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Dissertations / Theses on the topic 'Fluid dynamical problems'
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Zhen, Cui. "A study of three fluid dynamical problems." Thesis, University of Exeter, 2014. http://hdl.handle.net/10871/15119.
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In this thesis, three fluid dynamical problems are studied. First in chapter 2 we investigate, via both theoretical and experimental methods, the swimming motion of a magnetotactic bacterium having the shape of a prolate spheroid in a viscous liquid under the influence of an imposed magnetic field. The emphasis of the study is placed on how the shape of the non-spherical magnetotactic bacterium, marked by the size of its eccentricity, affects the pattern of its swimming motion. It is revealed that the pattern/speed of a swimming spheroidal magnetotactic bacterium is highly sensitive not only to the direction of its magnetic moment but also to its shape. Secondly, an important unanswered mathematical question in the theory of rotating fluids has been the completeness of the inviscid eigenfunctions which are usually referred to as inertial waves or inertial modes. In chapter 3 we provide for the first time a mathematical proof for the completeness of the inertial modes in a rotating annular channel by establishing the completeness relation, or Parseval’s equality, for any piecewise continuous, differentiable velocity of an incompressible fluid. Thirdly, in chapter 4 we investigate, through both asymptotic analysis and direct numerical simulation, precessionally driven flow of a homogeneous fluid confined in a fluid-filled circular cylinder that rotates rapidly about its symmetry axis and precesses about a different axis that is fixed in space. A particular emphasis is placed on the spherical-like cylinder whose diameter is nearly the same as its length. An asymptotic analytical solution in closed form is derived in the mantle frame of reference for describing weakly precessing flow in the spherical-like cylinder at asymptotically small Ekman numbers. We also construct a three-dimensional finite element model, which is checked against the asymptotic solution, in attempting to elucidate the structure of the nonlinear flow.
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Shaw, G. J. "Multigrid methods in fluid dynamics." Thesis, University of Oxford, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.371582.
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Zhao, Kun. "Initial-boundary value problems in fluid dynamics modeling." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31778.
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Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2010.Committee Chair: Pan, Ronghua; Committee Member: Chow, Shui-Nee; Committee Member: Dieci, Luca; Committee Member: Gangbo, Wilfrid; Committee Member: Yeung, Pui-Kuen. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Parolini, Nicola. "Computational fluid dynamics for naval engineering problems /." [S.l.] : [s.n.], 2004. http://library.epfl.ch/theses/?nr=3138.
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Park, Jungho. "Bifurcation and stability problems in fluid dynamics." [Bloomington, Ind.] : Indiana University, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3274924.
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Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2007.Source: Dissertation Abstracts International, Volume: 68-07, Section: B, page: 4529. Adviser: Shouhong Wang. Title from dissertation home page (viewed Apr. 22, 2008).
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Wright, Nigel George. "Multigrid solutions of elliptic fluid flow problems." Thesis, University of Leeds, 1988. http://etheses.whiterose.ac.uk/446/.
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An efficient FAS muldgrid solution strategy is presented for the accurate and economic simulation of convection dominated flows. The use of a high-order approximation to the convective transport terms found in the governing equations of motion has been investigated in conjunction with an unsegregated smoothing technique. Results are presented for a sequence of problems of increasing complexity requiring that careful attention be directed toward; the proper treatment of different types of boundary condition. The classical two-dimensional problem of flow in a lid-driven cavity is investigated in depth for flows at Reynolds numbers of 100,400 and 1000. This gives an extremely good indication of the power of a multigrid approach. Next, the solution methodology is applied to flow in a three-dimensional lid-driven cavity at different Reynolds numbers, with cross-reference being made to predictions obtained in the corresponding two-dimensional simulations, and to the flow over a step discontinuity in the case of an abruptly expanding channel. Although, at first sight, these problems appear to require only minor extensions to the existing approach, it is found that they are rather more idiosyncratic. Finally, the governing equations and numerical algorithm are extended to encompass the treatment of thermally driven flows. Ile solution to two such problems is presented and compared with corresponding results obtained by traditional methods.
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Noever, David Anthony. "Problems in gas dynamics and biological fluids." Thesis, University of Oxford, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.317799.
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Al-Wali, Azzam Ahmad. "Explicit alternating direction methods for problems in fluid dynamics." Thesis, Loughborough University, 1994. https://dspace.lboro.ac.uk/2134/6840.
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Recently an iterative method was formulated employing a new splitting strategy for the solution of tridiagonal systems of difference equations. The method was successful in solving the systems of equations arising from one dimensional initial boundary value problems, and a theoretical analysis for proving the convergence of the method for systems whose constituent matrices are positive definite was presented by Evans and Sahimi [22]. The method was known as the Alternating Group Explicit (AGE) method and is referred to as AGE-1D. The explicit nature of the method meant that its implementation on parallel machines can be very promising. The method was also extended to solve systems arising from two and three dimensional initial-boundary value problems, but the AGE-2D and AGE-3D algorithms proved to be too demanding in computational cost which largely reduces the advantages of its parallel nature. In this thesis, further theoretical analyses and experimental studies are pursued to establish the convergence and suitability of the AGE-1D method to a wider class of systems arising from univariate and multivariate differential equations with symmetric and non symmetric difference operators. Also the possibility of a Chebyshev acceleration of the AGE-1D algorithm is considered. For two and three dimensional problems it is proposed to couple the use of the AGE-1D algorithm with an ADI scheme or an ADI iterative method in what is called the Explicit Alternating Direction (EAD) method. It is then shown through experimental results that the EAD method retains the parallel features of the AGE method and moreover leads to savings of up to 83 % in the computational cost for solving some of the model problems. The thesis also includes applications of the AGE-1D algorithm and the EAD method to solve some problems of fluid dynamics such as the linearized Shallow Water equations, and the Navier Stokes' equations for the flow in an idealized one dimensional Planetary Boundary Layer. The thesis terminates with conclusions and suggestions for further work together with a comprehensive bibliography and an appendix containing some selected programs.
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Mora, Acosta Josue. "Numerical algorithms for three dimensional computational fluid dynamic problems." Doctoral thesis, Universitat Politècnica de Catalunya, 2001. http://hdl.handle.net/10803/6685.
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The target of this work is to contribute to the enhancement of numerical methods for the simulation of complex thermal systems. Frequently, the factor that limits the accuracy of the simulations is the computing power: accurate simulations of complex devices require fine three-dimensional discretizations and the solution of large linear equation systems.Their efficient solution is one of the central aspects of this work. Low-cost parallel computers, for instance, PC clusters, are used to do so. The main bottle-neck of these computers is the notwork, that is too slow compared with their floating-point performance.
Before considering linear solution algorithms, an overview of the mathematical models used and discretization techniques in staggered cartesian and cylindrical meshes is provided.
The governing Navier-Stokes equations are solved using an implicit finite control volume method. Pressure-velocity coupling is solved with segregated approaches such as SIMPLEC.
Different algorithms for the solution of the linear equation systems are reviewed: from incomplete factorizations such as MSIP, Krylov solvers such as BICGSTAB and GMRESR to acceleration techniques such as the Algebraic Multi Grid and the Multi Resolution Analysis with wavelts. Special attention is paid to preconditioned Krylov solvers for their application to parallel CFD problems.
The fundamentals of parallel computing in distributed memory computers as well as implemetation details of these algorithms in combination with the domain decomposition method are given. Two different distributed memory computers, a Cray T3E and a PC cluster are used for several performance measures, including network throughput, performance of algebraic subroutines that affect to the overall efficiency of algorithms, and the solver performance. These measures are addressed to show the capabilities and drawbacks of parallel solvers for several processors and their partitioning configurations for a problem model.
Finally, in order to illustrate the potential of the different techniques presented, a three-dimensional CFD problem is solved using a PC cluster. The numerical results obtained are validated by comparison with other authors. The speedup up to 12 processors is measured. An analysis of the computing time shows that, as expected, most of the computational effort is due to the pressure-correction equation,here solved with BiCGSTAB. The computing time algorithm , for different problem sizes, is compared with Schur-Complement and Multigrid.
El trabajo de tesis se centra en la solución numérica de las ecuaciones de navier-Stokes en regimen transitorio, tridimensional y laminar. Los algoritmos utilizados son del tipo segregado (SIMPLEC)y se basan en el uso de técnicas de volumenes finitos, con mallas estructurales del tipo staggered y discretizaciones temporales implícitas. En este contexto, el pricipal, problema son los elevados tiempos de cálculo de las simulaciones, que en buena parte se deben a la solución de los sistemas de ecuaciones lineales. Se hace una revisión de diferentes métodos utilizados típicamente en ordenadores secuenciales: GMRES, BICGSTAB, ACM, MSPIP.
A fin de reducir los tiempos de cálculo se emplean ordenadores paralelos de memoria distribuida, basados en la agrupacion de ordenadores personales convencionales (PC clusters). Por lo que respecta a la potencia de cálculo por procesador, estos sistemas son comparables a los ordenadores paralelos de memoria distribuida convencionales (como el Cray T3E) siendo, su principal problema la baja capacidad de comunicación (elevada latencia, bajo ancho de banda). Este punto condiciona toda la estrategia computacional, obligando a reducir al máximo el número y el tamaño de los mensajes intercambiados. Este aspecto se cuantifica detalladamente en la tesis, realizando medidas de tiempos de cálculo en ambos ordenadores para diversas operaciones críticas para los algoritmos lineales. Tambien se miden y comparan los tiempos de cálculo y speed ups obtenidos en la solución de los sistemas lineales con diferentes algoritmos paralelos (Jacobi, MSIP, GMRES, BICGSTAB) y para diferentes tamaños de malla.
Finalmente, se utilizan las técnicas anteriores para resolver el caso denominado driven cavity, en situacionies tridimensionales y con numeros de Reynolds de hasta 8000. Los resultados obtenidos se utilizan para validar los códigos desarrollados, en base a resultados de otros códigos y también se basa en la comparación con resultados experimentales procedentes de la bibliografía. Se utilizan hasta 12 procesadores, obteniendose spped ups de hasta 9.7 en el cluster de PCs. Se analizan los tiempos de cálculo de cada fase del código, señalandose areas para futuras mejoras. Se comparan los tiempos de cálculo con los algoritmos implementados en otros trabajos. La conclusión final es que los clusters de PCs son una plataforma de gran potencia en los cálculos de dinámica de fluidos computacional.
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Fabritius, Björn. "Application of genetic algorithms to problems in computational fluid dynamics." Thesis, University of Exeter, 2014. http://hdl.handle.net/10871/15236.
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In this thesis a methodology is presented to optimise non–linear mathematical models in numerical engineering applications. The method is based on biological evolution and uses known concepts of genetic algorithms and evolutionary compu- tation. The working principle is explained in detail, the implementation is outlined and alternative approaches are mentioned. The optimisation is then tested on a series of benchmark cases to prove its validity. It is then applied to two different types of problems in computational engineering. The first application is the mathematical modeling of turbulence. An overview of existing turbulence models is followed by a series of tests of different models applied to various types of flows. In this thesis the optimisation method is used to find improved coefficient values for the k–ε, the k–ω-SST and the Spalart–Allmaras models. In a second application optimisation is used to improve the quality of a computational mesh automatically generated by a third party software tool. This generation can be controlled by a set of parameters, which are subject to the optimisation. The results obtained in this work show an improvement when compared to non–optimised results. While computationally expensive, the genetic optimisation method can still be used in engineering applications to tune predefined settings with the aim to produce results of higher quality. The implementation is modular and allows for further extensions and modifications for future applications.
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Yang, Guodong. "Cartesian mesh techniques for moving body problems and shock wave modelling." Thesis, Manchester Metropolitan University, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.360893.
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Kunda, Wilkinson. "Two phase problems and two phase flow." Thesis, University of Hull, 1986. http://hydra.hull.ac.uk/resources/hull:5902.
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In section 1 of this thesis a two-dimensional mathematical model is used to investigate the circulation in a gas-bubble agitation system of a cylindrical vessel for the case of an orifice located at the centre of the base. The two-phase (liquid/gas) region is assumed to be confined to a cone-shaped region and is investigated using Wallis' Drift Flux Model. In the single-phase (liquid) region the turbulent Navier-Stokes equations, written in terms of the stream function, are used for the mathematical model. The analysis in the two-phase region yields the boundary conditions on the two-phase/single-phase boundary. The velocity field in the two-phase region is solved analytically giving results in closed form. A numerical algorithm is developed for calculating liquid flow in the single phase region, and numerical results are presented graphically in terms of the stream function. In section 2 two moving interface problems are investigated. Small time analytic solutions are found for three-dimensional inward solidification of a half space initially at fusion temperature in the first problem. In the second problem, perturbation solutions for melting of a cylindrical annulus with constant heat flux on inner surface are given. In both problems the interface immobilization technique is used. Interface locations at various times are calculated for the inward solidification problem and the results shown in three-dimensional graphs. First and second perturbation terms for the interface location are given for the second problem and graphs of each are presented for a particular case.
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Reid, Cynthia 1958. "A class of solutions in non-homogeneous fluid dynamics obtained by the Riemann-invariant method /." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66007.
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Kim, Tae Eun. "Quasi-solution Approach to Nonlinear Integro-differential Equations: Applications to 2-D Vortex Patch Problems." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1499793039477532.
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Harris, Paul John. "The numerical solution of the dynamic fluid-structure interaction problem." Thesis, University of Plymouth, 1989. http://hdl.handle.net/10026.1/2055.
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In this thesis we consider the problem of the dynamic fluid-structure interaction between a finite elastic structure and the acoustic field in an unbounded fluid-filled exterior domain. We formulate the exterior acoustic problem as an integral equation over the structure surface. However, the classical boundary integral equation formulations of this problem do not have unique solutions at certain characteristic frequencies (which depend on the surface) and it is necessary to employ modified boundary integral equation formulations which are valid for all frequencies. The modified integral equation formulation used here involves certain arbitrary parameters and we shall study the effect of these parameters on the stability and accuracy of the numerical methods used to solve the integral equation. We then couple the boundary element analysis of the exterior acoustic problem with a finite element analysis of the elastic structure to investigate the interaction between the structure and the acoustic field. Recently there has been some controversy over whether or not the coupled problem suffers from the non-uniqueness problems associated with the classical integral equation formulations of the exterior acoustic problem. We resolve this question by demonstrating that the solution to the coupled problem is not unique at the characteristic frequencies and that we need to employ an integral equation formulation valid for all frequencies. We discuss the accuracy of our numerical results for both the acoustic problem and the coupled problem, for a number of axisymmetric and fully three-dimensional problems. Finally, we apply our method to the problem of a piezoelectric sonar transducer transmitting an acoustic signal in water, and observe reasonable agreement between our theoretical predictions and some experimental results.
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Chemama, Michael Leopold. "Flames, Splashes and Microdroplets: A Mathematical Approach to Three Fluid Dynamics Problems." Thesis, Harvard University, 2015. http://nrs.harvard.edu/urn-3:HUL.InstRepos:14226101.
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Three different problems in fluid mechanics are presented in this thesis. The first one deals with the mechanism behind the extinction of a flame by an alternating electric field. A simple model for the interaction between the field and the ions produced by the reaction is presented, which agrees quantitatively with the experiments. It also indicates that charges diffusion is responsible for the non-zero time averaged force on the flame. The second problem focuses on the role of viscosity during the splash of liquid droplets. We show that contrary to what was done in previous theoretical studies, the role of viscosity cannot be investigated within the framework of a boundary layer approximation. Rather, the full viscous term must be included in the equations. Finally, we present the theory behind a new microfluidic device (called centipede) which produces microdroplets at a very high rate without relying on any active element to precipitate the detachment of the drops. We clearly show that the drops detach through a Rayleigh-Plateau instability in an otherwise quasi-static flow. We also predict how the throughput and size of the drops are affected by the geometrical parameters of the device.
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Brandén, Henrik. "Convergence Acceleration for Flow Problems." Doctoral thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-576.
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Convergence acceleration techniques for the iterative solution of system of equations arising in the discretisations of compressible flow problems governed by the steady state Euler or Navier-Stokes equations is considered. The system of PDE is discretised using a finite difference or finite volume method yielding a large sparse system of equations. A solution is computed by integrating the corresponding time dependent problem in time until steady state is reached. A convergence acceleration technique based on semicirculant approximations is applied. For scalar model problems, it is proved that the preconditioned coefficient matrix has a bounded spectrum well separated from the origin. A very simple time marching scheme such as the forward Euler method can be used, and the time step is not limited by a CFL-type criterion. Instead, the time step can asymptotically be chosen as a constant, independent of the number of grid points and the Reynolds number. Numerical experiments show that grid and parameter independent convergence is achieved also in more complicated problem settings. A comparison with a multigrid method shows that the semicirculant convergence acceleration technique is more efficient in terms of arithmetic complexity. Another convergence acceleration technique based on fundamental solutions is proposed. An algorithm based on Fourier technique is provided for the fast application. Scalar model problems are considered and a theory, where the preconditioner is represented as an integral operator is derived. Theory and numerical experiments show that for first order partial differential equations, grid independent convergence is achieved.
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Jordan, Donald Alfred. "Application of the continuous wavelet transform to science and engineering problems : fluid dynamics case studies /." Digital version accessible at:, 1998. http://wwwlib.umi.com/cr/utexas/main.
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Larrañaga, Maialen. "Dynamic control of stochastic and fluid resource-sharing systems." Thesis, Toulouse, INPT, 2015. http://www.theses.fr/2015INPT0075/document.
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Dans cette thèse, nous étudions le contrôle dynamique des systèmes de partage de ressources qui se posent dans divers domaines : réseaux de gestion des stocks, services de santé, réseaux de communication, etc. Nous visons à allouer efficacement les ressources disponibles entre des projets concurrents, selon certains critères de performance. Ce type de problème est de nature stochastique et peut être très complexe à résoudre. Nous nous concentrons donc sur le développement de méthodes heuristiques performantes. Dans la partie I, nous nous plaçons dans le cadre des Restless Bandit Problems, qui est une classe générale de problèmes d’optimisation dynamique stochastique. Relaxer la contrainte de trajectoire dans le problème d’optimisation permet de définir une politique d’index comme heuristique pour le modèle contraint d’origine, aussi appelée politique d’index de Whittle. Nous dérivons une expression analytique pour l’index de Whittle en fonction des probabilités stationnaires de l’état dans le cas où les bandits (ou projets) suivent un processus de naissance et de mort. D’une part, cette expression nécessite la vérification de plusieurs conditions techniques, d’autre part elle ne peut être calculée explicitement que dans certains cas spécifiques. Nous prouvons ensuite, que dans le cas particulier d’une file d’attente multi-classe avec abandon, la politique d’index de Whittle est asymptotiquement optimale aussi bien pour les régimes à faible trafic comme pour ceux à fort trafic. Dans la partie II, nous dérivons des heuristiques issues de l’approximation des systèmes stochastiques de partage de ressources par des modèles fluides déterministes. Nous formulons dans un premier temps une version fluide du problème d’optimisation relaxé que nous avons introduit dans la partie I, et développons une politique d’index fluide. L’index fluide peut toujours être calculé explicitement et surmonte donc les questions techniques qui se posent lors du calcul de l’index de Whittle. Nous appliquons les politiques d’index de Whittle et de l’index fluide à plusieurs cas : les fermes de serveurs éco-conscients, l’ordonnancement opportuniste dans les systèmes sans fil, et la gestion de stockage de produits périssables. Nous montrons numériquement que ces politiques d’index sont presque optimales. Dans un second temps, nous étudions l’ordonnancement optimal de la version fluide d’une file d’attente multi-classe avec abandon. Nous obtenons le contrôle optimal du modèle fluide en présence de deux classes de clients en concurrence pour une même ressource. En nous appuyant sur ces derniers résultats, nous proposons une heuristique pour le cas général de plusieurs classes. Cette heuristique montre une performance quasi-optimale lorsqu’elle est appliquée au modèle stochastique original pour des charges de travail élevées. Enfin, dans la partie III, nous étudions les phénomènes d’abandon dans le contexte d’un problème de distribution de contenu. Nous caractérisons une politique optimale de regroupement afin que des demandes issues d’utilisateurs impatients puissent être servies efficacement en mode diffusionIn this thesis we study the dynamic control of resource-sharing systems that arise in various domains: e.g. inventory management, healthcare and communication networks. We aim at efficiently allocating the available resources among competing projects according to a certain performance criteria. These type of problems have a stochastic nature and may be very complex to solve. We therefore focus on developing well-performing heuristics. In Part I, we consider the framework of Restless Bandit Problems, which is a general class of dynamic stochastic optimization problems. Relaxing the sample-path constraint in the optimization problem enables to define an index-based heuristic for the original constrained model, the so-called Whittle index policy. We derive a closed-form expression for the Whittle index as a function of the steady-state probabilities for the case in which bandits (projects) evolve in a birth-and-death fashion. This expression requires several technical conditions to be verified, and in addition, it can only be computed explicitly in specific cases. In the particular case of a multi-class abandonment queue, we further prove that the Whittle index policy is asymptotically optimal in the light-traffic and heavy-traffic regimes. In Part II, we derive heuristics by approximating the stochastic resource-sharing systems with deterministic fluid models. We first formulate a fluid version of the relaxed optimization problem introduced in Part I, and we develop a fluid index policy. The fluid index can always be computed explicitly and hence overcomes the technical issues that arise when calculating the Whittle index. We apply the Whittle index and the fluid index policies to several systems: e.g. power-aware server-farms, opportunistic scheduling in wireless systems, and make-to-stock problems with perishable items. We show numerically that both index policies are nearly optimal. Secondly, we study the optimal scheduling control for the fluid version of a multi-class abandonment queue. We derive the fluid optimal control when there are two classes of customers competing for a single resource. Based on the insights provided by this result we build a heuristic for the general multi-class setting. This heuristic shows near-optimal performance when applied to the original stochastic model for high workloads. In Part III, we further investigate the abandonment phenomena in the context of a content delivery problem. We characterize an optimal grouping policy so that requests, which are impatient, are efficiently transmitted in a multi-cast mode
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Pathak, Saurabh. "Quantification Of Internal Droplet Motion Using Particle Image velocimetry For Various Engineering Problem." University of Akron / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=akron1619458988178314.
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Gloth, Oliver. "An Object-Oriented Finite Volume Framework and its Application to Fluid Dynamics Problems." Gerhard-Mercator-Universitaet Duisburg, 2003. http://www.ub.uni-duisburg.de/ETD-db/theses/available/duett-07282003-103524/.
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This work describes the development of a framework for numerical simulation software, using the finite volume method. A major guideline has been flexibility. The framework is written in C++, making strong use of its object-oriented capabilities. Outlined are the benefits, as well as the pitfalls related to object-oriented programming, if used for numerical simulations. The text explains that flexibility has not only been tried to achieve in terms of software design, but also with respect to the numerical approaches used. The field of application in the scope of this work is computational fluid dynamics. Thus a brief overview over the necessary equations and the employed numerical techniques is given. Furthermore a number of example computations can be found in this text. An important part of this work deals with a novel approach for unstructured mesh generation. The approach is based on multi element type grids and uses level-sets as input to describe the geometry. It is well suited to create anisotropic layers, such as boundary layer grids for fluid dynamics problems. Furthermore it can deal with moving and even topologically changing geometries. In the scope of this work it is limited to two-dimensional problems.
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Schrecker, Matthew. "Hyperbolic problems in fluids and relativity." Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:2dec2eb9-4253-4625-a071-0c19d0c1f76d.
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In this thesis, we present a collection of newly obtained results concerning the existence of vanishing viscosity solutions to the one-dimensional compressible Euler equations of gas dynamics, with and without geometric structure. We demonstrate the existence of such vanishing viscosity solutions, which we show to be entropy solutions, to the transonic nozzle problem and spherically symmetric Euler equations in Chapter 4, in both cases under the simple and natural assumption of relative finite-energy. In Chapter 5, we show that the viscous solutions of the one-dimensional compressible Navier-Stokes equations converge, as the viscosity tends to zero, to an entropy solution of the Euler equations, again under the assumption of relative finite-energy. In so doing, we develop a compactness framework for the solutions and approximate solutions to the Euler equations under the assumption of a physical pressure law. Finally, in Chapter 6, we consider the Euler equations in special relativity, and show the existence of bounded entropy solutions to these equations. In the process, we also construct fundamental solutions to the entropy equations and develop a compactness framework for the solutions and approximate solutions to the relativistic Euler equations.
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Molina, Nicolás. "Quelques problèmes de contrôle et d’analyse pour des équations de la dynamique des fluides." Thesis, Université Paris sciences et lettres, 2020. http://www.theses.fr/2020UPSLD031.
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Dans cette thèse, on étudie des problèmes de contrôle et des problèmes de Cauchy dans la mécanique des milieux continus, en particulier sur la mécanique de fluides. On montre un résultat de contrôlabilité pour l'équation de Navier-Stokes non isentropique, où la pression dépend de la température et de la densité, un résultat de stabilisation avec un contrôle en boucle fermée dans la densité. Finalement, on montre un résultat d’existence pour le problème de Cauchy pour un solide élastique plongé dans un fluide EulerienIn this thesis we study control related problems and Cauchy problems that appear in continuum mechanics, with anemphasis in fluids. We present a local null controllability result for the non-isentropic Navier-Stokes equations where thepressure depends on the temperature as well as the density, a local stabilization with state feedback law on the densityfor the isentropic case of Navier-Stokes, and finally, we present an existence result for the Cauchy problem of a linearelastic solid submerged on an Eulerian fluid in the case of a finite number of modes approximation
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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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Lundvall, Johan. "Data Assimilation in Fluid Dynamics using Adjoint Optimization." Doctoral thesis, Linköping : Matematiska institutionen, Linköpings universitet, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-9684.
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Raju, Anil Roy Christopher J. "Discretization error estimation using the method of nearby problems one-dimensional cases/." Auburn, Ala., 2005. http://repo.lib.auburn.edu/2005%20Fall/Thesis/RAJU_ANIL_41.pdf.
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Yang, Zhiyun. "A Cartesian grid method for elliptic boundary value problems in irregular regions /." Thesis, Connect to this title online; UW restricted, 1996. http://hdl.handle.net/1773/6759.
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FILHO, GUENTHER CARLOS KRIEGER. "APPLICATION OF SELF-ADAPTIVE MESHES METHODS TO PROBLEMS IN FLUID DYNAMICS: A COMPARATIVE STUDY." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1991. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=33253@1.
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOEste trabalho aplica três métodos básicos de malhas auto-adaptativas em problemas de mecânica dos fluidos e transmissão de calor. Um método unidimensional é aplicado a problemas descritos pela equação generalizada de Burgers. Um método bidimensional é aplicado ao problema da. cavidade com tampa móvel para números de Reynolds Iguais a 100, 500 e 1000 e ao problema de convecção natural em uma cavidade para números de Rayleigh iguais a 10 elevado a 3,10 elevado a 4,10 elevado a 5 e 10 elevado a 6. Um terceiro método, fundamentado em um sistema de equações elípticas é proposto e aplicado ao problema de convecção natural na cavidade, para análise de desempenho. Procura-se definir, para cada aplicação, critérios como: a) variável indicada para dirigir a adaptação; b) especiacação da intensidade desejada na adaptação e c) justificação para o uso de malhas auto-adaptativas no problema em estudo. Observa-se, nos problemas unidimensionais, que quando o problema tem uma região única de intensos gradientes, a adaptação da malha funciona convenientemente, especialmente na presença de um termo de fonte. No problema da cavidade com, tampa móvel, verifica-se que a função de corrente deve dirigir a adaptação. Para Re igual a 1000 o método empregado consegue melhorar a descrição geral do problema. O problema de convecção natural apresenta melhores resultados para Ra: 10 elevado a 6 e com a adaptação dirigida pelo gradiente da temperatura que está diretamente relacionado ao termo de fonte do problema (forças de empuxo). São consideradas as características geométricas de ortogonalidade e suavidade das malhas adaptadas. Para isso, compara-se malhas obtidas pelos métodos bidimensionais implementados. Observa-se que o método fundamentado no sistema elíptíco consegue concentrar a malha nas regiões de intensos gradientes, sem danos excessivos naquelas características.
The present work is concerned to the study and implementation of self-adaptive grids to tluid mechanics and heat transfer problems. Initially, a ID method is applied to simple problems described by the generalized Burger-s equation, After that, a 2-D method is applied to the wall driven Cavity with Reynolds numbers equal to 100, 500 and 1000 and to the natural convection problem inside cavltles with Rayleigh numbers equal to 10 to the third power, 10 to the fourth power, 10 to the fifth power and 10 to the sixth power. A third method, based on a system of elliptic equations is proposed and applied to this natural convection problem, for error assessmet. For each application, one seeks to define criteria such as: a) most suitable dependent variable to drive the adaptive technique; b) intensity of the adaptive technique and c) need for the use of the technique at all. From the 1-D problems, it may be concluded that in presence of single regions of strong gradients, the technidne works line, specially shenever a source term is present. From the wall driven cavity problem, it appears that the stream function is most suitable to be the driving force for the adaptation. For instance, for Reynolds number on the order of 1000, the used method works well. The natural convectlon problem indicates best results for high Rayleigh numbers, say 10 to the sixth power, and with the use of the temperature gradient that is straight related to the source term, that is, buoyancy in the case. In the present work, geometric characteristics such as ortogonality and smooth are considered. Among the three methods, studied, it seems that the elliptic one, proposed here, is able to concentrate grid points Whenever needed, without severe penalization to those characteristics.
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Suliman, Ridhwaan. "A quadratic non-linear elasticity formulation for the dynamic behaviour of fluid-loaded structures." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/277824.
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This work details the development and implementation of a numerical model capable of solving strongly-coupled fluid-structure interaction problems involving long thin structures, which are common multi-physics problems encountered in many applications. In most fluid-structure interaction problems the deformation of the slender elastic bodies is significant and cannot be described by a purely linear analysis. We present a new formulation to model these larger displacements. By extending the standard modal decomposition technique for linear structural analysis, the governing equations and boundary conditions are updated to account for the leading-order non-linear terms and a new modal formulation with quadratic modes is derived. The quadratic modal approach is tested on standard benchmark problems of increasing complexity and compared with analytical and full non-linear numerical solutions. Two computational fluid-structure interaction approaches are then implemented in a partitioned manner: a finite volume method for discretisation of both the fluid and solid domains and the quadratic modal formulation for the structure coupled with a finite volume fluid solver. Strong-coupling is achieved by means of a fixed-point solver with dynamic relaxation. The fluid-structure interaction approaches are validated and compared on benchmark problems of increasing complexity and strength of coupling between the fluid and solid domains. Fluid-structure interaction systems may become unstable due to the interaction between the fluid-induced pressure and structural rigidity. A thorough stability analysis of finite elastic plates in uniform flow is conducted by varying the structural length and flow velocity showing that these are critical parameters. Validation of the results with those from analytical methods is done. An analysis of the dynamic interactions between multiple finite plates in various configurations is also conducted.
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Bozkaya, Canan. "Boundary Element Method Solution Of Initial And Boundary Value Problems In Fluid Dynamics And Magnetohydrodynamics." Phd thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12609552/index.pdf.
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In this thesis, the two-dimensional initial and boundary value problems invol-ving convection and diffusion terms are solved using the boundary element method (BEM). The fundamental solution of steady magnetohydrodynamic (MHD) flow equations in the original coupled form which are convection-diffusion type is established in order to apply the BEM directly to these coupled equations with the most general form of wall conductivities. Thus, the solutions of MHD flow in rectangular ducts and in infinite regions with mixed boundary conditions are obtained for high values of Hartmann number, M.
For the solution of transient convection-diffusion type equations the dual reciprocity boundary element method (DRBEM) in space is combined with the differential quadrature method (DQM) in time. The DRBEM is applied with the fundamental solution of Laplace equation treating all the other terms in the equation as nonhomogeneity. The use of DQM eliminates the need of iteration and very small time increments since it is unconditionally stable. Applications include unsteady MHD duct flow and elastodynamic problems. The transient Navier-Stokes equations which are nonlinear in nature are also solved with the DRBEM in space - DQM in time procedure iteratively in terms of stream function and vorticity. The procedure is applied to the lid-driven cavity flow for moderate values of Reynolds number. The natural convection cavity flow problem is also solved for high values of Rayleigh number when the energy equation is added.
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Gomes, Henrique Campelo. "Método dos elementos finitos com fronteiras imersas aplicado a problemas de dinâmica dos fluidos e interação fluido-estrutura." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/3/3144/tde-26122013-150059/.
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Este trabalho pode ser dividido em três etapas principais. Inicialmente é proposta uma formulação estabilizada do método dos elementos finitos (MEF) para solução de problemas de escoamento incompressível governado pela equação de Navier-Stokes. Esta formulação foi implementada em um código computacional e testada através de diversos exemplos numéricos. Alguns elementos finitos com diferentes pares de função de interpolação da velocidade e pressão, consagrados na literatura, e também elementos finitos menos populares, foram investigados e seus resultados e performance comparados. A segunda etapa consiste na formulação do problema estrutural. Buscou-se por uma formulação dinâmica, não linear, capaz de simular movimentos complexos de estruturas sujeitas a grandes deslocamentos e grandes deformações durante longos intervalos de tempo. A etapa final deste trabalho é a proposição de um método para solução de problemas de Interação Fluido Estrutura (IFE) que utiliza o conceito de fronteiras imersas como alternativa a abordagens ALE (Arbitrary Lagrangian Eulerian) clássicas. Elementos Finitos Generalizados, juntamente com Multiplicadores de Lagrange, são utilizados para prover descontinuidade nos campos de velocidade e pressão do fluido ao longo da interface com a estrutura. O acoplamento dos dois problemas é realizado utilizando um método implícito e alternado (staggered scheme), que possui a vantagem de permitir, facilmente, a implementação de códigos computacionais desenvolvidos para resolver isoladamente o problema fluido e/ou estrutural.This work is divided in three parts. Initially, it is presented a stabilized Finite Element Method formulation to solve fluid flow problems governed by the incompressible Navier-Stokes Equations. This formulation was implemented in a computer code and validated throughout several numeric simulations. Some well-known finite elements with different pairs of velocity/pressure approximations, as well as some other less popular elements, were investigated and their performance compared. The second part describes the Structural Problem formulation. This formulation is able to simulate nonlinear dynamic problems involving large displacements and finite strains during long period of time. In the final part of this work, it is proposed a Fluid-Structure Interaction method based on an immersed interface approach in opposition to classical ALE (Arbitrary Lagrangian Eulerian) approaches. Generalized Finite Elements, together with Lagrange Multipliers, are used to provide velocity and pressure discontinuities on the fluid domain across the immersed interface. To couple both fluid and structural problems, an implicit staggered scheme is adopted, which allows the easy implementation of already developed black box computer codes.
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Yoon, Sung Joon. "Numerical Navier-Stokes solutions of supersonic slot injection problems." Diss., Virginia Polytechnic Institute and State University, 1988. http://hdl.handle.net/10919/54473.
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Supersonic slot injection problems were studied by a finite volume method. The numerical technique used is the upwind method of Roe’s flux difference splitting (FDS) with vertical line Gauss-Seidel relaxation applied to the thin layer Navier-Stokes equations. To test the accuracy of the numerical methods without the complications and uncertainties of turbulence modeling, two sample cases were chosen with laminar flows. The sample problems were the compressible laminar boundary layer flow over a flat plate and the laminar boundary layer - shock interaction problem. For these problems, both the results from Roe’s FDS and van Leer’s flux vector splitting (FVS) are compared with exact solutions and experimental data. For the sample problems, comparisons showed that Roe’s FDS method is more accurate than van Leer’s FVS method. Because of the very complicated wave patterns and strong viscous-inviscid interaction produced by supersonic slot injection, an adaptive grid based on the equidistribution law was combined with the solution algorithm. The results from Roe’s FDS method with the adaptive grid showed good results for the supersonic slot injection over a flat plate. For the slot injection over a 10-degree wedge surface case, there is a significant difference between the numerical and experimental wall pressure distribution. Some potential reasons for the discrepancy including 3D effects and/or transition in the reattachment region in the experiments and possibly a need for a much finer grid in the calculations are discussed.Ph. D.
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Alsoy-akgun, Nagehan. "The Dual Reciprocity Boundary Element Solutions Of Helmholtz-type Equations In Fluid Dynamics." Phd thesis, METU, 2013. http://etd.lib.metu.edu.tr/upload/12615728/index.pdf.
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In this thesis, the two-dimensional, unsteady, laminar and incompressible fluid flow problems governed by partial differential equations are solved by using dual reciprocity boundary element method (DRBEM). First, the governing equations are transformed to the inhomogeneous modified Helmholtz equations, and then the fundamental solution of modified Helmholtz equation is used for obtaining boundary element method (BEM) formulation. Thus, all the terms in the equation except the modified Helmholtz operator are considered as inhomogeneity. All the inhomogeneity terms are approximated by using suitable radial basis functions, and corresponding particular solutions are derived by using the annihilator method. Transforming time dependent partial differential equations to the form of inhomogeneous modified Helmholtz equations in DRBEM application enables us to use more information from the original governing equation. These are the main original parts of the thesis. In order to obtain modified Helmholtz equation for the time dependent partial differential equations, the time derivatives are approximated at two time levels by using forward finite difference method. This also eliminates the need of another time integration scheme, and diminishes stability problems.
Stream function-vorticity formulations are adopted in physical fluid dynamics problems in DRBEM by using constant elements. First, the procedure is applied to the lid-driven cavity flow and results are obtained for Reynolds number values up to $2000.$ The natural convection flow is solved for Rayleigh numbers between $10^3$ to $10^6$ when the energy equation is added to the Navier-Stokes equations. Then, double diffusive mixed convection flow problem defined in three different physical domains is solved by using the same procedure. Results are obtained for various values of Richardson and Reynolds numbers, and buoyancy ratios. Behind these, DRBEM is used for the solution of natural convection flow under a magnetic field by using two different radial basis functions for both vorticity transport and energy equations. The same problem is also solved with differential quadrature method using the form of Poisson type stream function and modified Helmholtz type vorticity and energy equations. DRBEM and DQM results are obtained for the values of Rayleigh and Hartmann numbers up to $10^6$ and $300,$ respectively, and are compared in terms of accuracy and computational cost. Finally, DRBEM is used for the solution of inverse natural convection flow under a magnetic field using the results of direct problem for the missing boundary conditions.
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Alsoy-akgun, Nagehan. "The Dual Reciprocity Boundary Element Solution Of Helmholtz-type Equations In Fluid Dynamics." Phd thesis, METU, 2013. http://etd.lib.metu.edu.tr/upload/12615729/index.pdf.
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In this thesis, the two-dimensional, unsteady, laminar and incompressible fluid flow problems governed by partial differential equations are solved by using dual reciprocity boundary element method (DRBEM). First, the governing equations are transformed to the inhomogeneous modified Helmholtz equations, and then the fundamental solution of modified Helmholtz equation is used for obtaining boundary element method (BEM) formulation. Thus, all the terms in the equation except the modified Helmholtz operator are considered as inhomogeneity. All the inhomogeneity terms are approximated by using suitable radial basis functions, and corresponding particular solutions are derived by using the annihilator method. Transforming time dependent partial differential equations to the form of inhomogeneous modified Helmholtz equations in DRBEM application enables us to use more information from the original governing equation. These are the main original parts of the thesis. In order to obtain modified Helmholtz equation for the time dependent partial differential equations, the time derivatives are approximated at two time levels by using forward finite difference method. This also eliminates the need of another time integration scheme, and diminishes stability problems.
Stream function-vorticity formulations are adopted in physical fluid dynamics problems in DRBEM by using constant elements. First, the procedure is applied to the lid-driven cavity flow and results are obtained for Reynolds number values up to 2000. The natural convection flow is solved for Rayleigh numbers between 10^3 to 10^6 when the energy equation is added to the Navier-Stokes equations. Then, double diffusive mixed convection flow problem defined in three different physical domains is solved by using the same procedure. Results are obtained for various values of Richardson and Reynolds numbers, and buoyancy ratios. Behind these, DRBEM is used for the solution of natural convection flow under a magnetic field by using two different radial basis functions for both vorticity transport and energy equations. The same problem is also solved with differential quadrature method using the form of Poisson type stream function and modified Helmholtz type vorticity and energy equations. DRBEM and DQM results are obtained for the values of Rayleigh and Hartmann numbers up to 10^6 and 300, respectively, and are compared in terms of accuracy and computational cost. Finally, DRBEM is used for the solution of inverse natural convection flow under a magnetic field using the results of direct problem for the missing boundary conditions.
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Verdicchio, John Anthony. "The validation and coupling of computational fluid dynamics and finite element codes for solving 'industrial problems'." Thesis, University of Sussex, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270320.
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A modern gas turbine must be designed quicker, be more reliable, produce less emissions than its predecessors and yet the engine manufacturer must still make a profit. In order to sell their engines to the airlines, the manufacturer must show that their engines meet strict safety and reliability requirements. The creation of finite element models used for predicting temperatures and displacements of the engine component's is part of this design cycle. This thesis addresses the use of computational fluid dynamics (CFD) as a tool that can help in the prediction of iiietal temperatures for use with "industrial" problems and the associated requirements of accuracy and time-scales. The definition of 'industrial" accuracy and time-scales in this thesis is the accuracy required to enhance the modelling capability of a thermal engineer in design time-scales. A method is developed for using a commercial CFD code. FLUENT, for predicting flow and heat transfer. The code has been validated against several benchmark test cases and has shown good predictive capability and mesh independence for flow and heat transfer in the cavity between a rotating and stationary disc with and without through-flow. For cavities between co-rotating discs with radial througliflow, the predictions are acceptable, but some sensitivity of the heat transfer results to mesh spacing has been identified. The code has also been validated against some "industrial" test cases where experimental data has been available. The effects of buoyancy in the centrifugal force field are discussed and are related to a buoyancy number. The next part of the thesis develops a method of solving the heat transfer problem by coupling a finite element code, SC03, with FLUENT. The ideas are developed on two simple test cases and the problems of what information is to be passed across the coupling boundary and convergence issues are discussed. The results show that passing heat transfer coefficients and local air temperatures achieves the best convergence. The coupled method is their tested against two 'industrial problems. It is concluded that the method has considerable potential for use in design although some difficulties in applying the method are identified. Although not demonstrated, the method developed is not specific to SC03 or FLUENT and ally heat traiisfer/ CFD codes could be used.
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Radwan, Samir F. "Numerical solution of the three-dimensional boundary layer equations in the inverse mode using finite differences." Diss., Georgia Institute of Technology, 1985. http://hdl.handle.net/1853/12029.
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Webster, Robert Samuel. "A numerical study of the conjugate conduction-convection heat transfer problem." Diss., Mississippi State : Mississippi State University, 2001. http://library.msstate.edu/etd/show.asp?etd=etd-04102001-144805.
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Furbo, Eric. "Evaluation of RANS turbulence models for flow problems with signigicant impact of boundary layers." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-138757.
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This master’s thesis was provided by the Swedish Defence Research Agency, FOI. The task is to test several RANS (Reynolds-averaged Navier-Stokes) models on two different case geometries and compare the results with LES and experimental data. The first is two dimensional, constructed for flow separation at a sharp edge. The second is three dimensional and flow separation occurs at a smooth surface. The models tested are implemented in the open source CFD (Computational Fluid Dynamics) program, OpenFOAM. OpenFOAM uses the finite volume method and the SIMPLE algorithm as solution procedure. The main flow features evaluated is the shape, position and size of the flow separation. Most of the models tested have problems describing the complex dynamics of flow separation in these particular cases. In addition to the simulations, the RANS k-epsilon turbulence model is presented and the RANS equations and the equation for the turbulent kinetic energy are derived from the Navier-Stokes equations. The theory behind wall functions is described and these equations together with the equations in the k-epsilon model are compared with the equations implemented in OpenFOAM.
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Feldman, Jonathan. "Dynamic refinement and boundary contact forces in smoothed particle hydrodynamics with applications in fluid flow problems." Thesis, Swansea University, 2006. https://cronfa.swan.ac.uk/Record/cronfa42459.
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Smoothed Particle Hydrodynamics (SPH) is a relatively new, simple and effective numerical method that can be used to solve a variety of difficult problems in computational mechanics. It is a fully Lagrangian meshless method ideal for solving large deformation problems such as complex free surface fluid flows. This research was carried out with the support of BAE Systems and falls into two distinct areas. Firstly to investigate new methods for treating fixed boundaries and secondly to investigate refinement algorithms which allow for both sparsely and densely populated regions of particles within the same computational domain. Much work has been done in the modelling of particle-boundary interactions in SPH since the governing equations do not naturally incorporate essential boundary conditions. In this research a new technique for calculating boundary contact forces is developed. The forces are obtained from a variational principle and as such conserve both the linear and angular momentum of the system. The boundaries are explicitly defined using this new approach and so the need for additional boundary particles is removed. In the past most SPH derivations have been based on a uniform distribution of particles of equal mass. This leads to large simulations with many particles and long run times. In other mesh based schemes it has become common place to use mesh adaptivity to improve numerical results and reduce computation times. With a corresponding refinement strategy SPH can gain these same advantages. In this research a refinement strategy based upon particle splitting is developed. Candidate particles are split into several 'daughter' particles according to a given refinement pattern centred about the original particle position. Through the solution of a non-linear minimisation problem the optimal mass distribution for the daughter particles is obtained so as to reduce the errors introduced into the underlying density field. This procedure necessarily conserves the mass of the system. The unique daughter particle velocity configuration that conserves the linear and angular momentum of the system is also identified. The conclusion of the research was the successful implementation of these improvements into the existing SPH framework. As a result the capability and flexibility of the code is greatly increased and the computational expense needed for running large simulations has been reduced.
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Zarroug, Moundheur. "Asymptotic methods applied to some oceanography-related problems." Doctoral thesis, Stockholm : Department of Meteorology, Stockholm University, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-37763.
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Diss. (sammanfattning) Stockholm : Stockholms universitet, 2010.At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript.
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Mancilla, Alarcón Cristhian A. "Hydrodynamic loadings and responses of a floating guardwall a fluid-structure interaction problem /." Master's thesis, Mississippi State : Mississippi State University, 2005. http://library.msstate.edu/content/templates/?a=72.
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Tonin, Mateus Guimarães. "Análise isogeométrica aplicada a problemas de interação fluido-estrtura e superfície livre." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2017. http://hdl.handle.net/10183/163325.
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O presente trabalho tem por objetivo desenvolver uma formulação numérica baseada em Análise Isogeométrica para o estudo de problemas de interação fluido-estrutura (IFE) em aplicações envolvendo corpos rígidos submersos, onde escoamentos incompressíveis de fluidos Newtonianos com superfície livre são considerados. Propõe-se o emprego da Análise Isogeométrica por permitir a unificação entre os procedimentos de pré-processamento e análise, melhorando assim as condições de continuidade das funções de base empregadas tanto na discretização espacial do problema como na aproximação das variáveis do sistema de equações. O sistema de equações fundamentais do escoamento é formado pelas equações de Navier-Stokes e pela equação da conservação de massa, descrita segundo a hipótese de pseudo-compressibilidade, em uma formulação cinemática ALE (Arbitrary Lagrangean- Eulerian). A consideração da superfície livre no escoamento se dá tratando o fluido como um meio bifásico, através do método Level Set. O corpo rígido apresenta não linearidade na rotação e restrições representadas por vínculos elásticos e amortecedores viscosos, sendo a equação de equilíbrio dinâmico resolvida através do método de Newmark. O esquema de acoplamento sólido-fluido adotado é o particionado convencional, que impõe condições de compatibilidade cinemáticas e de equilíbrio sobre a interface sólido-fluido, analisando ambos os meios de maneira sequencial. A discretização das equações governantes é realizada através do esquema explícito de dois passos de Taylor-Galerkin, aplicado no contexto da Análise Isogeométrica. Por fim, são analisados alguns problemas da Dinâmica de Fluidos Computacional, de onde se concluiu que os resultados obtidos são bastante consistentes com os fenômenos envolvidos, com as ferramentas exclusivas da Análise Isogeométrica, como o refinamento k, melhorando a convergência dos resultados. Para escoamentos bifásicos, verificou-se que o método Level Set obteve resultados bastante promissores apresentando, entretanto, uma dissipação numérica excessiva. Propõe-se, para estudos futuros, a elaboração de esquemas numéricos que conservem melhor o volume da fase líquida do escoamento.The present work aims to development of a numerical formulation based on Isogeometric Analysis for the study of Fluid-Structure Interaction problems in applications involving rigid bodies submerged, considering incompressible Newtonian flows with free surface. The use of the Isogeometric Analysis allows unification between the preprocessing and analysis steps, improving then the continuity of the base functions employed, both in the spatial discretization and approximation of the variables in the system of equations. The fundamental flow equations are formed by the Navier-Stokes and the mass conservation, described by de pseudo-compressibility hypothesis, in an ALE (Arbitrary Lagrangean-Eulerian) kinematic formulation. The free surface consideration of the flow is handled treating the fluid like a two- phase medium, using the Level Set method. The rigid body considers nonlinearity in rotation, and restrictions represented by elastic springs and viscous dampers, with the dynamic equilibrium equation being resolved using the Newmark’s method. The solid-fluid coupling scheme is the conventional partitioned, which imposes kinematics and equilibrium compatibility conditions on the solid-fluid interface, analyzing both mediums in a sequential manner. The governing equations are discretized using the explicit two step Taylor-Galerkin method, applied in an Isogeometric Analisys context. Finally, some Computational Fluid Dinamics problems are analysed, from which it was concluded that the results obtained are quite consistent with phenomena involved, with the unique tools of Isogeometric Analysis, such as k-refinement, improving the convergence of the results. For biphasic flows, it was verified that the Level Set method obtained very promising results, presenting, however, an excessive numerical dissipation. For future studies, it is proposed the elaboration of numerical schemes that better preserve the volume of the liquid phase of the flow.
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Fjärstedt, Jenny. "Catheter Related Problems in Pediatric Oncology Treatment : A Technical Investigation Performed at Uppsala Akademsika Sjukhus." Thesis, Uppsala universitet, Tillämpad materialvetenskap, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-297294.
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In this project, problems related to loss of free flow in central venous catheter and implanted subcutaneous ports have been investigated. The catheters investigated in this project are intended for children with cancer diseases. The initial hypothesis was that the length, radius and curvature of the catheter would affect the flow. Two other things that can have a negative impact on the flow are if the catheter is squashed or kinked. Experiments and simulations have been performed in order to test the hypothesis and investigate how a deformation of the catheter affects the flow. The results from the experiments and simulations show that the length and radius of the catheter have major impact on the pressure drop, and hence the flow. The curvature of the catheter has less impact on the flow as long as the catheter is not kinked. Experiments with squashed catheters show a decrease in outlet pressure with a decrease of the catheter lumen.Denna projektrapport ämnar undersöka problem relaterade till fritt flöde i centrala venkatetrar och inopererade subkutana portar. Katetrarna som testats i detta projekt är till för barn med cancersjukdomar. Den ursprungliga hypotesen var att längden, radien och krökningen hos katetern påverkar flödet. Ytterligare två saker som skulle kunna ha negativ effekt på flödet är om katetern är klämd eller veckad. För att testa hypotesen om hur deformationer av katetern påverkar flödet har experiment och simuleringar utförts. Resultaten från experiment och simuleringar visar att kateterns längd och radie har störst effekt på tryckfallet och därmed flödet. Krökningen på katetern har mindre betydelse, så länge katetern inte är veckad. Experiment med klämd kateter visar att utloppstrycket minskar med minskad kateterlumen.
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Diniz, Dos Santos Nuno. "Méthodes numériques pour problèmes d'interaction fluide-structure avec valves." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2007. http://tel.archives-ouvertes.fr/tel-00521654.
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Cette thèse est motivée par la modélisation et la simulation numérique des phénomènes d'interaction fluide-structure autour de valves cardiaques. L'interaction avec la paroi des vaisseaux est traitée avec une formulation Arbitraire Lagrange Euler (ALE), tandis que l'interaction avec les valves est traitée à l'aide de multiplicateurs de Lagrange, dans une formulation de type Domaines Fictifs (FD). Après une présentation de synthèse des diverses méthodes utilisées en interaction fluide-structure dans les écoulements sanguins, nous décrivons une méthode permettant de simuler la dynamique d'une valve immergée dans un écoulement visqueux incompressible. L'algorithme de couplage est partionné, ce qui permet de conserver des solveurs fluides et structures indépendants. Le maillage du fluide est mobile pour suivre la paroi des vaisseaux, mais indépendant du maillage des valves. Ceci autorise des très grands déplacements sans nécessiter de remaillage. Nous proposons une stratégie pour gérer le contact entre plusieurs valves. L'algorithme est totalement indépendant des solveurs de structures et est bien adapté au couplage fluide-structure partionné. Enfin, nous proposons un schéma de couplage semi-implicite permettant de mêler efficacement les formulations ALE et FD. Toutes les méthodes considérées sont accompagnées de nombreux tests numériques en 2D et 3D.
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Latini, Chiara <1980>. "Numerical strategies for the solution of the magneto-fluid-dynamic problem at Low Magnetic Reynolds Numbers." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2011. http://amsdottorato.unibo.it/3269/.
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Lee, Hyung-Chun. "Analysis, finite element approximation, and computation of optimal and feedback flow control problems." Diss., Virginia Tech, 1994. http://hdl.handle.net/10919/37450.
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The analysis, finite element approximation, and numerical simulation of some control problems associated with fluid flows are considered.
First, we consider a coupled solid/fluid temperature control problem. This optimization problem is motivated by the desire to remove temperature peaks, i.e., "hot spots", along the bounding surface of containers of fluid flows. The heat equation of the solid container is coupled to the energy equation for the fluid. Control is effected by adjustments to the temperature of the fluid at the inflow boundary. We give a precise statement of the mathematical model, prove the existence and uniqueness of optimal solutions, and derive an optimality system. We study a finite element approximation and provide rigorous error estimates for the error in the approximate solution of the optimality system. We then develop and implement an iterative algorithm to compute the approximate solution.
Second, a computational study of the feedback control of the magnitude of the lift in flow around a cylinder is presented. The uncontrolled flow exhibits an unsymmetric Karman vortex street and a periodic lift coefficient. The size of the oscillations in the lift is reduced through an active feedback control system. The control used is the injection and suction of fluid through orifices on the cylinder; the amount of fluid injected or sucked is determined, through a simple feedback law, from pressure measurements at stations along the surface of the cylinder.
The results of some computational experiments are given; these indicate that the simple feedback law used is effective in reducing the size of the oscillations in the lift.
Finally, some boundary value problems which arise from a feedback control problem are considered. We give a precise statement of the mathematical problems and then prove the existence and uniqueness of solutions to the boundary value problems for the Laplace and Stokes equations by studying the boundary integral equation method.Ph. D.
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Wood, Dylan M. "Solving Unsteady Convection-Diffusion Problems in One and More Dimensions with Local Discontinuous Galerkin Methods and Implicit-Explicit Runge-Kutta Time Stepping." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1461181441.
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Kurzen, Matthew James. "Discretization Error Estimation and Exact Solution Generation Using the 2D Method of Nearby Problems." Thesis, Virginia Tech, 2010. http://hdl.handle.net/10919/31239.
Full textAbstract:
This work examines the Method of Nearby Problems as a way to generate analytical exact solutions to problems governed by partial differential equations (PDEs). The method involves generating a numerical solution to the original problem of interest, curve fitting the solution, and generating source terms by operating the governing PDEs upon the curve fit. Adding these source terms to the right-hand-side of the governing PDEs defines the nearby problem.
In addition to its use for generating exact solutions the MNP can be extended for use as an error estimator. The nearby problem can be solved numerically on the same grid as the original problem. The nearby problem discretization error is calculated as the difference between its numerical solution and exact solution (curve fit). This is an estimate of the discretization error in the original problem of interest.
The accuracy of the curve fits is quite important to this work. A method of curve fitting that takes local least squares fits and combines them together with weighting functions is used. This results in a piecewise fit with continuity at interface boundaries. A one-dimensional Burgersâ equation case shows this to be a better approach then global curve fits.
Six two-dimensional cases are investigated including solutions to the time-varying Burgersâ equation and to the 2D steady Euler equations. The results show that the Method of Nearby Problems can be used to create realistic, analytical exact solutions to problems governed by PDEs. The resulting discretization error estimates are also shown to be reasonable for several cases examined.Master of Science
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Dickenson, Paul. "Development of GPU-based incompressible SPH and application to sloshing problems in the oil industry." Thesis, University of Cambridge, 2014. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.648452.
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Silverberg, Jon P. "On Lagrangian meshless methods in free-surface flows." Thesis, (1.7 MB), 2005. http://edocs.nps.edu/AR/topic/theses/2005/Jan/05Jan_Silverberg.pdf.
Full textAbstract:
Thesis (Master of Engineering in Ocean Engineering)--University of California at Berkeley, 2004."January 2005." Description based on title screen as viewed on May 25, 2010. DTIC Descriptor(s): Fluid Dynamics, Lagrangian Functions, Equations Of Motion, Acceleration, Formulations, Grids, Continuum Mechanics, Gaussian Quadrature, Derivatives (Mathematics), Compact Disks, Boundary Value Problems, Polynomials, Interpolation, Pressure, Operators (Mathematics). DTIC Identifier(s): Multimedia (CD-Rom), Moving Grids, Meshless Discretization, Lifs (Lagrange Implicit Fraction Step), Lagrangian Dynamics, Meshless Operators, Mlip (Multidimensional Lagrange Interpolating Polynomials), Flux Boundary Conditions, Radial Basis Functions Includes bibliographical references (58-59).