget-Hår-förmodan håller för lösningar som uppfyller en ytterligare a priori uppskattning, en uppskattning som vi visar gäller i T3-Gowdy-symmetri.
QC 20171220
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Young, Roland Michael Brendon. "Predictability of a laboratory analogue for planetary atmospheres." Thesis, University of Oxford, 2009. http://ora.ox.ac.uk/objects/uuid:b4f483a6-437c-4914-b94e-cb04d996b337.
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The thermally-driven rotating annulus is a laboratory experiment used to study the dynamics of planetary atmospheres under controlled and reproducible conditions. The predictability of this experiment is studied by applying the same principles used to predict the atmosphere. A forecasting system for the annulus is built using the analysis correction method for data assimilation and the breeding method for ensemble generation. The results show that a range of flow regimes with varying complexity can be accurately assimilated, predicted, and studied in this experiment. This framework is also intended to demonstrate a proof-of-concept: that the annulus could be used as a testbed for meteorological techniques under laboratory conditions. First, a regime diagram is created using numerical simulations in order to select points in parameter space to forecast, and a new chaotic flow regime is discovered within it. The two components of the framework are then used as standalone algorithms to measure predictability in the perfect model scenario and to demonstrate data assimilation. With a perfect model, regular flow regimes are found to be predictable until the end of the forecasts, and chaotic regimes are predictable over hundreds of seconds. There is a difference in the way predictability is lost between low-order chaotic regimes and high-order chaos. Analysis correction is shown to be accurate in both regular and chaotic regimes, with residual velocity errors about 3-8 times the observational error. Specific assimilation scenarios studied include information propagation from data-rich to data-poor areas, assimilation of vortex shedding observations, and assimilation over regime and rotation rate transitions. The full framework is used to predict regular and chaotic flow, verifying the forecasts against laboratory data. The steady wave forecasts perform well, and are predictable until the end of the available data. The amplitude and structural vacillation forecasts lose quality and skill by a combination of wave drift and wavenumber transition. Amplitude vacillation is predictable up to several hundred seconds ahead, and structural vacillation is predictable for a few hundred seconds.
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Peynaud, Emilie. "Rayonnement sonore dans un écoulement subsonique complexe en régime harmonique : analyse et simulation numérique du couplage entre les phénomènes acoustiques et hydrodynamiques." Thesis, Toulouse, INSA, 2013. http://www.theses.fr/2013ISAT0019/document.
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La thèse porte sur la simulation, en régime fréquentiel, du rayonnement acoustique en écoulement subsonique quelconque et dans un domaine infini. L'approche choisie s'appuie sur la résolution d'un système équivalent aux équations d'Euler linéarisées : le modèle de Galbrun. Ce modèle repose sur une représentation mixte Lagrange-Euler et aboutit à une équation dont l'unique inconnue est la perturbation du déplacement Lagrangien. Une des difficultés de l'approche de Galbrun est qu'une discrétisation directe de cette équation par une méthode d'éléments finis standard n'est pas stable. Un moyen de contourner cet obstacle est d'écrire une équation augmentée en ajoutant une nouvelle inconnue, le rotationnel du déplacement, appelée par abus vorticité. Cette approche conduit à un système qui couple une équation de type équation des ondes avec une équation de transport en régime fréquentiel. Et elle permet l'utilisation de couches parfaitement adaptées (PML) pour borner le domaine de calcul. La première partie du manuscrit est dédiée à l’étude de l’équation de transport harmonique et de sa résolution numérique, en particulier par un schéma de type Galerkin discontinu. Un des points délicats est lié au caractère oscillant des solutions de l'équation. Une fois cette étape franchie, la résolution du problème de propagation acoustique a été abordée. Une approximation basée sur l'utilisation d'éléments finis mixtes continus-discontinus avec couches parfaitement adaptées (PML) a été étudiée. En particulier, les caractères bien posés des problèmes continu et discret ainsi que la convergence du schéma numérique ont été démontrés sous certaines conditions sur l'écoulement porteur. Enfin, une mise en œuvre a été effectuée. Les résultats montrent la validité de cette approche mais aussi sa pertinence dans le cas d'écoulements complexes, voire d'écoulements dits instablesThis thesis deals with the numerical simulation of time harmonic acoustic propagation in an arbitrary mean flow in an unbounded domain. Our approach is based on an equation equivalent to the linearized Euler equations called the Galbrun equation. It is derived from a mixed Eulerian-Lagrangian formulation and results in a single equation whose only unknown is the perturbation of the Lagrangian displacement. A direct solution using finite elements is unstable but this difficulty can be overcome by using an augmented equation which is constructed by adding a new unknown, the vorticity, defined as the curl of the displacement. This leads to a set of equations coupling a wave like equation with a time harmonic transport equation which allows the use of perfectly matched layers (PML) at artificial boundaries to bound the computational domain. The first part of the thesis is a study of the time harmonic transport equation and its approximation by means of a discontinuous Galerkin scheme, the difficulties coming from the oscillating behaviour of its solutions. Once these difficulties have been overcome, it is possible to deal with the resolution of the acoustic propagation problem. The approximation method is based on a mixed continuous-Galerkin and discontinuous-Galerkin finite element scheme. The well-posedness of both the continuous and discrete problems is established and the convergence of the approximation under some mean flow conditions is proved. Finally a numerical implementation is achieved and numerical results are given which confirm the validity of the method and also show that it is relevant in complex cases, even for unstable flows
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Mthethwa, Thulani Richard. "New classes of exact solutions for charged perfect fluids." Thesis, 2012. http://hdl.handle.net/10413/10533.
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We investigate techniques to generate new classes of exact solutions to the Einstein-
Maxwell field equations which represent the gravitational field of charged perfect fluid
spherically symmetric distributions of matter. Historically, a large number of solutions
have been proposed but only a small number have been demonstrated to satisfy
elementary conditions for physical acceptability. Firstly we examine the case of the
constant density and constant electric field charged fluid sphere and show empirically
that such configurations of matter are unlikely to exist as basic physical requirements
are violated. We then make an ansatz relating the fluid's electric field intensity to
one of the gravitational potentials thereby simplifying the system of partial differential
equations. This prescription yields an algorithmic process to generate new classes of
exact solutions. We present a number of new solutions and comment on their viability
as stellar models. Graphical plots generated by symbolic software of the main dynamical
and geometrical quantities verify that one of our models is suitable to represent
a physically relevant distribution of charged matter in the form of a spherical shell.
In particular, positive definiteness of energy density and pressure are guaranteed, a
pressure free hypersurface denoting the boundary of the star exists, the sound speed
is shown to be sub-luminal and the energy conditions are satisfied everywhere in the
interior of the star.Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2012.
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Mewalal, Narenee. "Exact solutions for perfect fluids conformal to a Petrov type D spacetime." Thesis, 2011. http://hdl.handle.net/10413/6288.
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Radford, James Edward. "Symmetry, Reduction and Swimming in a Perfect Fluid." Thesis, 2003. https://thesis.library.caltech.edu/2431/1/Radford_je_2003.pdf.
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This thesis presents a geometric picture of a deformable body in a perfect fluid and a way to approximate its dynamics and the motion, resulting from cyclic shape deformations, of the body and, interestingly, the fluid as well. Emphasis is placed on the group structure of the configuration space of the body fluid system and the resulting symmetry in their equations of motion. Symmetry is also used to reduce a series expansion for the flow of a time dependent vector field in order to obtain a novel expansion for the path-ordered exponential. This can be used to approximate holonomy, or geometric phase, in a principal bundle when its evolution is governed by a connection on the bundle and it is subject to periodic shape inputs. Simple models for swimming in and the stirring of a perfect fluid are proposed and examined.
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Masood-ul-Alam, A. K. M. "The topology of asymptotically Euclidean static perfect fluid space-time." Phd thesis, 1985. http://hdl.handle.net/1885/136573.
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In this thesis we prove that a (geodesically) complete, asymptotically
Euclidean, static perfect fluid space-time with connected fluid reglon and
satisfying the time-like convergence condition lS diffeomorphic to R³ x R .
It is believed that such a space-time would be spherically symmetric at
least for physically reasonable conditions on the density function p and
the pressure function p .
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Tichý, Jakub. "Kvalitativní vlastnosti řešení rovnic mechaniky tekutin." Doctoral thesis, 2014. http://www.nusl.cz/ntk/nusl-332562.
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Qualitative properties of solutions to equations of fluid mechanics Mgr. Jakub Tichý Supervisor: doc. Mgr. Petr Kaplický, Ph.D. Department: Department of Mathematical Analysis Abstract This thesis is devoted to the boundary regularity of weak solutions to the system of nonlinear partial differential equations describing incompressible flows of a certain class of generalized Newtonian fluids in bounded domains. Equations of motion and continuity equation are complemented with perfect slip boundary conditions. For stationary generalized Stokes system in Rn with growth condi- tion described by N-function Φ the existence of the second derivatives of velocity and their regularity up to the boundary are shown. For the same system of equa- tions integrability of velocity gradients is proven. Lq estimates are obtained also for classical evolutionary Stokes system via interpolation-extrapolation scales. Hölder continuity of velocity gradients and pressure is shown for evolutionary generalized Navier-Stokes equations in R2 . Keywords Generalized Stokes and Navier - Stokes equations, incompressible fluids, perfect slip boundary conditions, regularity up to the boundary
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D'Ambroise, Jennie. "Generalized EMP and Nonlinear Schrodinger-type Reformulations of Some Scaler Field Cosmological Models." 2010. https://scholarworks.umass.edu/open_access_dissertations/225.
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We show that Einstein’s gravitational field equations for the Friedmann- Robertson-Lemaître-Walker (FRLW) and for two conformal versions of the Bianchi I and Bianchi V perfect fluid scalar field cosmological models, can be equivalently reformulated in terms of a single equation of either generalized Ermakov-Milne- Pinney (EMP) or (non)linear Schrödinger (NLS) type. This work generalizes or presents an alternative to similar reformulations published by the authors who inspired this thesis: R. Hawkins, J. Lidsey, T. Christodoulakis, T. Grammenos, C. Helias, P. Kevrekidis, G. Papadopoulos and F.Williams. In particular we cast much of these authors’ works into a single framework via straightforward derivations of the EMP and NLS equations from a simple linear combination of the relevant Einstein equations. By rewriting the resulting expression in terms of the volume expansion factor and performing a change of variables, we obtain an uncoupled EMP or NLS equation that is independent of the imposition of additional conservation equations. Since the correspondences shown here present an alternative route for obtaining exact solutions to Einstein’s equations, we reconstruct many known exact solutions via their EMP or NLS counterparts and show by numerical analysis the stability properties of many solutions.
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Mbarek, Saoussen. "Les bulles de masse négative dans un espace de de Sitter." Thèse, 2013. http://hdl.handle.net/1866/10429.
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Nous étudions différentes situations de distribution de la matière d’une bulle de masse négative. En effet, pour les bulles statiques et à symétrie sphérique, nous commençons par l’hypothèse qui dit que cette bulle, étant une solution des équations d’Einstein, est une déformation au niveau d’un champ scalaire. Nous montrons que cette idée est à rejeter et à remplacer par celle qui dit que la bulle est formée d’un fluide parfait. Nous réussissons à démontrer que ceci est la bonne distribution de matière dans une géométrie Schwarzschild-de Sitter, qu’elle satisfait toutes les conditions et que nous sommes capables de résoudre numériquement ses paramètres de pression et de densité.We study different situations of matter distribution of a negative mass bubble. For the case of static and spherically symmetric bubbles, we start with the hypothesis saying that this kind of bubble, being a solution of Einstein equations, is a deformation of scalar field. We show that this idea must be rejected and replaced by another saying that the bubble is formed by a perfect fluid. We succeed to demonstrate that this is the proper matter distribution within Schwarzschild-De Sitter geometry, that it satisfies all conditions and that we’re capable of resolving numerically its parameters of pressure and density.
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Zingan, Valentin Nikolaevich. "Discontinuous Galerkin Finite Element Method for the Nonlinear Hyperbolic Problems with Entropy-Based Artificial Viscosity Stabilization." Thesis, 2012. http://hdl.handle.net/1969.1/ETD-TAMU-2012-05-10845.
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This work develops a discontinuous Galerkin finite element discretization of non- linear hyperbolic conservation equations with efficient and robust high order stabilization built on an entropy-based artificial viscosity approximation.
The solutions of equations are represented by elementwise polynomials of an arbitrary degree p > 0 which are continuous within each element but discontinuous on the boundaries. The discretization of equations in time is done by means of high order explicit Runge-Kutta methods identified with respective Butcher tableaux.
To stabilize a numerical solution in the vicinity of shock waves and simultaneously preserve the smooth parts from smearing, we add some reasonable amount of artificial viscosity in accordance with the physical principle of entropy production in the interior of shock waves. The viscosity coefficient is proportional to the local size of the residual of an entropy equation and is bounded from above by the first-order artificial viscosity defined by a local wave speed. Since the residual of an entropy equation is supposed to be vanishingly small in smooth regions (of the order of the Local Truncation Error) and arbitrarily large in shocks, the entropy viscosity is almost zero everywhere except the shocks, where it reaches the first-order upper bound.
One- and two-dimensional benchmark test cases are presented for nonlinear hyperbolic scalar conservation laws and the system of compressible Euler equations. These tests demonstrate the satisfactory stability properties of the method and optimal convergence rates as well. All numerical solutions to the test problems agree well with the reference solutions found in the literature.
We conclude that the new method developed in the present work is a valuable alternative to currently existing techniques of viscous stabilization.