Dissertations / Theses: 'Euler equations of motion'

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Ricca, Renzo L. "Geometric and topological aspects of vortex filament motion." Thesis, University of Cambridge, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319585.

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Schneider, David. "Nonholonomic Euler-Poincaré equations and stability in Chaplygin's sphere /." Thesis, Connect to this title online; UW restricted, 2000. http://hdl.handle.net/1773/5783.

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Williams, Rhys L. "Exact, asymptotic and numerical solutions to certain steady, axisymmetric, ideal fluid flow problems in IRÂ³." Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299262.

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Zendegan, Saeid. "3D trajectory optimization of an acrobatic air race with direct collocation method and quaternion equations of motion." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18025/.

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The main purpose of this thesis is to develop a software to optimize the 3D air race trajectory. Air race competitions such as Red Bull are becoming very popular around the world, but behind this eye catching competitions there are always engineers supporting every team to help their pilots to make the fastest lap time in order to win the competition. Nowadays, by the help of advanced computing systems and proficient optimization algorithm, engineers are able to model the trajectory of these air races and optimize them offline. These optimized trajectories are handed to the pilots before the competition, in order to help them train themselves in a simulator and then with a real aircraft. In this thesis the equations of motion (EOM) of point-mass model is used for optimization. The first approach was with the EOM based on Euler angles. As we know from flight dynamics, with the Euler angles we will have a singularity in our equations when the aircraft is experiencing the ±π/2 pitch angle. In order to avoid the singularity in the Euler case, we switch to EOM based on Quaternions. Although the quaternions are used for the optimization of the trajectory, we will also represent the results for Euler based EOM. The software used to develop the code for this optimization is MATLAB 2016b. Algorithm is proposed and implemented by the author. Build-in optimization function (FMINCON) is used to optimize the trajectory based on the proposed algorithm.

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Hassainia, Zineb. "Dynamique des tourbillons pour quelques modèles de transport non-linéaires." Thesis, Rennes 1, 2015. http://www.theses.fr/2015REN1S016/document.

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Cette thèse est consacrée à l'étude théorique de quelques modèles d'évolution non-linéaires issus de la mécanique des fluides. Nous distinguons trois parties indépendantes. La première partie de la thèse traite essentiellement de l'existence des poches de tourbillon en rotation uniforme (appelées aussi V-states) pour un modèle quasi-géostrophique non visqueux. Notre étude est répartie sur deux chapitres où les poches présentent des structures topologiques différentes. Dans le premier chapitre nous étudions le cas simplement connexe et nous validons l'existence de ces structures dans un voisinage du tourbillon de Rankine en utilisant des techniques de bifurcation. Dans le deuxième chapitre nous abordons le cas doublement connexe où la poche admet un seul trou. Plus précisément, proche d'un anneau donné, nous décrivons cette famille par des branches dénombrables bifurquant de cet anneau à certaines valeurs explicites des vitesses angulaires liées aux fonctions de Bessel. Notre étude théorique a été complétée par des simulations numériques portant sur les V-states limites et un bon nombre de constatations ont été formulées ouvrant la porte à de nouvelles perspectives de recherche. La seconde partie concerne l'étude du problème de Cauchy pour le système de Boussinesq non visqueux 2D avec des données initiales de type Yudovich. Le problème est dans un certain sens critique à cause de quelques termes comportant la transformée de Riesz dans la formulation tourbillon-densité. Nous donnons une réponse positive pour une sous-classe comprenant les poches de tourbillon régulières et singulières. Dans la dernière partie nous analysons le problème de la limite incompressible pour les équations d'Euler isentropiques 2D associées à des données initiales très mal préparées et pour lesquelles les tourbillons ne sont pas forcément bornés mais appartiennent plutôt à des espaces de type ''BMO'' à poids. On utilise principalement deux ingrédients: d'un côté les estimations de Strichartz pour contrôler la partie acoustique. D'un autre côté, on se sert de la structure de transport compressible du tourbillon et on démontre une estimation de propagation linéaire dans l'esprit d'un travail récent de Bernicot et Keraani mené dans le cas incompressible
In this dissertation, we are concerned with the study of some non-linear evolution models arising in fluid mechanics. We distinguish three independent parts. The first part of the thesis deals with the existence of the rotating vortex patches (called also V-states) for an inviscid quasi-geostrophic model. Our study is divided into two chapters dealing with different topological structures of the V-states. In the first chapter we study the simply connected case and we prove the existence of such structures in a neighborhood of the Rankine vortices by using the bifurcation theory. In the second chapter we discuss the doubly connected case where the patches admit only one hole. More precisely, close to a given annulus we describe this family by countable branches bifurcating from this annulus at some explicit angular velocities related to Bessel functions of the first kind. Our theoretical study was completed by numerical simulations on the limiting V-states and a number of interesting numerical observation were formulated opening new research perspectives. The second part of the thesis concerns the local well-posedness theory for the inviscid Boussinesq system with rough initial data. The problem is in some sense critical due to some terms involving Riesz transforms in the vorticity-density formulation. We give a positive answer for a special sub-class of Yudovich data including smooth and singular vortex patches. In the last part we address the problem of the incompressible limit for the 2D isentropic fluids associated to ill-prepared initial data and for which the vortices are not necessarily bounded and belong to some weighted BMO spaces. We mainly use two ingredients: On one hand, the Strichartz estimates to control the acoustic part and prove that it does not contribute for low Mach number. On the other hand, we use the transport compressible structure of the vorticity and we establish a linear propagation estimate in the spirit of a recent work of Bernicot and Keraani conducted in the incompressible case. The first part of the thesis deals with the existence of the rotating vortex patches (called also V-states) for an inviscid quasi-geostrophic model. Our study is divided into two chapters dealing with different topological structures of the V-states. In the first chapter we study the simply connected case and we prove the existence of such structures in a neighborhood of the Rankine vortices by using the bifurcation theory. In the second chapter we discuss the doubly connected case where the patches admit only one hole. More precisely, close to a given annulus we describe this family by countable branches bifurcating from this annulus at some explicit angular velocities related to Bessel functions of the first kind. Our theoretical study was completed by numerical simulations on the limiting V-states and a number of interesting numerical observation were formulated opening new research perspectives. The second part of the thesis concerns the local well-posedness theory for the inviscid Boussinesq system with rough initial data. The problem is in some sense critical due to some terms involving Riesz transforms in the vorticity-density formulation. We give a positive answer for a special sub-class of Yudovich data including smooth and singular vortex patches. In the last part we address the problem of the incompressible limit for the 2D isentropic fluids associated to ill-prepared initial data and for which the vortices are not necessarily bounded and belong to some weighted BMO spaces. We mainly use two ingredients: On one hand, the Strichartz estimates to control the acoustic part and prove that it does not contribute for low Mach number. On the other hand, we use the transport compressible structure of the vorticity and we establish a linear propagation estimate in the spirit of a recent work of Bernicot and Keraani conducted in the incompressible case

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Sekerci, Yadigar. "Some recent simulation techniques of diffusion bridge." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-5749.

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We apply some recent numerical solutions to diffusion bridges written in Iacus (2008). One is an approximate scheme from Bladt and S{\o}rensen (2007), another one, from Beskos et al (2006), is an algorithm which is exact: no numerical error at given grid points!

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Schulze, Bert-Wolfgang, and Nikolai N. Tarkhanov. "Euler solutions of pseudodifferential equations." Universität Potsdam, 1998. http://opus.kobv.de/ubp/volltexte/2008/2521/.

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We consider a homogeneous pseudodifferential equation on a cylinder C = IR x X over a smooth compact closed manifold X whose symbol extends to a meromorphic function on the complex plane with values in the algebra of pseudodifferential operators over X. When assuming the symbol to be independent on the variable t element IR, we show an explicit formula for solutions of the equation. Namely, to each non-bijectivity point of the symbol in the complex plane there corresponds a finite-dimensional space of solutions, every solution being the residue of a meromorphic form manufactured from the inverse symbol. In particular, for differential equations we recover Euler's theorem on the exponential solutions. Our setting is model for the analysis on manifolds with conical points since C can be thought of as a 'stretched' manifold with conical points at t = -infinite and t = infinite.

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Chterental, Igor. "Two-dimensional Euler equations solver." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape8/PQDD_0018/MQ45872.pdf.

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9

Paisley, M. F. "Finite volume methods for the steady Euler equations." Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.375309.

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French, A. D. "Solution of the Euler equations on Cartesian grids." Thesis, Cranfield University, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.303684.

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Yildirim, B. Gazi. "A global preconditioning method for the Euler equations." Master's thesis, Mississippi State : Mississippi State University, 2003. http://library.msstate.edu/etd/show.asp?etd=etd-07152003-164237.

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Skipper, Jack. "Energy conservation for the Euler equations with boundaries." Thesis, University of Warwick, 2018. http://wrap.warwick.ac.uk/106455/.

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In this thesis we study energy conservation for the incompressible Euler equations that model non-viscous fluids. This has been a topic of interest since Onsager conjectured regularity conditions for solutions to conserve energy in 1949. Very recently the full conjecture has been resolved in the case without boundaries. We first perform a study of the different conditions used to ensure energy conservation for domains without boundaries. Results are presented in Chapter 2, as well as an analysis of the similarities between the weakest of these conditions and the conditions we use later with a boundary. We then study the time regularity in Chapter 3 and present a detailed proof for energy conservation without boundaries imposing the conditions ꭒ Ꞓ2 LꝪ (0; T ; L3 ) and Lim │y│→0 1│y│ ∫ ꓔ 0 ∫ │ꭒ(x + y) −u(x│3 dx dt = 0: In Chapters 4 and 5 we consider the easiest case of a at finite boundary corresponding to the domain T2x R+. In Chapter 4 we use an extension argument and impose a condition of continuity at the boundary to prove energy conservation under the conditions that ꭒ Ꞓ2 LꝪ (0; T ; L3 (T2x R+)), Lim │y│∫T0 T2∫∞ │u(x + y) . u(x)j3 dx3dx2dx1dt = 0; ꭒ ꞒL3 (0; T ; L∞ (T2 x[0;ẟ )) and u is continuous at the boundary. We then improve this result further by making it a local method in Chapter 5 and use a different definition of a weak solution where there is no pressure term involved. Chapter 6 considers various different definitions of weak solutions for the incompressible Euler equations on a bounded domain. We study the relations between these varying definitions with and without pressure terms. We then use the recent work of Bardos & Titi (2018), who showed energy conservation with pressure terms included, to get a condition for energy conservation when we consider a weak solution without reference to the pressure term.

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Bruner, Christopher William Stuteville. "Parallelization of the Euler Equations on Unstructured Grids." Diss., Virginia Tech, 1996. http://hdl.handle.net/10919/30397.

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Several different time-integration algorithms for the Euler equations are investigated on two distributed-memory parallel computers using an explicit message-passing paradigm: these are classic Euler Explicit, four-stage Jameson-style Runge-Kutta, Block Jacobi, Block Gauss-Seidel, and Block Symmetric Gauss-Seidel. A finite-volume formulation is used for the spatial discretization of the physical domain. Both two- and three-dimensional test cases are evaluated against five reference solutions to demonstrate accuracy of the fundamental sequential algorithms. Different schemes for communicating or approximating data that are not available on the local compute node are discussed and it is shown that complete sharing of the evolving solution to the inner matrix problem at every iteration is faster than the other schemes considered. Speedup and efficiency issues pertaining to the various time-integration algorithms are then addressed for each system. Of the algorithms considered, Symmetric Block Gauss-Seidel has the overall best performance. It is also demonstrated that using parallel efficiency as the sole means of evaluating performance of an algorithm often leads to erroneous conclusions; the clock time needed to solve a problem is a much better indicator of algorithm performance. A general method for extending one-dimensional limiter formulations to the unstructured case is also discussed and applied to Van Albada’s limiter as well as Roe’s Superbee limiter. Solutions and convergence histories for a two-dimensional supersonic ramp problem using these limiters are presented along with computations using the limiters of Barth & Jesperson and Venkatakrishnan — the Van Albada limiter has performance similar to Venkatakrishnan’s.
Ph. D.

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Tsuge, Naoki. "Spherically symmetric flow of the compressible Euler equations." 京都大学 (Kyoto University), 2004. http://hdl.handle.net/2433/147790.

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Hartmann, Ralf. "Adaptive finite element methods for the compressible Euler equations." [S.l. : s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=964933071.

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Latypov, Azat. "Numerical solution of Euler equations on streamline-aligned meshes." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0010/NQ52411.pdf.

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Elgindi, Tarek Mohamed. "Some Results on the Euler Equations for Incompressible Flow." Thesis, New York University, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3635128.

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The key purpose of this work is to study an array of problems related to the flow of an ideal fluid. Though the subject of mathematical fluid dynamics is quite old, there is still a great number of open problems--indeed open fields--that have not been solved and/or considered. At the heart of the study of the Euler equations is the non-locality, which is brought forth by the presence of the pressure term. In this thesis we will discuss some important features of the Euler equations including: well/ill posedness in critical spaces vis a vis the spontaneous formation of small scales as well as a study of the vanishing viscosity limit in critical spaces. We will also discuss two other related models: one from the study of active scalar equations and the other from viscoelasticity. The final chapter is about the vanishing viscosity limit for the free-boundary Navier Stokes equations with surface tension.

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Edwards, M. G. "Moving element methods with emphasis on the Euler equations." Thesis, University of Reading, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.378193.

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Dhaouadi, Firas. "An augmented lagrangian approach for Euler-Korteweg type equations." Thesis, Toulouse 3, 2020. http://www.theses.fr/2020TOU30139.

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On présente un modèle hyperbolique quasi-linéaire de premier ordre approximant les équations d'Euler-Korteweg (E-K), qui décrivent des écoulements de fluides compressibles dont l'énergie dépend du gradient de la densité. Le système E-K peut être vu comme les équations d'Euler-Lagrange d'un Lagrangien soumis à la conservation de la masse. Vu la présence du gradient de la densité dans le Lagrangien, des dérivées d'ordre élevé de la densité apparaissent dans les équations du mouvement. L'approche présentée ici permet d'obtenir un système d'équations hyperboliques qui approxime le système E-K. L'idée est d'introduire un nouveau paramètre d'ordre qui approxime la densité via une méthode de pénalisation classique. Le gradient de cette nouvelle variable remplace alors le gradient de la densité dans le Lagrangien, ce qui permet de construire le Lagrangien augmenté. Les équations d'Euler-Lagrange associées à celui-ci, sont des équations hyperboliques avec des termes sources raides et des vitesses de caractéristiques rapides. Ce système est analysé puis résolu numériquement en utilisant des schémas de type IMEX. En particulier, cette approche a été appliquée à l'équation de Schrödinger non-linéaire défocalisante (qui peut être réduite au système E-K via la transformée de Madelung), pour laquelle des comparaisons avec des solutions exactes et asymptotiques ont été faites, notamment pour des solitons gris et des ondes de choc dispersives. La même approche a été également appliquée aux équations de filmes minces avec capillarité, pour lesquelles une comparaison avec des résultats numériques de référence et des résultats expérimentaux a été faite. Il a été démontré que le modèle augmenté peut aussi bien s'appliquer pour des modèles dont le terme de capillarité est non-linéaire. Dans ce même cadre, une étude de gouttes stationnaires sur un substrat solide horizontal a été établie afin de classifier les profils possibles de gouttes selon leur énergie. Ceci a permis également de faire des comparaisons du modèle augmenté sur des solutions stationnaires. Enfin, une partie indépendante de ce travail est consacrée à l'étude des équations équivalentes associées aux schémas numériques, où l'on démontre que les conditions de stabilité qui dérivent d'une troncature de l'équation équivalente, n'a du sens que si la série correspondante dans l'espace de Fourier est convergente, sur les longueurs d'onde admissibles dans la pratique
An approximate first order quasilinear hyperbolic model for Euler-Korteweg (E-K) equations, describing compressible fluid flows whose energy depend on the gradient of density, is derived. E-K system can be seen as the Euler-Lagrange equations to a Lagrangian submitted to the mass conservation constraint. Due to the presence of the density gradient in the Lagrangian, one recovers high-order derivatives of density in the motion equations. The approach presented here permits us to obtain a system of hyperbolic equations that approximate E-K system. The idea is to introduce a new order parameter which approximates the density via a carefully chosen penalty method. The gradient of this new independent variable will then replace the original gradient of density in the Lagrangian, resulting in the so-called augmented Lagrangian. The Euler-Lagrange equations of the augmented Lagrangian result in a first order hyperbolic system with stiff source terms and fast characteristic speeds. Such a system is then analyzed and solved numerically by using IMEX schemes. In particular, this approach was applied to the defocusing nonlinear Schrödinger equation (which can be reduced to the E-K equations via the Madelung transform), for which a comparison with exact and asymptotic solutions, namely gray solitons and dispersive shock waves was performed. Then, the same approach was extended to thin film flows with capillarity, for which comparison of the numerical results with both reference numerical solutions and experimental results was performed. It was shown that the augmented model is also extendable to models with full nonlinear surface tension. In the same setting, a study of stationary droplets on a horizontal solid substrate was conducted in an attempt to classify droplet profiles depending on their energy forms. This also allowed to compare the augmented Lagrangian approach in the case of stationary solutions, and which showed excellent agreement with the reference solutions. Lastly, an independent part of this work is devoted to the study of modified equations associated to numerical schemes for stability purposes. It is shown that for a linear scheme, stability conditions which are obtained from a truncation of the associated modified equation, are only relevant if the corresponding series in Fourier space is convergent for the admissible wavenumbers

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Choi, Sang Keun. "A Cartesian finite-volume method for the Euler equations." Diss., Virginia Polytechnic Institute and State University, 1987. http://hdl.handle.net/10919/76511.

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A numerical procedure has been developed for the computation of inviscid flows over arbitrary, complex two-dimensional geometries. The Euler equations are solved using a finite-volume method with a non-body-fitted Cartesian grid. A new numerical formulation for complicated body geometries is developed in conjunction with implicit flux-splitting schemes. A variety of numerical computations have been performed to validate the numerical methodologies developed. Computations for supersonic flow over a flat plate with an impinging shock wave are used to verify the numerical algorithm, without geometric considerations. The supersonic flow over a blunt body is utilized to show the accuracy of the non-body-fitted Cartesian grid, along with the shock resolution of flux-vector splitting scheme. Geometric complexities are illustrated with the flow through a two-dimensional supersonic inlet with and without an open bleed door. The ability of the method to deal with subsonic and transonic flows is illustrated by computations over a non-lifting NACA 0012 airfoil. The method is shown to be accurate, efficient and robust and should prove to be particularly useful in a preliminary design mode, where flows past a wide variety of complex geometries can be computed without complicated grid generation procedures.
Ph. D.

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21

Cloke, Martin. "Vortical equilibria of the Euler equations : construction and stability." Thesis, Imperial College London, 2007. http://hdl.handle.net/10044/1/1276.

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22

Johansson, Stefan. "High order difference approximations for the linearized Euler equations." Licentiate thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-86306.

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The computers of today make it possible to do direct simulation of aeroacoustics, which is very computational demanding since a very high resolution is needed. In the present thesis we study issues of relevance for aeroacoustic simulations. Paper A considers standard high order difference methods. We study two different ways to apply boundary conditions in a stable way. Numerical experiments are done for the 1D linearized Euler equations. In paper B we develop difference methods which give smaller dispersion errors than standard central difference methods. The new methods are applied to the 1D wave equation. Finally in Paper C we apply the new difference methods to aeroacoustic simulations based on the 2D linearized Euler equations. Taken together, the methods presented here lead to better approximation of the wave number, which in turn results in a smaller L2-error than obtained by previous methods found in the literature. The results are valid when the problem is not fully resolved, which usually is the case for large scale applications.

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Sebastianutti, Marco. "Geodesic motion and Raychaudhuri equations." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18755/.

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The work presented in this thesis is devoted to the study of geodesic motion in the context of General Relativity. The motion of a single test particle is governed by the geodesic equations of the given space-time, nevertheless one can be interested in the collective behavior of a family (congruence) of test particles, whose dynamics is controlled by the Raychaudhuri equations. In this thesis, both the aspects have been considered, with great interest in the latter issue. Geometric quantities appear in these evolution equations, therefore, it goes without saying that the features of a given space-time must necessarily arise. In this way, through the study of these quantities, one is able to analyze the given space-time. In the first part of this dissertation, we study the relation between geodesic motion and gravity. In fact, the geodesic equations are a useful tool for detecting a gravitational field. While, in the second part, after the derivation of Raychaudhuri equations, we focus on their applications to cosmology. Using these equations, as we mentioned above, one can show how geometric quantities linked to the given space-time, like expansion, shear and twist parameters govern the focusing or de-focusing of geodesic congruences. Physical requirements on matter stress-energy (i.e., positivity of energy density in any frame of reference), lead to the various energy conditions, which must hold, at least in a classical context. Therefore, under these suitable conditions, the focusing of a geodesics "bundle", in the FLRW metric, bring us to the idea of an initial (big bang) singularity in the model of a homogeneous isotropic universe. The geodesic focusing theorem derived from both, the Raychaudhuri equations and the energy conditions acts as an important tool in understanding the Hawking-Penrose singularity theorems.

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Karlgaard, Christopher David. "Second-Order Relative Motion Equations." Thesis, Virginia Tech, 2001. http://hdl.handle.net/10919/34025.

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This thesis presents an approximate solution of second order relative motion equations. The equations of motion for a Keplerian orbit in spherical coordinates are expanded in Taylor series form using reference conditions consistent with that of a circular orbit. Only terms that are linear or quadratic in state variables are kept in the expansion. A perturbation method is employed to obtain an approximate solution of the resulting nonlinear differential equations. This new solution is compared with the previously known solution of the linear case to show improvement, and with numerical integration of the quadratic differential equation to understand the error incurred by the approximation. In all cases, the comparison is made by computing the difference of the approximate state (analytical or numerical) from numerical integration of the full nonlinear Keplerian equations of motion.
Master of Science

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C, Praveen. "Development and Application of Kinetic Meshless Methods for Euler Equations." Thesis, Indian Institute of Science, 2004. http://hdl.handle.net/2005/154.

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Meshless methods are a relatively new class of schemes for the numerical solution of partial differential equations. Their special characteristic is that they do not require a mesh but only need a distribution of points in the computational domain. The approximation at any point of spatial derivatives appearing in the partial differential equations is performed using a local cloud of points called the "connectivity" (or stencil). A point distribution can be more easily generated than a grid since we have less constraints to satisfy. The present work uses two meshless methods; an existing scheme called Least Squares Kinetic Upwind Method (LSKUM) and a new scheme called Kinetic Meshless Method (KMM). LSKUM is a "kinetic" scheme which uses a "least squares" approximation} for discretizing the derivatives occurring in the partial differential equations. The first part of the thesis is concerned with some theoretical properties and application of LSKUM to 3-D point distributions. Using previously established results we show that first order LSKUM in 1-D is positivity preserving under a CFL-like condition. The 3-D LSKUM is applied to point distributions obtained from FAME mesh. FAME, which stands for Feature Associated Mesh Embedding, is a composite overlapping grid system developed at QinetiQ (formerly DERA), UK, for store separation problems. The FAME mesh has a cell-based data structure and this is first converted to a node-based data structure which leads to a point distribution. For each point in this distribution we find a set of nearby nodes which forms the connectivity. The connectivity at each point (which is also the "full stencil" for that point) is split along each of the three coordinate directions so that we need six split (or half or one-sided) stencils at each point. The split stencils are used in LSKUM to calculate the split-flux derivatives arising in kinetic schemes which gives the upwind character to LSKUM. The "quality" of each of these stencils affects the accuracy and stability of the numerical scheme. In this work we focus on developing some numerical criteria to quantify the quality of a stencil for meshless methods like LSKUM. The first test is based on singular value decomposition of the over-determined problem and the singular values are used to measure the ill-conditioning (generally caused by a flat stencil). If any of the split stencils are found to be ill-conditioned then we use the full stencil for calculating the corresponding split flux derivative. A second test that is used is based on an accuracy measurement. The idea of this test is that a "good" stencil must give accurate estimates of derivatives and vice versa. If the error in the computed derivatives is above some specified tolerance the stencil is classified as unacceptable. In this case we either enhance the stencil (to remove disc-type degenerate structure) or switch to full stencil. It is found that the full stencil almost always behaves well in terms of both the tests. The use of these two tests and the associated modifications of defective stencils in an automatic manner allows the solver to converge without any blow up. The results obtained for a 3-D configuration compare favorably with wind tunnel measurements and the framework developed here provides a rational basis for approaching the connectivity selection problem. The second part of the thesis deals with a new scheme called Kinetic Meshless Method (KMM) which was developed as a consequence of the experience obtained with LSKUM and FAME mesh. As mentioned before the full stencil is generally better behaved than the split stencils. Hence the new scheme is constructed so that it does not require split stencils but operates on a full stencil (which is like a centered stencil). In order to obtain an upwind bias we introduce mid-point states (between a point and its neighbour) and the least squares fitting is performed using these mid-point states. The mid-point states are defined in an upwind-biased manner at the kinetic/Boltzmann level and moment-method strategy leads to an upwind scheme at the Euler level. On a standard 4-point Cartesian stencil this scheme reduces to finite volume method with KFVS fluxes. We can also show the rotational invariance of the scheme which is an important property of the governing equations themselves. The KMM is extended to higher order accuracy using a reconstruction procedure similar to finite volume schemes even though we do not have (or need) any cells in the present case. Numerical studies on a model 2-D problem show second order accuracy. Some theoretical and practical advantages of using a kinetic formulation for deriving the scheme are recognized. Several 2-D inviscid flows are solved which also demonstrate many important characteristics. The subsonic test cases show that the scheme produces less numerical entropy compared to LSKUM, and is also better in preserving the symmetry of the flow. The test cases involving discontinuous flows show that the new scheme is capable of resolving shocks very sharply especially with adaptation. The robustness of the scheme is also very good as shown in the supersonic test cases.

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26

Lu, Ming 1968. "A Lagrangian formulation of the Euler equations for subsonic flows /." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103268.

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This thesis presents a Lagrangian formulation of the Euler equations for subsonic flows. A special coordinate transformation is used to define the Lagrangian coordinates, namely the stream function and the Lagrangian distance, in function of the Cartesian coordinates. This Lagrangian formulation introduces two new geometry state variables, and a Lagrangian behavior parameter defining a pseudo-Lagrangian time used during the iteration procedure to obtain the solution for subsonic flows.
The eigenstructure and characteristics analysis for the new system of equations is based on a linear Jacobian matrix-mapping procedure, which starts from the well-known eigenstructure and characteristics in the Eulerian plane and uses the coordinate transformation to find their counterparts in the Lagrangian plane. This analysis studies the basic properties of the Euler equations in the Lagrangian formulation, such as hyperbolicity, homogeneity and rotational invariance. The Riemann problem in the Lagrangian plane is also studied. Those elements are used to construct the numerical scheme for solving the Euler equations in the Lagrangian formulation.
The numerical scheme is constructed using first and second-order dimensional-splitting with hybrid flux operators, based on flux vector splitting and Godunov methods, which include a 2-D Riemann solver in the Lagrangian plane. The numerical method is validated by comparing the present solutions with the results obtained with an Eulerian formulation for several internal flows.
This numerical method based on a Lagrangian formulation has also been extended for the solution of unsteady subsonic flows by using a dual time approach. The method validation in this case has been done by comparison with the Eulerian formulation solutions for several internal subsonic flows with oscillating boundaries.

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27

Zimmermann, Susanne A. "Properties of the method of transport for the Euler equations /." [S.l.] : [s.n.], 2001. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=13957.

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28

Clarke, Nicholas. "On high resolution finite difference schemes for the Euler equations." Thesis, Manchester Metropolitan University, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.315273.

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29

Nazarov, Murtazo. "An adaptive finite element method for the compressible Euler Equations /." Licentiate thesis, Stockholm : Skolan för datavetenskap och kommunikation, Kungliga Tekniska högskolan, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-10582.

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30

Huh, Kevin S. (Kevin Sangmin). "Computational aeroacoustics via linearized Euler equations in the frequency domain." Thesis, Massachusetts Institute of Technology, 1993. http://hdl.handle.net/1721.1/12713.

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31

Shapiro, Richard Abraham. "An adaptive finite element solution algorithm for the Euler equations." Thesis, Massachusetts Institute of Technology, 1988. http://hdl.handle.net/1721.1/35946.

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32

CAMALET, EUGENE. "Methodes de couplage euler-lagrange pour les equations d'euler-poisson." Paris 6, 1995. http://www.theses.fr/1995PA066276.

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Nous etudions dans une premiere partie la modelisation d'un plasma froid par les equations d'euler-poisson sans pression. La description lagrangienne des equations de convection permet de prendre en compte les phenomenes de deferlement (vitesses multivoques) apparaissant dans ce type de plasma. Les instabilites dues a la methode particule/maille sont resorbees par l'introduction d'une pression numerique. La seconde partie est consacree a la simulation de dispositifs semiconducteurs de type mesfet et diode par un modele hydrodynamique isotherme. Les collisions sont modelisees par un terme de relaxation en temps. On utilise la methode numerique developpee dans la premiere partie. Enfin on etudie un modele sans pression ou la vitesse derive d'un potentiel couple a l'equation de poisson. Dans le cadre gravitationnel on montre que les solutions sont caracterisees par un principe de minimisation de l'energie. Si la densite est bornee on montre que les vitesses gagnent en regularite dans le cadre electrostatique et gravitationnel

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33

Hu, Guanghui. "Numerical simulations of the steady Euler equations on unstructured grids." HKBU Institutional Repository, 2009. http://repository.hkbu.edu.hk/etd_ra/1106.

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34

Onur, Omer. "Effect Of Jacobian Evaluation On Direct Solutions Of The Euler Equations." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/2/1098268/index.pdf.

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A direct method is developed for solving the 2-D planar/axisymmetric Euler equations. The Euler equations are discretized using a finite-volume method with upwind flux splitting schemes, and the resulting nonlinear system of equations are solved using Newton&
#8217
s Method. Both analytical and numerical methods are used for Jacobian calculations. Numerical method has the advantage of keeping the Jacobian consistent with the numerical flux vector without extremely complex or impractical analytical differentiations. However, numerical method may have accuracy problem and may need longer execution time. In order to improve the accuracy of numerical method detailed error analyses were performed. It was demonstrated that the finite-difference perturbation magnitude and computer precision are the most important parameters that affect the accuracy of numerical Jacobians. A relation was developed for optimum perturbation magnitude that can minimize the error in numerical Jacobians. Results show that very accurate numerical Jacobians can be calculated with optimum perturbation magnitude. The effects of the accuracy of numerical Jacobians on the convergence of flow solver are also investigated. In order to reduce the execution time for numerical Jacobian evaluation, flux vectors with perturbed flow variables are calculated for only related cells. A sparse matrix solver based on LU factorization is used for the solution, and to improve the Jacobian matrix solution some strategies are considered. Effects of different flux splitting methods, higher-order discretizations and several parameters on the performance of the solver are analyzed.

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35

Cismas, Emanuel-Ciprian [Verfasser]. "Euler-Poincaré-Arnold equations on semi-direct products / Emanuel-Ciprian Cismas." Hannover : Technische Informationsbibliothek und Universitätsbibliothek Hannover (TIB), 2015. http://d-nb.info/1080271619/34.

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36

Keats, William A. "Two-Dimensional Anisotropic Cartesian Mesh Adaptation for the Compressible Euler Equations." Thesis, University of Waterloo, 2004. http://hdl.handle.net/10012/948.

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Simulating transient compressible flows involving shock waves presents challenges to the CFD practitioner in terms of the mesh quality required to resolve discontinuities and prevent smearing. This document discusses a novel two-dimensional Cartesian anisotropic mesh adaptation technique implemented for transient compressible flow. This technique, originally developed for laminar incompressible flow, is efficient because it refines and coarsens cells using criteria that consider the solution in each of the cardinal directions separately. In this document the method will be applied to compressible flow. The procedure shows promise in its ability to deliver good quality solutions while achieving computational savings. Transient shock wave diffraction over a backward step and shock reflection over a forward step are considered as test cases because they demonstrate that the quality of the solution can be maintained as the mesh is refined and coarsened in time. The data structure is explained in relation to the computational mesh, and the object-oriented design and implementation of the code is presented. Refinement and coarsening algorithms are outlined. Computational savings over uniform and isotropic mesh approaches are shown to be significant.

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37

Keats, W. Andrew. "Two-dimensional anisotropic cartesian Mesh adaption for the compressible Euler equations." Waterloo, Ont. : University of Waterloo, 2004. http://etd.uwaterloo.ca/etd/wakeats2004.pdf.

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Thesis (M.A.Sc.)--University of Waterloo, 2004.
"A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Master of Applied Science in Mechanical Engineering. Includes bibliographical references.

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38

Wehner, Edward. "A Newton-Krylov solver for the Euler equations on unstructured grids." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/MQ62898.pdf.

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39

Pareja, Victor David. "IMPULSE FORMULATIONS OF THE EULER EQUATIONS FOR INCOMPRESSIBLE AND COMPRESSIBLE FLUIDS." Master's thesis, University of Central Florida, 2007. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3265.

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The purpose of this paper is to consider the impulse formulations of the Euler equations for incompressible and compressible fluids. Different gauges are considered. In particular, the Kuz'min gauge provides an interesting case as it allows the fluid impulse velocity to describe the evolution of material surface elements. This result affords interesting physical interpretations of the Kuz'min invariant. Some exact solutions in the impulse formulation are studied. Finally, generalizations to compressible fluids are considered as an extension of these results. The arrangement of the paper is as follows: in the first chapter we will give a brief explanation on the importance of the study of fluid impulse. In chapters two and three we will derive the Kuz'min, E & Liu, Maddocks & Pego and the Zero gauges for the evolution equation of the impulse density, as well as their properties. The first three of these gauges have been named after their authors. Chapter four will study two exact solutions in the impulse formulation. Physical interpretations are examined in chapter five. In chapter six, we will begin with the generalization to the compressible case for the Kuz'min gauge, based on Shivamoggi et al. (2007), and we will derive similar results for the remaining gauges. In Chapter seven we will examine physical interpretations for the compressible case.
M.S.
Department of Mathematics
Sciences
Mathematical Science MS

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40

Dea, John R. "High-order non-reflecting boundary conditions for the linearized Euler equations." Monterey, Calif. : Naval Postgraduate School, 2008. http://edocs.nps.edu/npspubs/scholarly/theses/2008/Sept/08Sep%5FDea%5FPhD.pdf.

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Dissertation (Ph.D. in Applied Mathematics)--Naval Postgraduate School, September 2008.
Dissertation Advisor(s): Neta, Beny. "September 2008." Description based on title screen as viewed on November 6, 2008. Includes bibliographical references (p. 161-170). Also available in print.

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41

Drela, Mark. "Two-dimensional transonic aerodynamic design and analysis using the Euler equations." Thesis, Massachusetts Institute of Technology, 1985. http://hdl.handle.net/1721.1/14974.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1986.
MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERO
Bibliography: leaves 139-143.
by Mark Drela.
Ph.D.

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42

Rydin, Ylva. "Modeling Sound Propagation from Wind Turbines using Linearized 3D Euler Equations." Thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-301607.

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In this report sound propagation from wind turbines is modeled using the 3D linearized Euler equations which allows varying atmospheric fields containing wind. The Euler Equations are linearized and a stable high order finite difference approximation of the equations in 1D and 3D is obtained. Stability and convergence of the problem are proven and numerically verified.

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43

Pooley, Benjamin C. "On some alternative formulations of the Euler and Navier-Stokes equations." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/87302/.

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In this thesis we study well-posedness problems for certain reformulations and models of the Euler equations and the Navier{Stokes equations. We also prove several global well-posedness results for the diffusive Burgers equations. We discuss the Eulerian-Lagrangian formulation of the incompressible Euler equations considered by Constantin (2000). Using this formulation we give a new proof that the Euler equations are locally well-posed in Hs (Td ) for s > d/2 + 1. Constantin proved a local well-posedness result for this system in the Hӧlder spaces C1; for μ> 0, but an analysis in Sobolev spaces is perhaps more natural. After suggesting a possible Eulerian-Lagrangian formulation for the incompressible Navier{Stokes equations in which the back-to-labels map is not di used, we obtain the formulation written in terms of the so-called magnetization variables, as studied by Montgomery-Smith and Pokornẏ (2001). We give a rigorous analysis of the equivalence between this formulation and the classical one, in the context of weak solutions. Noting certain similarities between this formulation and the diffusive Burgers equations we begin a study of the latter. We prove that the diffusive Burgers equations are globally well-posed in Lp ∩ L2 (Ω ) for certain domains Rd , p > d, and d = 2 or d = 3. Moreover, we prove a global well-posedness result in H1= 2 (T3 ). Lastly, we consider a new model of the Navier{Stokes equations, obtained by modifying one of the nonlinear terms in the magnetization variables formulation. This new system admits a maximum principle and we prove a global well-posedness result in H1=2 (T3 ) following our analysis of the Burgers equations.

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44

Brock, Jerry S. "A consistent direct-iterative inverse design method for the Euler equations." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/40033.

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A new, consistent direct-iterative method is proposed for the solution of the aerodynamic inverse design problem. Direct-iterative methods couple analysis and shape modification methods to iteratively determine the geometry required to support a target surface pressure. The proposed method includes a consistent shape modification method wherein the identical governing equations are used in both portions of the design procedure. The new shape modification method is simple, having been developed from a truncated, quasi-analytical Taylor's series expansion of the global governing equations. This method includes a unique solution algorithm and a design tangency boundary condition which directly relates the target pressure to shape modification. The new design method was evaluated with an upwind, cell-centered finite-volume formulation of the two-dimensional Euler equations. Controlled inverse design tests were conducted with a symmetric channel where the initial and target geometries were known. The geometric design variable was a channel-wall ramp angle, 0, which is nominally five degrees. Target geometries were defined with ramp angle perturbations of J10 = 2 %, 10%, and 20 %. The new design method was demonstrated to accurately predict the target geometries for subsonic, transonic, and supersonic test cases; M=0.30, 0.85, and 2.00. The supersonic test case efficiently solved the design tests and required very few iterations. A stable and convergent solution process was also demonstrated for the lower speed test cases using an under-relaxed geometry update procedure. The development and demonstration of the consistent direct-iterative method herein represent the important first steps required for a new research area for the advancement of aerodynamic inverse design methods.
Ph. D.

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45

Akargun, Yigit Hayri. "Least-squares Finite Element Solution Of Euler Equations With Adaptive Mesh Refinement." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614138/index.pdf.

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Least-squares finite element method (LSFEM) is employed to simulate 2-D and axisymmetric flows governed by the compressible Euler equations. Least-squares formulation brings many advantages over classical Galerkin finite element methods. For non-self-adjoint systems, LSFEM result in symmetric positive-definite matrices which can be solved efficiently by iterative methods. Additionally, with a unified formulation it can work in all flight regimes from subsonic to supersonic. Another advantage is that, the method does not require artificial viscosity since it is naturally diffusive which also appears as a difficulty for sharply resolving high gradients in the flow field such as shock waves. This problem is dealt by employing adaptive mesh refinement (AMR) on triangular meshes. LSFEM with AMR technique is numerically tested with various flow problems and good agreement with the available data in literature is seen.

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46

McNeil, C. Y. "Efficient upwind algorithms for solution of the Euler and Navier-stokes equations." Thesis, Cranfield University, 1995. http://hdl.handle.net/1826/4147.

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An efficient three-dimensionasl tructured solver for the Euler and Navier-Stokese quations is developed based on a finite volume upwind algorithm using Roe fluxes. Multigrid and optimal smoothing multi-stage time stepping accelerate convergence. The accuracy of the new solver is demonstrated for inviscid flows in the range 0.675 :5M :5 25. A comparative grid convergence study for transonic turbulent flow about a wing is conducted with the present solver and a scalar dissipation central difference industrial design solver. The upwind solver demonstrates faster grid convergence than the central scheme, producing more consistent estimates of lift, drag and boundary layer parameters. In transonic viscous computations, the upwind scheme with convergence acceleration is over 20 times more efficient than without it. The ability of the upwind solver to compute viscous flows of comparable accuracy to scalar dissipation central schemes on grids of one-quarter the density make it a more accurate, cost effective alternative. In addition, an original convergencea cceleration method termed shock acceleration is proposed. The method is designed to reduce the errors caused by the shock wave singularity M -+ 1, based on a localized treatment of discontinuities. Acceleration models are formulated for an inhomogeneous PDE in one variable. Results for the Roe and Engquist-Osher schemes demonstrate an order of magnitude improvement in the rate of convergence. One of the acceleration models is extended to the quasi one-dimensiona Euler equations for duct flow. Results for this case d monstrate a marked increase in convergence with negligible loss in accuracy when the acceleration procedure is applied after the shock has settled in its final cell. Typically, the method saves up to 60% in computational expense. Significantly, the performance gain is entirely at the expense of the error modes associated with discrete shock structure. In view of the success achieved, further development of the method is proposed.

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47

Wiedemann, Emil [Verfasser]. "Weak and measure-valued solutions of the incompressible Euler equations / Emil Wiedemann." Bonn : Universitäts- und Landesbibliothek Bonn, 2012. http://d-nb.info/1043911308/34.

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48

Pueyo, Alberto. "An efficient Newton-Krylov method for the Euler and Navier-Stokes equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq35288.pdf.

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49

Heritage, Matthew Christopher. "Vorticity alignment phenomena in the three dimensional Euler and Navier-Stokes equations." Thesis, Imperial College London, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.298846.

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50

Miller, Jonathan Cross Michael Clifford Cross Michael Clifford. "Statistical mechanics of two-dimensional Euler equations and Jupiter's great red spot /." Diss., Pasadena, Calif. : California Institute of Technology, 1991. http://resolver.caltech.edu/CaltechETD:etd-07182007-073652.

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Dissertations / Theses on the topic 'Euler equations of motion'

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