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Shuttleworth, Robert. "Block preconditioning the Navier-Stokes equations." College Park, Md. : University of Maryland, 2007. http://hdl.handle.net/1903/7002.
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Thesis (Ph. D.) -- University of Maryland, College Park, 2007.Thesis research directed by: Applied Mathematics and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Neklyudov, Mikhail. "Navier-Stokes equations and vector advection." Thesis, University of York, 2006. http://etheses.whiterose.ac.uk/11011/.
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Rejaiba, Ahmed. "Equations de Stokes et de Navier-Stokes avec des conditions aux limites de Navier." Thesis, Pau, 2014. http://www.theses.fr/2014PAUU3050/document.
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Résumé : Cette thèse est consacrée à l'étude des équations de Stokes et de Navier-Stokes avec des conditions aux limites de Navier dans un ouvert borné de . Le manuscrit ici est composé de trois chapitres. Dans le premier, nous considérons les équations de Stokes stationnaires avec des conditions aux limites de Navier. Nous démontrons l'existence, l'unicité et la régularité de la solution d'abord dans un cadre hilbertien puis dans le cadre de la théorie . Nous traitons aussi le cas de solutions très faibles. Dans le deuxième chapitre, nous nous intéressons aux équations de Navier-Stokes avec la condition de Navier. Sous certaines hypothèses sur les données, nous démontrons l'existence de solution faible dans , avec en utilisant un théorème du point fixe appliqué à un problème d'Oseen. Nous démontrons examinons ensuite les questions de régularité des solutions en particulier dans . Dans le dernier chapitre, nous étudions le problème d'évolution de Stokes avec la condition de Navier. La résolution de ce problème se fait au moyen de la théorie des semi-groupes analytiques qui jouent un rôle important pour établir l'existence et l'unicité de la solution dans le cas homogène. Nous traitons le cas du problème non homogène par le biais des puissances imaginaires de l'opérateur de StokesThis thesis is devoted to the study of the Stokes equations and Navier-Stokes equations with Navier boundary conditions in a bounded domain of . The work contains three chapters: In the first chapter, we consider the stationary Stokes equations with Navier boundary condition. We show the existence, uniqueness and regularity of the solution in the Hilbert case and in the -theory. We prove also the case of very weak solutions. In the second chapter, we focus on the Navier-Stokes equations with the Navier boundary condition. We show the existence of the weak solution in , with by a fixed point theorem over the Oseen equation. We show also the existence of the strong solution in . In chapter three, we study the evolution Stokes problem with Navier boundary condition. For this, we apply the analytic semi-groups theory, which plays a crucial role in the study of existence and uniqueness of solution in the case of the homogeneous evolution problem. We treat the case of non-homogeneous problem through imaginary powers of the Stokes operator
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Benson, D. J. A. "Finite volume solution of Stokes and Navier-Stokes equations." Thesis, University of Oxford, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302883.
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Al-Jaboori, Mustafa Ali Hussain. "Navier-Stokes equations on the β-plane." Thesis, Durham University, 2012. http://etheses.dur.ac.uk/5582/.
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Mathematical analysis has been undertaken for the vorticity formulation of the two dimensional Navier–Stokes equation on the β-plane with periodic boundary conditions. This equation describes the flow of fluid near the equator of the Earth. The long time behaviour of the solution of this equation is investigated and we show that, given a sufficiently regular forcing, the solution of the equation is nearly zonal. We use this result to show that, for sufficiently large β, the global attractor of this system reduces to a point. Another result can be obtained if we assume that the forcing is time-independent and sufficiently smooth. If the forcing lies in some Gevrey space, the slow manifold of the Navier–Stokes equation on the β-plane can be approximated with O(εn/2) accuracy for arbitrary n = 0, 1, · · · , as well as with exponential accuracy.
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Haddon, E. W. "Numerical studies of the Navier-Stokes equations." Thesis, University of East Anglia, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.377745.
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Tang, Tao. "Numerical solutions of the Navier-Stokes equations." Thesis, University of Leeds, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328961.
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Słomka, Jonasz. "Generalized Navier-Stokes equations for active turbulence." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/117861.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 211-227).
Recent experiments show that active fluids stirred by swimming bacteria or ATPpowered microtubule networks can exhibit complex flow dynamics and emergent pattern scale selection. Here, I will investigate a simplified phenomenological approach to 'active turbulence', a chaotic non-equilibrium steady-state in which the solvent flow develops a dominant vortex size. This approach generalizes the incompressible Navier-Stokes equations by accounting for active stresses through a linear instability mechanism, in contrast to externally driven classical turbulence. This minimal model can reproduce experimentally observed velocity statistics and is analytically tractable in planar and curved geometry. Exact stationary bulk solutions include Abrikosovtype vortex lattices in 2D and chiral Beltrami fields in 3D. Numerical simulations for a plane Couette shear geometry predict a low viscosity phase mediated by stress defects, in qualitative agreement with recent experiments on bacterial suspensions. Considering the active analog of Stokes' second problem, our numerical analysis predicts that a periodically rotating ring will oscillate at a higher frequency in an active fluid than in a passive fluid, due to an activity-induced reduction of the fluid inertia. The model readily generalizes to curved geometries. On a two-sphere, we present exact stationary solutions and predict a new type of upward energy transfer mechanism realized through the formation of vortex chains, rather than the merging of vortices, as expected from classical 2D turbulence. In 3D simulations on periodic domains, we observe spontaneous mirror-symmetry breaking realized through Beltrami-like flows, which give rise to upward energy transfer, in contrast to the classical direct Richardson cascade. Our analysis of triadic interactions supports this numerical prediction by establishing an analogy with forced rigid body dynamics and reveals a previously unknown triad invariant for classical turbulence.
by Jonasz Słomka.
Ph. D.
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Ghosh, Amrita. "Naviers-Stokes equations with Navier boundary condition." Thesis, Pau, 2018. http://www.theses.fr/2018PAUU3021/document.
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Le titre de ma thèse de doctorat est "Equations de Stokes et de Navier-Stokes avec la con- dition de Navier", où j’ai considéré l’écoulement d’un fluide newtonien visqueux, incompressible dans un domaine borné de R3. L’écoulement du fluide est décrit par les équations bien connues de Navier-Stokes, données par le système suivant ∂t − ∆u + (u • ∇)u + ∇π = 0, div u = 0 dans Ω × (0, T )u • n = 0, 2[(Du)n]τ + αuτ = 0 sur Γ × (0, T )u(0) = u0 dans Ω (0.1) dans un domaine borné Ω ⊂ R3 de frontière Γ, éventuellement non simplement connexe, de classe C1,1. La vitesse initiale u0 et le coefficient de friction α, scalaire, sont des fonctions don- nées. Les vecteurs unitaires normal extérieur et tangents à Γ sont notés n et τ respectivement et Du = 1 (∇u + ∇uT ) est le tenseur des déformations. Les fonctions u et π décrivent respective- ment les champs de vitesses et de pression du fluide dans Ω satisfaisant la condition aux limites (0.1.2).Cette condition aux limites, proposée par H. Navier en 1823, a été abondamment étudiée ces dernières années, qui pour de nombreuses raisons convient parfois mieux que la condition aux limites de Dirichlet sans glissement : elle offre plus de liberté et est susceptible de fournir une solution physiquement acceptable au moins pour certains des phénomènes paradoxaux résultant de la condition de non-glissement, comme par exemple le paradoxe de D’Alembert ou le paradoxe de non-collision.Ma thèse comporte trois parties. Dans la première, je cherche à savoir si le problème (0.1) est bien posé en théorie Lp, en particulier l’existence, l’unicité de solutions faibles, fortes dans W 1,p(Ω) et W 2,p(Ω) pour tout p ∈ (1, ∞), en considérant la régularité minimale du coefficient de friction α. Ici α est une fonction, pas simplement une constante qui reflète les diverses propriétés du fluide et/ou de la frontière, ce qui nous permet d’analyser le comportement de la solution par rapport au coefficient de frottement.Utilisant le fait que les solutions sont bornées indépendamment de α, on montre que la solution des équations de Navier-Stokes avec la condition de Navier converge fortement vers une solution des équations de Navier-Stokes avec la condition de Dirichlet, correspondant à la même donnée initiale dans l’espace d’énergie lorsque α → ∞. Des résultats similaires ont été obtenus pour le cas stationnaire.Le dernier chapitre concerne les estimations pour le problème de Robin pour le laplacien : l’opérateur elliptique de second ordre suivant, sous forme divergentielle dans un domaine bornéΩ ⊂ Rn de classe C1, avec la condition aux limites de Robin a été considéré div(A∇)u = divf + F dans Ω, ∂u+ αu = f n + g sur Γ.∂n (0.2) Les coefficients de la matrice symétrique A sont supposés appartenir à l’espace V MO(R3). Aussi α est une fonction appartenant à un certain espace Lq . En plus de prouver l’existence, l’unicité de solutions faibles et fortes, nous obtenons une borne sur u, uniforme par rapport à α pour α suffisamment large, en norme Lp. Pour plus de clarté, nous avons étudié séparément les deux cas: l’estimation intérieure et l’estimation au bordMy PhD thesis title is "Navier-Stokes equations with Navier boundary condition" where I have considered the motion of an incompressible, viscous, Newtonian fluid in a bounded do- main in R3. The fluid flow is described by the well-known Navier-Stokes equations, given by thefollowing system 1 )t − L1u + (u ⋅ ∇)u + ∇n = 0, div u = 01u ⋅ n = 0, 2[(IDu)n]r + aur = 0 in Q × (0, T )on Γ × (0, T ) (0.1) 11lu(0) = u0 in Qin a bounded domain Q ⊂ R3 with boundary Γ, possibly not connected, of class C1,1. The initialvelocity u0 and the (scalar) friction coefficient a are given functions. The unit outward normal and tangent vectors on Γ are denoted by n and r respectively and IDu = 1 (∇u + ∇uT ) is the rate of strain tensor. The functions u and n describe respectively the velocity2 and the pressure of a fluid in Q satisfying the boundary condition (0.1.2).This boundary condition, first proposed by H. Navier in 1823, has been studied extensively in recent years, among many reasons due to its contrast with the no-slip Dirichlet boundary condition: it offers more freedom and are likely to provide a physically acceptable solution at least to some of the paradoxical phenomenons, resulting from the no-slip condition, for example, D’Alembert’s paradox or no-collision paradox.My PhD work consists of three parts. primarily I have discussed the Lp -theory of well-posedness of the problem (0.1), in particular existence, uniqueness of weak and strong solutions in W 1,p (Q) and W 2,p (Q) for all p ∈ (1, ∞) considering minimal regularity on the friction coefficienta. Here a is a function, not merely a constant which reflects various properties of the fluid and/or of the boundary. Moreover, I have deduced estimates showing explicitly the dependence of u on a which enables us to analyze the behavior of the solution with respect to the friction coefficient.Using this fact that the solutions are bounded with respect to a, we have shown the solution of the Navier-Stokes equations with Navier boundary condition converges strongly to a solution of the Navier-Stokes equations with Dirichlet boundary condition corresponding to the sameinitial data in the energy space as a → ∞. The similar results have also been deduced for thestationary case.The last chapter is concerned with estimates for a Laplace-Robin problem: the following second order elliptic operator in divergence form in a bounded domain Q ⊂ Rn of class C1, withthe Robin boundary condition has been considered1div(A∇)u = divf + F in Q, 11 )u + u = f ⋅ n + g on Γ. (0.2) 2The coefficient matrix A is symmetric and belongs to V MO(R3). Also a is a function belonging to some Lq -space. Apart from proving existence, uniqueness of weak and strong solutions, we obtain the bound on u, uniform in a for a sufficiently large, in the Lp -norm. We have separately studied the two cases: the interior estimate and the boundary estimate to make the main idea clear in the simple set up
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Landmann, Björn. "A parallel discontinuous Galerkin code for the Navier-Stokes and Reynolds-averaged Navier-Stokes equations." [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-35199.
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Landmann, Björn. "A parallel discontinuous Galerkin code for the Navier-Stokes and Reynolds averaged Navier-Stokes equations." München Verl. Dr. Hut, 2007. http://d-nb.info/988422433/04.
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Vong, Seak Weng. "Two problems on the Navier-Stokes equations and the Boltzmann equation /." access full-text access abstract and table of contents, 2005. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b19885805a.pdf.
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Thesis (Ph.D.)--City University of Hong Kong, 2005."Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy" Includes bibliographical references (leaves 72-77)
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Wachsmuth, Daniel. "Optimal control of the unsteady Navier-Stokes equations." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=982143419.
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Weickert, J. "Navier-Stokes equations as a differential-algebraic system." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800942.
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Nonsteady Navier-Stokes equations represent a differential-algebraic system of strangeness index one after any spatial discretization. Since such systems are hard to treat in their original form, most approaches use some kind of index reduction. Processing this index reduction it is important to take care of the manifolds contained in the differential-algebraic equation (DAE). We investigate for several discretization schemes for the Navier-Stokes equations how the consideration of the manifolds is taken into account and propose a variant of solving these equations along the lines of the theoretically best index reduction. Applying this technique, the error of the time discretisation depends only on the method applied for solving the DAE.
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Li, Ming. "Numerical solutions for the incompressible Navier-Stokes equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0016/NQ37725.pdf.
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Li, Yuhong. "Asymptotical behaviour of 2D stochastic Navier-Stokes equations." Thesis, University of Hull, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.411901.
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Osborne, Daniel. "Navier-Stokes equations and stochastic models of turbulence." Thesis, University of Oxford, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.497064.
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Ryou, H. S. "Viscous/inviscid matching using imbedded Navier/Stokes equations." Thesis, Imperial College London, 1988. http://hdl.handle.net/10044/1/47236.
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Schäfer, Christian Thomas. "Elastohydrodynamic lubrication based on the Navier-Stokes equations." Thesis, Liverpool John Moores University, 2005. http://researchonline.ljmu.ac.uk/5788/.
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Newman, Christopher K. "Exponential Integrators for the Incompressible Navier-Stokes Equations." Diss., Virginia Tech, 2003. http://hdl.handle.net/10919/29340.
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We provide an algorithm and analysis of a high order projection scheme for time integration of the incompressible Navier-Stokes equations (NSE). The method is based on a projection onto the subspace of divergence-free (incompressible) functions interleaved with a Krylov-based exponential time integration (KBEI). These time integration methods provide a high order accurate, stable approach with many of the advantages of explicit methods, and can reduce the computational resources over conventional methods. The method is scalable in the sense that the computational costs grow linearly with problem size.
Exponential integrators, used typically to solve systems of ODEs, utilize matrix vector products of the exponential of the Jacobian on a vector. For large systems, this product can be approximated efficiently by Krylov subspace methods. However, in contrast to explicit methods, KBEIs are not restricted by the time step. While implicit methods require a solution of a linear system with the Jacobian, KBEIs only require matrix vector products of the Jacobian. Furthermore, these methods are based on linearization, so there is no non-linear system solve at each time step.
Differential-algebraic equations (DAEs) are ordinary differential equations (ODEs) subject to algebraic constraints. The discretized NSE constitute a system of DAEs, where the incompressibility condition is the algebraic constraint. Exponential integrators can be extended to DAEs with linear constraints imposed via a projection onto the constraint manifold. This results in a projected ODE that is integrated by a KBEI. In this approach, the Krylov subspace satisfies the constraint, hence the solution at the advanced time step automatically satisfies the constraint as well. For the NSE, the projection onto the constraint is typically achieved by a projection induced by the L2 inner product. We examine this L2 projection and an H1 projection induced by the H1 semi-inner product. The H1 projection has an advantage over the L2 projection in that it retains tangential Dirichlet boundary conditions for the flow. Both the H1 and L2 projections are solutions to saddle point problems that are efficiently solved by a preconditioned Uzawa algorithm.Ph. D.
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Zahed, Hanadi. "Computation of bifurcations for the Navier-Stokes equations." Thesis, University of Manchester, 2010. https://www.research.manchester.ac.uk/portal/en/theses/computation-of-bifurcations-for-the-navierstokes-equations(6f5f55ac-0379-495b-8652-7baaeb117a4b).html.
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We investigate a two-dimensional boundary layer flow in a channel with a suction slot on the upper wall by solving the steady Navier-Stokes equations to compute steady state solutions and we investigate their stability using global stability analysis together with linear temporal simulation and a continuation method. Our primary aim in this work is to investigate bifurcations occurring in separated flows at large Reynolds numbers (R). Another motivation is to investigate the stability of a separated flow. The 2D steady Navier-Stokes equations in stream function(ψ)-vorticity (ω) are solved numerically using a hybrid finite difference and spectral method combined with pseudo arc length continuation techniques to track turning points and bifurcations. We are able to calculate two branches of solutions and the turning point bifurcation in this particular problem. Global stability results indicate that the first solution on the lower branch, where the separation bubble is short, is stable, while the second solution on the upper branch, where the separation bubble is large, is unstable. The presence of the turning point is confirmed by the changing signs in the eigenvalue spectrum, as it moves from the lower, stable solution branch to the upper, unstable solution branch. The numerical simulation confirms the stability of the lower branch solutions and confirms that the upper branch is unstable; it is also in good agreement with global stability behaviour.
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Montoya, Zambrano Cristhian David. "Inverse source problems and controllability for the stokes and navier-stokes equations." Tesis, Universidad de Chile, 2016. http://repositorio.uchile.cl/handle/2250/141346.
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Doctor en Ciencias de la Ingeniería, Mención Modelación MatemáticaThis thesis is focused on the Navier{Stokes system for incompressible uids with either Dirichlet or nonlinear Navier{slip boundary conditions. For these systems, we exploit some ideas in the context of the control theory and inverse source problems. The thesis is divided in three parts. In the rst part, we deal with the local null controllability for the Navier{Stokes system with nonlinear Navier{slip conditions, where the internal controls have one vanishing component. The novelty of the boundary conditions and the new estimates with respect to the pressure term, has allowed us to extend previous results on controllability for the Navier{ Stokes system. The main ingredients to build our result are the following: a new regularity result for the linearized system around the origin, and a suitable Carleman inequality for the adjoint system associated to the linearized system. Finally, xed point arguments are used in order to conclude the proof. In the second part, we deal with an inverse source problem for the N- dimensional Stokes system from local and missing velocity measurements. More precisely, our main result establishes a reconstruction formula for the source F(x; t) = (t)f(x) from local observations of N ����� 1 components of the velocity. We consider that f(x) is an unknown vectorial function, meanwhile (t) is known. As a consequence, the uniqueness is achieved for f(x) in a suitable Sobolev space. The main tools are the following: connection between null controllability and inverse problems throughout a result on null controllability for the N- dimensional Stokes system with N ����� 1 scalar controls, spectral analysis of the Stokes operator and Volterra integral equations. We also implement this result and present several numerical experiments that show the feasibility of the proposed recovering formula. Finally, the last chapter of the thesis presents a partial result of stability for the Stokes system when we consider a source F(x; t) = R(x; t)g(x), where R(x; t) is a known vectorial function and g(x) is unknown. This result involves the Bukhgeim-Klibanov method for solving inverse problems and some topics in degenerate Sobolev spaces.
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Bochev, Pavel B. "Least squares finite element methods for the Stokes and Navier-Stokes equations." Diss., This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-06062008-165910/.
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Skøien, Are Arstad. "Cartesian grid methods for the compressible Navier-Stokes equations." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for energi- og prosessteknikk, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-19361.
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A Cartesian grid method has been developed for solving the 2D Euler and Navier-Stokes equations for viscous and inviscid compressible flow, respectively. Both steady and unsteady flows have been considered. Using a simplified ghost point treatment, we consider the closest grid points as mirror points of the ghost points. Wall boundary conditions are imposed at the ghost points of the immersed boundary. The accuracy of the method has been investigated for various test cases. We show computed examples of supersonic flow past a diamond-wedge airfoil and compare with analytical results. Further we compute time accurate solutions of the compressible Euler equations for an incident shock over a cylinder and compare the pressure time history with other work. The supersonic viscous flow around a NACA0012 airfoil is computed, and the lift and drag coefficients along with the pressure coefficient profile are compared with the literature. The method is also tested for supersonic flow over a cylinder, and the computed skin friction profiles have been used to assess the accuracy. Lastly the supersonic flow around a 2D F-22 fighter aircraft with simulated jet engine outflow is shown to illustrate the flexibility of the method. The present method is built on a previously established simplified ghost point treatment, but performs better. The results are comparable, although not as accurate as other more complex methods.
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Grzesiak, Katarzyna. "Optimal control for Navier-Stokes equations using nonstandard analysis." Thesis, University of Hull, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.289785.
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Klimowcz, Alexandre Nicolas Francois. "Multigrid Preconditioning of the Free-suface Navier-Stokes Equations." Thesis, University of Manchester, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.503655.
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Yung, Hoi Yan Ada, and 翁凱欣. "On block preconditioners for the incompressible Navier-Stokes equations." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B44907138.
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Daube, Johannes [Verfasser], and Dietmar [Akademischer Betreuer] Kröner. "Sharp-Interface limit for the Navier-Stokes-Korteweg equations." Freiburg : Universität, 2016. http://d-nb.info/112590609X/34.
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Keim, Christopher [Verfasser]. "Collocation Methods for the Navier-Stokes Equations / Christopher Keim." München : Verlag Dr. Hut, 2017. http://d-nb.info/1128467828/34.
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Ajmani, Kumud. "Preconditioned conjugate gradient methods for the Navier-Stokes equations." Diss., Virginia Tech, 1991. http://hdl.handle.net/10919/39840.
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A generalized Conjugate Gradient like method is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. Preconditioning techniques are employed with the Conjugate Gradient like method to enhance the stability and convergence rate of the overall iterative method. The superiority of the new solver is established by comparisons with a conventional Line GaussSeidel Relaxation (LGSR) solver. Comparisons are based on 'number of iterations required to converge to a steady-state solution' and 'total CPU time required for convergence'. Three test cases representing widely varying flow physics are chosen to investigate the performance of the solvers. Computational test results for very low speed (incompressible flow over a backward facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (shockon- shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the 1vfach 0.1 case, speed-up factors of 30 (in terms of iterations) and 20 (in terms of CPU time) are found in favor of the new solver when compared with the LGSR solver. The corresponding speed-up factors for the transonic flow case are 20 and 18, respectively. The hypersonic case shows relatively lower speed-up factors of 5 and 4, respectively. This study reveals that preconditioning can greatly enhance the range of applicability and improve the performance of Conjugate Gradient like methods.Ph. D.
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Marx, Yves. "Etude d'algorithmes pour les equations de navier-stokes compressibles." Nantes, 1987. http://www.theses.fr/1987NANT2039.
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On presente une methode numerique du type volumes finis. On obtient une precision du second ordre en utilisant des champs evoluant lineairement a l'interieur de chaque maille. Validation de la methode sur le cas test de la tuyere a double col
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BACHA, JEAN-LUC. "Resolution numerique des equations de navier-stokes compressibles bidimensionnelles." Paris 6, 1993. http://www.theses.fr/1993PA066014.
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Aujourd'hui, les methodes de simulation numerique d'ecoulements de fluides parfaits en aerodynamique, modelises par les equations d'euler, sont efficaces et tres utilisees. Pour une meilleure comprehension des phenomenes physiques plus complexes, l'etape suivante consiste a mettre en uvre des methodes efficaces de resolution d'ecoulements de fluides visqueux compressibles, modelises par les equations de navier-stokes. L'etude que nous presentons fait suite a la mise en place d'un code de resolution des equations d'euler en dimension 2 et consiste en l'implementation de la resolution des equations de navier-stokes compressibles bidimensionnelles. Nous suivons la demarche suivante: 1) nous rappelons la nature mathematique des equations de navier-stokes; 2) nous cherchons a definir des conditions aux limites stables a partir d'une methode d'energie pour avoir un probleme bien pose; 3) nous resolvons numeriquement les equations a partir du schema de lax-wendroff a 1 pas de temps associe a la methode des volumes finis pour l'integration en espace, nous etudions sa stabilite et implementons les conditions aux limites proposees; 4) une serie de tests classiques nous permet de valider les differentes options choisies; 5) dans une derniere partie nous etudions et mettons en uvre deux techniques d'acceleration de la convergence correspondant a la methode multigrille et a la methode de sequence de grilles
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Wang, Yushan. "Solving incompressible Navier-Stokes equations on heterogeneous parallel architectures." Thesis, Paris 11, 2015. http://www.theses.fr/2015PA112047/document.
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Dans cette thèse, nous présentons notre travail de recherche dans le domaine du calcul haute performance en mécanique des fluides. Avec la demande croissante de simulations à haute résolution, il est devenu important de développer des solveurs numériques pouvant tirer parti des architectures récentes comprenant des processeurs multi-cœurs et des accélérateurs. Nous nous proposons dans cette thèse de développer un solveur efficace pour la résolution sur architectures hétérogènes CPU/GPU des équations de Navier-Stokes (NS) relatives aux écoulements 3D de fluides incompressibles.Tout d'abord nous présentons un aperçu de la mécanique des fluides avec les équations de NS pour fluides incompressibles et nous présentons les méthodes numériques existantes. Nous décrivons ensuite le modèle mathématique, et la méthode numérique choisie qui repose sur une technique de prédiction-projection incrémentale.Nous obtenons une distribution équilibrée de la charge de calcul en utilisant une méthode de décomposition de domaines. Une parallélisation à deux niveaux combinée avec de la vectorisation SIMD est utilisée dans notre implémentation pour exploiter au mieux les capacités des machines multi-cœurs. Des expérimentations numériques sur différentes architectures parallèles montrent que notre solveur NS obtient des performances satisfaisantes et un bon passage à l'échelle.Pour améliorer encore la performance de notre solveur NS, nous intégrons le calcul sur GPU pour accélérer les tâches les plus coûteuses en temps de calcul. Le solveur qui en résulte peut être configuré et exécuté sur diverses architectures hétérogènes en spécifiant le nombre de processus MPI, de threads, et de GPUs.Nous incluons également dans ce manuscrit des résultats de simulations numériques pour des benchmarks conçus à partir de cas tests physiques réels. Les résultats obtenus par notre solveur sont comparés avec des résultats de référence. Notre solveur a vocation à être intégré dans une future bibliothèque de mécanique des fluides pour le calcul sur architectures parallèles CPU/GPUIn this PhD thesis, we present our research in the domain of high performance software for computational fluid dynamics (CFD). With the increasing demand of high-resolution simulations, there is a need of numerical solvers that can fully take advantage of current manycore accelerated parallel architectures. In this thesis we focus more specifically on developing an efficient parallel solver for 3D incompressible Navier-Stokes (NS) equations on heterogeneous CPU/GPU architectures. We first present an overview of the CFD domain along with the NS equations for incompressible fluid flows and existing numerical methods. We describe the mathematical model and the numerical method that we chose, based on an incremental prediction-projection method.A balanced distribution of the computational workload is obtained by using a domain decomposition method. A two-level parallelization combined with SIMD vectorization is used in our implementation to take advantage of the current distributed multicore machines. Numerical experiments on various parallel architectures show that this solver provides satisfying performance and good scalability.In order to further improve the performance of the NS solver, we integrate GPU computing to accelerate the most time-consuming tasks. The resulting solver can be configured for running on various heterogeneous architectures by specifying explicitly the numbers of MPI processes, threads and GPUs. This thesis manuscript also includes simulation results for two benchmarks designed from real physical cases. The computed solutions are compared with existing reference results. The code developed in this work will be the base for a future CFD library for parallel CPU/GPU computations
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Naughton, Michael John Kreiss H. "On numerical boundary conditions for the Navier-Stokes equations /." Diss., Pasadena, Calif. : California Institute of Technology, 1986. http://resolver.caltech.edu/CaltechETD:etd-03192008-094428.
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Raval, Ashish. "Numerical simulation of water waves using Navier-Stokes equations." Thesis, University of Leeds, 2008. http://etheses.whiterose.ac.uk/11280/.
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The main purpose of this thesis is to use state of the art computational fluid dynamics techniques to solve the problem of water-wind waves which are related to air-sea interaction. In general, air-sea interaction is studied in a de-coupled manner where both air and water phases are separate and the water phase is either considered as a smooth or rough wall which is stationary or moving. However, in real ocean waves the air and water are coupled. Mass, momentum, heat and energy exchange takes place mostly on the surface waves and this process is culminated when the waves break. Numerical modelling to study these processes requires the solution of the full Navier-Stokes equations along with capturing the interface boundary of the wave with high accuracy, thereby helping us to understand the physical processes taking place on the air-water interface and improve current wave modelling techniques. Our primary motivation is two fold: (1) to investigate the accuracy and reliability of the state of the art numerical techniques available for simulating free surface flows and model air-water wave interaction and (2) to study various near surface physical processes taking place at the transient, viscous, rotational and nonlinear air-water wave interface and understand its effects on the momentum and energy exchange in wind waves. The work presented in this thesis investigates a numerical model to solve the full Navier Stokes equations required to model transient, viscous, rotational and nonlinear water waves. The first step in the process is to model the water waves when the average wind speed is zero. Various other physical aspects related to wave dynamics are discussed for intermediate depth and deep water waves with different steepnesses. They are compared with earlier experimental and theoretical works available in order to verify the accuracy of the model . The second step is to model these water waves in the presence of wind blowing at different speeds and analyze its effects on various near surface physical properties and its effect on the motions in the air and underlying water. The other purpose of this thesis is to investigate some very interesting aspects related to wave dynamics such as vorticity and shear stress which are little studied due to complexities surrounding near surface flow measurements and the lack of an accurate analytical solution. The current work provides a tool for the application of CFD techniques to reliably predict wind-wave interaction by using numerical modelling techniques used in multi-phase flow environments. The accuracy and convergence of the numerical technique used in this thesis is illustrated by comparing the numerical results with analytical and theoretical results available. The technique is demonstrated to be accurate in the simulation of twodimensional flows where turbulent effects are negligible. At higher wind speeds, the use of suitable turbulence closure models is recommended. The main conclusions drawn from the study are: (1) accurate simulation of two and three dimensional, unsteady, viscous and nonlinear water waves is possible with current CFD techniques; (2) The role played by shear stress and vorticity in the wind wave interaction is important and cannot be ignored; (3) the vertical velocity gradients observed inside the water in intermediate depth water waves are found to be stronger than deep water waves; and (4) the effect of the bottom boundary on the magnitude of free surface vorticity is not found to be high.
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Eriksson, Gustav. "A Numerical Solution to the Incompressible Navier-Stokes Equations." Thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-387386.
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A finite difference based solution method is derived for the velocity-pressure formulation of the two-dimensional incompressible Navier-Stokes equations. The method is proven stable using the energy method, facilitated by SBP operators, for characteristic and Dirichlet boundary condition implemented using the SAT technique. The numerical experiments show the utility of high-order finite difference methods as well as emphasize the problem of pressure boundary conditions. Furthermore, we demonstrate that a discretely divergence free solution can be obtained by use of the projection method.
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Sommerville, Lesley Laverne. "A Parabolized navier-stokes model for static mixers." Thesis, Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/19535.
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He, Qiaolin. "Numerical study of solutions to Prandtl equations and N-S equations /." View abstract or full-text, 2007. http://library.ust.hk/cgi/db/thesis.pl?MATH%202007%20HE.
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Hess, Matthias. "Analysis of the Navier-Stokes equations for geophysical boundary layers." Berlin Logos-Verl, 2009. http://d-nb.info/997726792/04.
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Kyed, Mads [Verfasser]. "Time-Periodic Solutions to the Navier-Stokes Equations / Mads Kyed." Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2012. http://d-nb.info/1106454014/34.
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Khurshid, Hassan. "High-order incompressible Navier-stokes equations solver for blood flow." Wichita State University, 2012. http://hdl.handle.net/10057/5520.
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A high-order finite difference solver was written to solve the incompressible Navier-Stokes (NS) equations and was applied to analyze the blood flow. First, a computer code was written to solve incompressible Navier- Stokes equations using the exact projection method/fractional step scheme. A fifth-order weighted essentially nonoscillatory (WENO) spatial operator was applied to the convective terms of Navier-Stokes equations. The diffusion term was solved by using a sixth-order compact central difference scheme. A fractional step scheme in conjunction with the third-order Runge-Kutta total variation diminishing (RK TVD) scheme was used for the time discretization. At this stage, non-Newtonian effects and the pulsatile nature of the flow were not included. The developed Newtonian flow code was tested using benchmark problems for incompressible flow, namely, the driven cavity flow, Couette flow, Taylor-Green vortex problem, double shear layer problem, and skewed cavity flow. The results were compared with existing published experimental data in order to build confidence that the computer code was working properly in the simple blood flow conditions, i.e., as a Newtonian fluid. In the second stage, the backward-facing step was analyzed for Newtonian steady and pulsatile flow, and for non-Newtonian steady and pulsatile flow. The results were compared with experimental data and found to be in agreement. In the third stage, the computer program was extended to three dimensions. Flow through an infinite long pipe and through a 90-degree bend was carried out. The velocity profile in the pipe and at different locations of the bend was obtained, and the numerical values indicate good agreement with analytical and experimental values.Thesis (Ph.D.)--Wichita State University, College of Engineering, Dept. of Aerospace Engineering
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Wake, Brian E. "Solution procedure for the Navier-Stokes equations applied to rotors." Diss., Georgia Institute of Technology, 1987. http://hdl.handle.net/1853/13088.
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Malham, Simon J. A. "Regularity assumptions and length scales for the Navier-Stokes equations." Thesis, Imperial College London, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.337924.
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Muniandy, Sithi V. "Wavelet-Galerkin modelling of the two dimensional Navier-Stokes equations." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.284538.
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Enright, Brendan Edward. "A nonstandard approach to the stochastic nonhomogeneous Navier-Stokes equations." Thesis, University of Hull, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.322365.
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Anthony, Peter. "Infinite energy solutions for Navier-Stokes equations in a strip." Thesis, University of Surrey, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.616879.
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This thesis deals with infinite energy solutions of the Navier-Stokes and Boussinesq equations in a strip. Here, the properly chosen Uniformly local Sobolev Spaces of functions are used as the phase spaces for the problem considered. The global well-posedness and dissipativity of the Navier-Stokes equations was first established in a paper by Zelik [37] on Spatially Nondecaying Solutions of the 2D Navier-Stokes equations in a strip. However, the proof given there contains error which emmanated from wrong estimation of the solutions of the auxiliary non-autonomous linear Stokes problem with non-homogeneous divergence. In this thesis, we correct the aforementioned error and show that the main results of [37], i.e the well-posedness of the Navier-Stokes problem in uniformly local spaces, remains true. Albeit, only a weaker version of the postulated results in [37] was amenable; therefore, we reworked most part of the non-linear theory as well as to show that they are sufficient for the well-posedness of the non-linear system. We also extended these results to the thermal convection problem in a strip and associated Boussinesq equations. We considered the temperature equation and proved, using maximum principle, the well-posedness of the full Boussinesq system in a Strip. 1
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Beaven, F. "Numerical solutions of the Navier-Stokes equations on generalised grids." Thesis, Swansea University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.636065.
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This thesis presents a numerical procedure for the solution of compressible laminar viscous flow in two and three dimensions. The scheme is based on the finite volume method due to Jameson for the solution of the compressible Euler equations on triangular meshes. The method has been extended for the solution of flows on generalised structured and unstructured grids. Three flow solvers have been written, a 2-D cell centre code, a 2-D cell vertex code and a 3-D cell centre code. Particular attention has been paid to the discretization of the viscous fluxes and the artificial dissipation terms. A contour integral method is used for the calculation of variable gradients. A number of different stencils for such a calculation are presented and discussed. A finite volume type discretization, due to Natakusumah, has been implemented in the 2-D cell centre code and has been extended to 3-D. A finite element type discretization, due to Jameson, has been implemented in the cell vertex code. Two methods are presented for the calculation of artificial dissipation. An edge differencing method due to Jameson, with additional scaling terms for application to viscous solutions, is presented and is shown to work well provided the mesh is smoothly varying. An alternative contour integral method is shown to produce superior results on unsmooth meshes. Finally, some examples are presented which demonstrate the flexibility of the methods discussed, in particular is the ability to obtain accurate solutions on a large variety of grid types.
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Bredberg, Irene. "The Einstein and the Navier-Stokes Equations: Connecting the Two." Thesis, Harvard University, 2012. http://dissertations.umi.com/gsas.harvard:10214.
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This thesis establishes a precise mathematical connection between the Einstein equations of general relativity and the incompressible Navier-Stokes equation of fluid dynamics. We carry out a holographic analysis which relates solutions to the Einstein equations to the behaviour of a dual fluid living in one fewer dimensions. Gravitational systems are found to exhibit Navier-Stokes behaviour when we study the dynamics of the region near an event horizon. Thus, we find non-linear deformations of Einstein solutions which, after taking a suitable near horizon limit and imposing our particular choice of boundary conditions, turn out to be precisely characterised by solutions to the incompressible Navier-Stokes equation. In other words, for any solution to the Navier-Stokes equation, the set-up we present provides a solution to the Einstein equations near a horizon. We consider the cases of fluids flowing on the plane and on the sphere. Fluid dynamics on the plane is analysed foremost in the context of a flat background geometry whilst the spherical analysis is undertaken for Schwarzschild black holes and the static patch of four-dimensional de Sitter space.Physics
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Lonsdale, G. "Multigrid methods for the solution of the Navier-Stokes equations." Thesis, University of Manchester, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.379162.
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Dhariwal, Gaurav. "A study of constrained Navier-Stokes equations and related problems." Thesis, University of York, 2017. http://etheses.whiterose.ac.uk/18403/.
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Fundamental questions in the theory of partial differential equations are that of existence and uniqueness of the solution. In this thesis we address these questions corresponding to two models governing the dynamics of incompressible fluids, both being the modification of classical Navier-Stokes equations: constrained Navier-Stokes equations and tamed Navier-Stokes equations. The former being Navier-Stokes equations with a constraint on the L^2 norm of the solution considered on a two-dimensional domain with periodic boundary conditions. We prove existence of the unique global-in-time solution in deterministic setting and establish existence of a pathwise unique strong solution under the impact of a stochastic forcing. The tamed Navier-Stokes equations were introduced by Röckner and Zhang [75], to study the properties of solutions of the 3D Navier-Stokes equations. We use three new ideas to prove the existence of a strong solution and existence of invariant measures: approximating equation on an infinite dimensional space in contrast to classical Faedo-Galerkin approximation; tightness criterion related to the Dubinsky's compactness theorem introduced recently by Brzeźniak and Motyl [23]; and lastly proving the existence of invariant measures based on continuity and compactness in the weak topologies [62].