Dissertations / Theses on the topic 'Spectral flow'
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Meng, Sha. "A spectral element method for viscoelastic fluid flow." Thesis, De Montfort University, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.369907.
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Aven, Matthew. "Daily Traffic Flow Pattern Recognition by Spectral Clustering." Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/cmc_theses/1597.
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This paper explores the potential applications of existing spectral clustering algorithms to real life problems through experiments on existing road traffic data. The analysis begins with an overview of previous unsupervised machine learning techniques and constructs an effective spectral clustering algorithm that demonstrates the analytical power of the method. The paper focuses on the spectral embedding method’s ability to project non-linearly separable, high dimensional data into a more manageable space that allows for accurate clustering. The key step in this method involves solving a normalized eigenvector problem in order to construct an optimal representation of the original data.
While this step greatly enhances our ability to analyze the relationships between data points and identify the natural clusters within the original dataset, it is difficult to comprehend the eigenvalue representation of the data in terms of the original input variables. The later sections of this paper will explore how the careful framing of questions with respect to available data can help researchers extract tangible decision driving results from real world data through spectral clustering analysis.
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Butsuntorn, Nawee. "Time spectral method for rotorcraft flow with vorticity confinement /." May be available electronically:, 2008. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.
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Azamov, Nurulla, and azam0001@infoeng flinders edu au. "Spectral shift function in von Neumann algebras." Flinders University. Informatics and Engineering, 2008. http://catalogue.flinders.edu.au./local/adt/public/adt-SFU20080129.121422.
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The main subsect of this thesis is the theory of Lifshits-Krein spectral shift function in semifinite von Neumann algebras and its connection with the theory of spectral flow.
Main results are an analogue of the Krein trace formula for semifinite von Neumann algebras, the semifinite analogue of the Birman-Solomyak spectral averaging formula, a connection between the spectral shift function and the spectral flow and a Lidskii type formula for Dixmier traces. In particular, it is established that in the case of operators with compact resolvent, the spectral shift function and the spectral flow are identical notions.
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Parkinson, Steven. "Modelling free-surface flow with bathymetry variation using spectral methods." Thesis, University of Bristol, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.570859.
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Generation of electricity, by harnessing tidal currents with turbines, has the potential to contribute to a more sustainable future. However, knowledge of the fluid velocity, at a certain depth, is required in order to predict the available energy resource. Therefore, a modelling framework is described, which is computationally efficient, with only a few tunable parameters, and yields good results in comparison to experimental work and computational fluid dynamics. Existing approximate analysis methods, which describe fluid flow over varying topography are discussed. It is found that these theories are incapable of satisfying our objective. From field measurements of a tidal channel, a model is developed that describes turbulent free-surface flow over varying bathymetry. The flow is modelled using the steady incompressible two- dimensional shallow water equations. Turbulence closure is achieved using the eddy-viscosity model. The equations are solved using spectral methods. Convergence of the method is tested by varying the number of modes and the mixing parameterisation. A comparison with experimental work and a regional scale ocean circulation model, for free-surface flow over a ridge, is made. Close agreement is found using pseudo spectral methods. The Galerkin method does not achieve the same level of accuracy. In addition, numerical instability is found to occur on the downstream face of the ridge. However, provided the bathymetry gradients are sufficiently shallow, the solution procedure performs well. A three-dimensional model is achieved by calculating the two-dimensional depth-averaged flow through a tidal channel. Upon calculation of the streamlines from the depth-averaged flow solution, the vertical structure of the flow is calculated. The full flow profile can be obtained by piecing together outputs from each streamline. This is then compared to a one-dimensional hydraulic model where good agreement is found. Finally, flow for a real channel is computed.
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Lott, P. Aaron. "Fast solvers for models of fluid flow with spectral elements." College Park, Md.: University of Maryland, 2008. http://hdl.handle.net/1903/8743.
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Thesis (Ph. D.) -- University of Maryland, College Park, 2008.Thesis research directed by: Applied Mathematics & Statistics, 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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David, Jean-Yves. "Modern spectral analysis techniques for blood flow velocity and spectral measurements with a 20 MHZ pulsed doppler ultrasound catheter." Thesis, Georgia Institute of Technology, 1989. http://hdl.handle.net/1853/17791.
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Tugluk, Ozan. "Direct Numerical Simulation Of Pipe Flow Using A Solenoidal Spectral Method." Phd thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614293/index.pdf.
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In this study, which is numerical in nature, direct numerical simulation (DNS) of the pipe flow is performed. For the DNS a solenoidal spectral method is employed, this involves the expansion of the velocity using divergence free functions which also satisfy the prescribed boundary conditions, and a subsequent projection of the N-S equations onto the corresponding dual space. The solenoidal functions are formulated in Legendre polynomial space, which results in more favorable forms for the inner product integrals arising from the Petrov-Galerkin scheme employed. The developed numerical scheme is also used to investigate the effects of spanwise oscillations and phase randomization on turbulence statistics, and drag, in turbulent incompressible pipe flow for low to moderate Reynolds numbers (i.e. $mathrm{Re} sim 5000$) ).
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Akcan, Zekai. "Uniform flow past a rigid sphere by the spectral numerical methods." Thesis, Monterey, California. Naval Postgraduate School, 1997. http://hdl.handle.net/10945/9101.
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Approved for public release; distribution is unlimitedA steady, axially symmetric, incompressible, viscous flow past a rigid sphere is numerically simulated by using a numerical scheme, based on spectral methods. The equations have been reduced to two sets of nonlinear second order partial differential equations in terms of vorticity and stream function. The calculations have been carried out for Reynolds numbers, based on the sphere diameter, in the range 0.1 to 104. The numerical results have verified that there is excellent agreement with Stokes theory at very low Reynolds numbers. At moderate to intermediate Reynolds numbers there is good general agreement with available experimental data and flow visualization pictures. The Reynolds number at which separation occurs is estimated as 20. The approach to boundary-layer behavior with increasing Reynolds numbers is also verified by comparison with potential flow theory and analytical boundary-layer solution.
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Chaurasia, Hemant Kumar. "A time-spectral hybridizable discontinuous Galerkin method for periodic flow problems." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/90647.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2014.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 110-120).
Numerical simulations of time-periodic flows are an essential design tool for a wide range of engineered systems, including jet engines, wind turbines and flapping wings. Conventional solvers for time-periodic flows are limited in accuracy and efficiency by the low-order Finite Volume and time-marching methods they typically employ. These methods introduce significant numerical dissipation in the simulated flow, and can require hundreds of timesteps to describe a periodic flow with only a few harmonic modes. However, recent developments in high-order methods and Fourier-based time discretizations present an opportunity to greatly improve computational performance. This thesis presents a novel Time-Spectral Hybridizable Discontinuous Galerkin (HDG) method for periodic flow problems, together with applications to flow through cascades and rotor/stator assemblies in aeronautical turbomachinery. The present work combines a Fourier-based Time-Spectral discretization in time with an HDG discretization in space, realizing the dual benefits of spectral accuracy in time and high-order accuracy in space. Low numerical dissipation and favorable stability properties are inherited from the high-order HDG method, together with a reduced number of globally coupled degrees of freedom compared to other DG methods. HDG provides a natural framework for treating boundary conditions, which is exploited in the development of a new high-order sliding mesh interface coupling technique for multiple-row turbomachinery problems. A regularization of the Spalart-Allmaras turbulence model is also employed to ensure numerical stability of unsteady flow solutions obtained with high-order methods. Turning to the temporal discretization, the Time-Spectral method enables direct solution of a periodic flow state, bypasses initial transient behavior, and can often deliver substantial savings in computational cost compared to implicit time-marching. An important driver of computational efficiency is the ability to select and resolve only the most important frequencies of a periodic problem, such as the blade-passing frequencies in turbomachinery flows. To this end, the present work introduces an adaptive frequency selection technique, using the Time-Spectral residual to form an inexpensive error indicator. Having selected a set of frequencies, the accuracy of the Time-Spectral solution is greatly improved by using optimally selected collocation points in time. For multi-domain problems such as turbomachinery flows, an anti-aliasing filter is also needed to avoid errors in the transfer of the solution across the sliding interface. All of these aspects contribute to the Adaptive Time-Spectral HDG method developed in this thesis. Performance characteristics of the method are demonstrated through applications to periodic ordinary differential equations, a convection problem, laminar flow over a pitching airfoil, and turbulent flow through a range of single- and multiple-row turbomachinery configurations. For a 2:1 rotor/stator flow problem, the Adaptive Time-Spectral HDG method correctly identifies the relevant frequencies in each blade row. This leads to an accurate periodic flow solution with greatly reduced computational cost, when compared to sequentially selected frequencies or a time-marching solution. For comparable accuracy in prediction of rotor loading, the Adaptive Time- Spectral HDG method incurs 3 times lower computational cost (CPU time) than time-marching, and for prediction of only the 1st harmonic amplitude, these savings rise to a factor of 200. Finally, in three-row compressor flow simulations, a high-order HDG method is shown to achieve significantly greater accuracy than a lower-order method with the same computational cost. For example, considering error in the amplitude of the 1st harmonic mode of total rotor loading, a p = 1 computation results in 20% error, in contrast to only 1% error in a p = 4 solution with comparable cost. This highlights the benefits that can be obtained from higher-order methods in the context of turbomachinery flow problems.
by Hemant Kumar Chaurasia.
Ph. D.
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Walther, Julia, and Edmund Koch. "Lateral resonant Doppler flow measurement by spectral domain optical coherence tomography." SPIE, 2017. https://tud.qucosa.de/id/qucosa%3A34981.
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In spectral domain optical coherence tomography (SD-OCT), any transverse motion component of a detected obliquely moving sample results in a nonlinear relationship between the Doppler phase shift and the axial sample velocity restricting phase-resolved Doppler OCT. To circumvent the limitation, we propose the lateral resonant Doppler flow quantification in spectral domain OCT, where the scanner movement velocity is matched to the transverse velocity component of the sample motion.
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Abolmoali, Philip. "Spectral Energy Transfers in Transonic Cavity Flows with High Frequency Flow Control from Powered Resonance Tubes." University of Cincinnati / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1511867795447293.
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Melotte, David John. "Superfluid turbulence." Thesis, University of Newcastle Upon Tyne, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.287825.
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Elling, Volker Wilhelm. "A spectral method for mapping dataflow graphs." Thesis, Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/8161.
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Zeybek, Birol. "Numerical simulation of flow induced by a spinning sphere using spectral methods." Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1997. http://handle.dtic.mil/100.2/ADA331206.
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Cagnone, Jean-Sébastien. "A non linear frequency domain-spectral difference scheme for unsteady periodic flows /." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=111614.
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This research presents a new, more efficient computational scheme for complex periodic flows, and brings forward two novel ideas. The first consists in the use of a Fourier space time representation in conjunction with a high-order spatial discretization. The second is based on the efficient treatment of the resulting set of equations using a fast, implicit solver. This thesis describes the formulation and implementation of the proposed framework. Firstly, a high-order spectral difference scheme for the Euler equations is introduced. Secondly, the non-linear frequency domain method resolving the unsteady behavior of the flow is discussed. Thirdly, a mathematical and experimental validation of the proposed algorithm is carried out. Numerical experiments performed in this thesis suggest that the methodology could be an attractive new avenue for large scale time-dependent problems, alleviating the computational cost traditionally associated with such simulations.
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Dumas, Guy Leonard Anthony. "Study of spherical couette flow via 3-D spectral simulations : large and narrow-gap flows and their transitions /." Diss., Pasadena, Calif. : California Institute of Technology, 1991. http://resolver.caltech.edu/CaltechETD:etd-04162004-103555.
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Dechamps, Xavier. "Numerical simulation of incompressible magnetohydrodynamic duct and channel flows by a hybrid spectral, finite element solver." Doctoral thesis, Universite Libre de Bruxelles, 2014. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209203.
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In this dissertation, we are concerned with the numerical simulation for flows of electrically conducting fluids exposed to an external magnetic field (also known as magnetohydrodynamics or in short MHD). The aim of the present dissertation is twofold. First, the in-house CFD hydrodynamic solver SFELES is extended to MHD problems. Second, MHD turbulence is studied in the simple configuration of a MHD pipe flow within an external transverse magnetic field. Chapter 2 of this dissertation aims at reminding the physical equations that govern incompressible MHD problems. Two equivalent formulations are put forward in the particular case of quasi-static MHD. Chapter 3 is devoted to the detailed development of the hybrid spectral - stabilized finite element methods for quasi-static MHD problems. The extension of SFELES is made for both Cartesian and axisymmetric systems of coordinates. The short chapter 4 follows to provide the performances of SFELES executed by several processes in a parallel environment. The addition of a parallel direct solver is studied in regards with the memory and time requirements. The extension of SFELES is then validated in chapter 5 with test cases of increasing complexity. For this purpose, laminar flows with an existing analytical-asymptotic solution are considered. The subject of chapter 6 is the MHD turbulent pipe flow within an external transverse and uniform magnetic field. The results are partially compared with the corresponding hydrodynamic flow and with a few data available in the literature. / Le thème de cette thèse de doctorat est la simulation numérique d'écoulements de fluides conducteurs d'électricité qui sont exposés à un champ magnétique extérieur (également connu sous le nom de magnétohydrodynamique ou encore MHD). L'objectif de ce travail est double. Premièrement, le code CFD maison SFELES est étendu aux problèmes MHD. Deuxièmement, la turbulence MHD est étudiée dans la configuration de l'écoulement en conduite cylindrique à l'intérieur d'un champ magnétique transverse. Le chapitre 2 de cette thèse a pour but de rappeler les équations qui gouvernent les problèmes de MHD incompressible. Deux formulations équivalente sont mises en évidence dans le cas particulier de la MHD quasi-statique. Le chapitre 3 est dévoué au développement détaillé des méthodes spectrale - éléments finis pour la MHD quasi-statique. L'extension de SFELES est réalisée dans les systèmes de coordonnées cartésiennes et axisymétriques. Le court chapitre 4 suit pour fournir les performances de SFELES exécuté sur plusieurs processeurs dans un environnement parallèle. L'ajout d'un solveur parallèle direct est étudié en ce qui concerne les demandes en temps et mémoire. L'extension de SFELES est alors validée dans le chapitre 5 avec des cas d'étude de complexité croissante. Dans ce but, des écoulements laminaires avec solution théorique-asymptotique sont envisagés. Le sujet du chapitre 6 est l'écoulement MHD turbulent en conduite cylindrique à l'intérieur d'un champ magnétique transverse et uniforme. Les résultats sont partiellement comparés avec l'écoulement hydrodynamique correspondant et avec des données disponibles dans la littérature.Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished
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Engin, Erjona. "Dynamic Analysis Of Flow In Two Dimensional Flow." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12609374/index.pdf.
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The Poiseuille Flow is the flow of a viscous incompressible fluid in a channel between two infinite parallel plates. The behaviour of flow is properly described by the well-known Navier-Stokes Equations. The fact that Navier-Stokes equations are partial differential equations makes their solution difficult. They can rarely be solved in closed form. On the other hand, numerical techniques can be applied successfully to the well-posed partial differential equations.
In the present study pseudo-spectral method is implemented to analyze the Poiseuille Flow. The pseudo-spectral method is a high-accuracy numerical modelling technique. It is an optimum choice for the Poiseuille flow analysis due to the flows simple geometry. The method makes use of Fourier Transform and by handling operations in the Fourier space reduces the difficulty in the solution. Fewer terms are required in a pseudo-spectral orthogonal expansion to achieve the same accuracy as a lower order method.
Karhunen-Loève (KL) decomposition is widely used in computational fluid dynamics to achieve reduced storage requirements or construction of relatively low-dimensional models. In this study the KL basis is extracted from the flow field obtained from the direct numerical simulation of the Poiseuille flow.
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Akdag, Osman. "Incompressible Flow Simulations Using Least Squares Spectral Element Method On Adaptively Refined Triangular Grids." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614944/index.pdf.
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The main purpose of this study is to develop a flow solver that employs triangular grids to solve two-dimensional, viscous, laminar, steady, incompressible flows. The flow solver is based on Least Squares Spectral Element Method (LSSEM). It has p-type adaptive mesh refinement/coarsening capability and supports p-type nonconforming element interfaces. To validate the developed flow solver several benchmark problems are studied and successful results are obtained. The performances of two different triangular nodal distributions, namely Lobatto distribution and Fekete distribution, are compared in terms of accuracy and implementation complexity. Accuracies provided by triangular and quadrilateral grids of equal computational size are compared. Adaptive mesh refinement studies are conducted using three different error indicators, including a novel one based on elemental mass loss. Effect of modifying the least-squares functional by multiplying the continuity equation by a weight factor is investigated in regards to mass conservation.
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Laird, Alistair. "A hybrid spectral discretisation and iterative solution methods for acoustic models in potential flow." Thesis, University of Oxford, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.403764.
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Shin, James Jang-Sik. "A spectral element formulation for fluid-structure interactions : applications to flow through collapsible channels." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/41003.
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Bellis, Stephen John. "VLSI implementation of a spectral estimator for use with pulsed ultrasonic blood flow detectors." Thesis, Bangor University, 1996. https://research.bangor.ac.uk/portal/en/theses/vlsi-implementation-of-a-spectral-estimator-for-use-with-pulsed-ultrasonic-blood-flow-detectors(aada8831-f06d-4e23-94d6-341d021a3e62).html.
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The focus of this thesis is on the design and selection of systolic architectures for ASIC implementation of the real-time digital signal processing task of Modi- fied Covariance spectral estimation. When used with pulsed Doppler ultrasound blood flow detectors, the Modified Covariance spectral estimator offers increased sensitivity in the detection of arterial disease over conventional Fourier transform based methods. The systolic model of computation is considered because through pipelining and parallel processing high levels of concurrency can be achieved to attain the nec- essary throughput for real-time operation. Systolic arrays of simple processing units are also well suited for implementation on VLSI. The versatility of the de- sign of systolic arrays using the rigorous data dependence graph methodology is demonstrated throughout the thesis by application to all sections of the spectral estimator design at both word and bit levels. Systolic array design for the model order 4 Modified Covariance spectral estima- tor, known to offer accurate estimation of blood flow mean velocity and d1stur- bance at an acceptable computational burden, is initially discussed. A variety of problem size dependent systolic arrays for real-time implementation of the fixed model order spectral estimator are designed using data dependence graph mapping methods. Optimal designs are chosen by comparison of hardware, com- munication and control costs, as well as efficiency, timing, data flow and accuracy considerations. A cost/benefit analysis, based on results from structural simula- tion of the arrays, allows the most suitable word-lengths to be chosen. Problem size independent systolic arrays are then discussed as means of coping with the huge increases in computational burden for a Modified Covariance spec- tral estimator which is programmable up to high model orders. This type of array can be used to reduce the number of PEs and increase efficiency when compared to the problem size dependent arrays and the research culminates in the proposal of a novel spiral systolic array for Cholesky decomposition.
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Brooks, Donald Ray. "Development of Specialized Laser Doppler Velocimeters for High Resolution Flow Profile and Turbulence Spectral Measurements." Thesis, Virginia Tech, 2014. http://hdl.handle.net/10919/78089.
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Fluid dynamicists are always in need of innovative instruments for flow velocity measurements. An ideal instrument would be non-intrusive, have a very fine spatial resolution as well as a very fine temporal resolution, be able to measure three-components of velocity, and be compact. Through recent advancements, laser Doppler velocimetry can now meet all of those requirements making it an important part of aerodynamicist's research toolbox.
The first paper presented in this manuscript style thesis explains the development of an advanced three-velocity component, spatially-resolving laser-Doppler velocimetry (LDV) system for highly resolved velocity measurements in situations with limited optical access. The new instrument, a next generation version of the previously developed 'comprehensive' LDV technology, enables measurements of three components of velocity and particle position in the axial direction all through a single transceiving lens. Described here is the design process and the final design for the 'compact, comprehensive' LDV (Comp²LDV). The probe was designed to achieve ± 10 micron root-mean-square uncertainties in axial particle position, which combined with the long measurement volume, allow researchers to obtain a three-velocity-component velocity statistics profiles over a span of approximately 1.5mm without the need for traversing. Results from measurements in a flat plate turbulent boundary layer very near the wall have compared favorably to data from previous studies.
The second paper focuses on the motion and evolution of coherent structures in supersonic jet flows and how that relates to the intense noise the flows generate. As a preliminary study to experimentally address these relationships, novel non-intrusive measurements using two-component laser Doppler velocimetry (LDV) have been conducted at exceptionally high data rates to lend insight into the statistical behavior of noise-generating flow structures. A new heated supersonic jet facility has been constructed to provide supersonic flow at total temperatures ratios (T₀/Tₐ) up to 3. In the present work, the instrumentation is validated via comparison of LDV measurements along the centerline of a screeching cold jet with microphone and high-speed shadowgraph results. Reynolds stress spectra are presented for an over-expanded case (nozzle pressure ratio of 3.2) of a design Mach number 1.65 nozzle operated cold (T₀/Tₐ = 1). A preliminary study was then conducted in the near-nozzle shear layer, up to x/d = 4.0, at design nozzle pressure ratio (4.58) and total temperature ratio of 2.0. Results are presented for Reynolds stress time-delay correlations and power spectra at Re_d = 1.1M for this case. The stream-wise Reynolds normal stress spectra are compared with published spectral behavior reported by other researchers, indicating a similar spectral shape in the downstream stations as previously measured with LDV and hot wire anemometry for cold jets, but which differ in shape from density-based techniques.Master of Science
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Cerocchi, Filippo. "Dynamical and Spectral applications of Gromov-Hausdorff Theory." Thesis, Grenoble, 2013. http://www.theses.fr/2013GRENM077/document.
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Cette thèse est divisée en deux parties. La première est consacrée à la méthode du barycentre, introduite en 1995 par G. Besson, G. Courtois et S. Gallot pour résoudre la conjecture de l'Entropie Minimale. Dans le Chapitre 1 nous décrivons ses développements les plus récents, notamment l'extension de cette méthode au cadre des variétés dont la courbure sectionnelle est de signe quelconque (voir les énoncés 1.2.1 et 1.4.1). Dans le Chapitre 2 et 3 nous présentons des résultats dans lesquels la méthode du barycentre joue un rôle important. Le problème “deux variétés dont les flots géodésiques sont conjugués sont-elles isométriques ?” (problème de la rigidité par conjugaison des flots) est le thème du Chapitre 2. Après avoir montré que deux telles variétés ont la même géométrie à grande échelle, on montre comment on peut utiliser ce résultat et la méthode du barycentre pour donner une nouvelle preuve de la rigidité (par conjugaison des flots) des variétés plates. Dans le Chapitre 3 nous utilisons la méthode du barycentre (en courbure de signe quelconque) et des inégalités de Sobolev itérées pour démontrer un théorème de comparaison entre les spectres de deux variétés riemanniennes (Y , g) et (X , g') de volumes proches, sachant qu'il existe une approximation de Gromov-Hausdorff de degré non nul entre ces deux variétés. Il s'agit d'un résultat d'approximation avec majoration de l'erreur d'approximation (et pas seulement d'un résultat de convergence). Remarquons qu'il n'est fait aucune autre hypothèse géométrique (et en particulier aucune hypothèse de courbure) sur la variété (Y , g), ce qui autorise un grand nombre de contre-exemples prouvant que le résultat est optimal. Dans la deuxième partie de la thèse (chapitre 4), on démontre un Lemme de Margulis sans hypothèse sur la courbure, qui s'applique aux variétés dont les groupes fondamentaux sont des produits libres (et qui ne possèdent pas d'élément de torsion d'ordre 2). Nous donnons également une borne inférieure de la systole des variétés dont le diamètre et l'entropie volumique sont majorés et dont le groupe fondamental est isomorphe à un produit libre sans torsion. Comme conséquences de ce dernier résultat nous obtenons des résultats de précompacité et de finitude topologique ou différentiable pour les variétés riemanniennes et une minoration de leur volume, tout ceci sans faire d'hypothèse de courbureThis Ph.D. Thesis is divided into two parts. In the first part we present the barycenter method, a technique which has been introduced by G. Besson, G. Courtois and S. Gallot in 1995, in order to solve the Minimal Entropy conjecture. In Chapter 1 we are interested in the more recent developments of this method, more precisely in the recent extension of the method to the case of manifolds having sectional curvature of variable sign. In Chapters 2 and 3 we shall present some new results whose proofs make use of the barycenter method. The Conjugacy Rigidity problem is the theme of Chapter 2. First we show a general result which provide a comparison between the large scale geometry of the Riemannian universal coverings of two compact manifolds whose geodesic flows are conjugates. Then we shall show how we can apply the latter result and the barycenter method in curvature of variable sign in order to give a new proof of the conjugacy rigidity of flat manifolds. In Chapter 3 we shall give a proof of a spectra comparison theorem for a compact Riemannian manifold which admits a Gromov-Hausdorff-approximation of non zero absolute degree on a fixed compact manifold (X,g') and which has volume almost smaller than the one of the reference manifold. The proof relies on the barycenter method in curvature of variable sign and on iterated Sobolev inequalities. We underline that it is an approximation result (and not just a convergence result) and that no curvature assumptions are made or inferred on (Y,g). The second part of the Thesis consists of a single chapter. In this chapter we prove a Margulis Lemma without curvature assumptions for Riemannian manifolds having decomposable 2-torsionless fundamental group. We shall give also a proof of a universal lower bound for the homotopy systole of compact Riemannian manifolds having bounded volume entropy and diameter, and decomposable torsionless fundamental group. As a consequence of the latter result we shall deduce a Precompactness and Finiteness theorem and a Volume estimate without curvature assumptions
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Alescio, Giuseppe. "Chebyshev spectral method for incompressible viscous flow with boundary layer control via suction or blowing." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/35585.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2006.Includes bibliographical references (p. 155-157).
The MISES quasi 3-D design/analysis code implements a two-equation integral method with empirical closure relations to solve the boundary layer flow problem with or without suction, but lacks the option of flow control via blowing. The integral method is parameterized with the shape parameter H _ 6*/0 which cannot be applied to the blowing problem since 0 - 0 downstream of the injection slot causing H -, co - a computational disaster. In this thesis, two alternate approaches are proposed to solve the blowing problem. First, a two-equation integral method parameterized with the profile parameters of a multi-deck representation of a turbulent jet based on Coles' law of the wake was formulated. The appearance of spurious singularities in the Jacobian matrices associated with the system of equations and the vector of unknowns prevented this method from being implemented. Second, a Chebyshev spectral method using the wall function technique was applied to the defect form of the incompressible viscous momentum equation. A turbulent jet profile was computed with N = 40 modes, a number low enough to allow the method's implementation into the MISES framework.
(cont.) For the spectral approach, a stand-alone code was developed to solve laminar and turbulent flow over a flat plate with the following configurations: solid wall, porous wall with vertical suction/blowing, and fluid injection from an inclined slot. For the turbulent case, the Reynolds stress was replaced with a composite model for the eddy viscosity based on Spalding's law of the wall for the inner layer and Clauser's outer layer formulation. In the laminar regime, N - 10 modes are required for an accurate solution whereas the two-layer structure of a turbulent boundary layer increases this number to N 100 modes. The incorporation of a wall function, consistent with the inner layer eddy viscosity model, in the approximation of the streamwise velocity, reduced the required number of modes by an order of magnitude - a major computational advantage. The more general Spalart-Allmaras turbulence model was implemented in the spectral formulation to investigate the effect of using a wall function based on Spalding's law of the wall.
(cont.) For the flat plate case (solid wall), a small inconsistency between the wall function and the eddy viscosity model produced an erroneous shear stress near the wall. Nevertheless, the velocity profile was in close agreement with an accurate representation constructed from Spalding's law of the wall and Coles' law of the wake.
by Giuseppe Alescio.
Ph.D.
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Silas, Kevin Alexander. "Phase Transform Time Delay Estimation to Counteract Spectral Haystacking Effects in Jet Exhaust Flow Measurements." Thesis, Virginia Tech, 2021. http://hdl.handle.net/10919/104892.
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This study determined a superior data processing technique for correlating an acoustic signal passing through a subsonic jet engine exhaust in order to estimate the traversal time of the signal. Thrust measurement is possible with enough time delay estimates across different portions of the exhaust. This preliminary study did not take the full array of data necessary to measure thrust, but did validate key aspects of the measurement process. The turbulent shear layers of the exhaust spectrally broaden the signal, creating the appearance of spectral "haystacks", making traditional correlation methods unworkable. An experiment was performed to evaluate the ability of a novel sound source to produce a signal from which a reliable and precise time delay estimate could be found. The test apparatus was installed on either side of a Honeywell TFE731-2 turbofan research engine exhaust cone, with the source and receivers placed near the jet exit plane. The signal was then directed across the jet exhaust. This flow environment is considered an extreme challenge for accurate acoustic signal propagation. A key contribution of this paper is the determination that the Phase Transform processor of the Generalized Cross-Correlation (GCC) method produces the most reliable time delay estimates, for the given signal and flow conditions. Several alternative time delay estimators and GCC processors were examined and evaluated on this data. A proposed explanation is provided for why this time delay estimation technique produces the most accurate results, as well as explanations for why the technique became less reliable as the flow environment became more challenging, with an observed 22% anomalous TDE selection rate for the N1Corr = 60% and N1Corr = 70% conditions combined, versus only 6% for the idle and N1Corr = 50% conditions combined. This paper also details the development and first use of a novel acoustic source that produces a two-tone narrowband signal emanating from a single point – the dual Hartmann generator.Master of Science
This study builds on a Computational Tomography (CT) technique that uses an acoustic signal and an array of receivers to measure the velocity and temperature of a gas flow field. In particular, the velocity and temperature field tested involves multiple turbulent and disruptive elements, requiring a loud and specifically designed signal. As such, a novel acoustic signal generator, the dual Hartmann generator, was designed that is both loud and produces a specific two-toned signal. The key contribution of the study was to process the data, comparing the sets of transmitted and received signals, in order to estimate the time delay amongst receiver pairs – a key input in the CT method. Traditional cross-correlation methods were inadequate, and multiple alternatives were evaluated. The Phase Transform (PHAT) technique showed the most promise, and an explanation is given for why this technique is most suitable for this type of signal.
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Yu, Bo. "Surface Mean Flow and Turbulence Structure in Tropical Cyclone Winds." FIU Digital Commons, 2007. http://digitalcommons.fiu.edu/etd/25.
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Hurricanes are one of the deadliest and costliest natural hazards affecting the Gulf coast and Atlantic coast areas of the United States. An effective way to minimize hurricane damage is to strengthen structures and buildings. The investigation of surface level hurricane wind behavior and the resultant wind loads on structures is aimed at providing structural engineers with information on hurricane wind characteristics required for the design of safe structures. Information on mean wind profiles, gust factors, turbulence intensity, integral scale, and turbulence spectra and co-spectra is essential for developing realistic models of wind pressure and wind loads on structures. The research performed for this study was motivated by the fact that considerably fewer data and validated models are available for tropical than for extratropical storms. Using the surface wind measurements collected by the Florida Coastal Monitoring Program (FCMP) during hurricane passages over coastal areas, this study presents comparisons of surface roughness length estimates obtained by using several estimation methods, and estimates of the mean wind and turbulence structure of hurricane winds over coastal areas under neutral stratification conditions. In addition, a program has been developed and tested to systematically analyze Wall of Wind (WoW) data, that will make it possible to perform analyses of baseline characteristics of flow obtained in the WoW. This program can be used in future research to compare WoW data with FCMP data, as gust and turbulence generator systems and other flow management devices will be used to create WoW flows that match as closely as possible real hurricane wind conditions. Hurricanes are defined as tropical cyclones for which the maximum 1-minute sustained surface wind speeds exceed 74 mph. FCMP data include data for tropical cyclones with lower sustained speeds. However, for the winds analyzed in this study the speeds were sufficiently high to assure that neutral stratification prevailed. This assures that the characteristics of those winds are similar to those prevailing in hurricanes. For this reason in this study the terms tropical cyclones and hurricanes are used interchangeably.
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Merle, Matthieu. "Approches numériques pour l'analyse globale d'écoulements pariétaux en régime subsonique." Thesis, Paris, ENSAM, 2015. http://www.theses.fr/2015ENAM0026/document.
Full textAbstract:
Dans le cadre de l'étude des écoulements ouverts, deux types de dynamiques coexistent. Les écoulements de type oscillateur qui présentent une fréquence propre d'oscillation indépendante des perturbations extérieures (dynamique intrinsèque), ainsi que les écoulements de type amplificateur sélectif de bruit comme les écoulements de jets ou de couches limites décollées, caractérisés par une plus large gamme de fréquences dépendantes essentiellement de bruit extérieur (dynamique extrinsèque). Les études de couches limites décollées en régime incompressible ont montré un lien entre le phénomène auto-entretenu de basse fréquence qui apparaît et l'interaction non normale des modes globaux instables existants pour ce type de configuration. L'objectif de ce travail consiste à étendre cette interprétation lorsque l'écoulement est en régime subsonique. Dans ce but, un travail d'adaptation des conditions aux limites non-réfléchissantes aux problèmes de stabilité globale a été réalisé. Une méthode de zone absorbante de type Perfectly Matched Layer a été implémentée dans un code de simulation numérique utilisant des méthodes de collocation spectrale. Une méthode de décomposition de domaine adaptée aux calculs des solutions stationnaires ainsi qu'aux problèmes de stabilité globale a également été utilisée pour permettre la validation des conditions aux limites implémentées sur un cas d'écoulement rayonnant de cavité ouverte. Enfin, les études de stabilité d'un écoulement de couche limite décollée derrière une géométrie de type bosse ont été réalisées. L'étude des instabilités bidimensionnelles, responsables du phénomène basse fréquence (flapping), et réalisées en régime subsonique montre que le mécanisme observé en régime incompressible est aussi observé en régime subsonique. La stabilité de cet écoulement vis-à-vis de perturbations tri-dimensionnelles, et plus particulièrement les instabilités centrifuges ont aussi été étudiées en fonction du nombre de MachIn open flows context, there are generally two types of dynamic : oscillators, such as cylinder flow, exhibit a well defined frequency insensitive to external perturbations (intrinsic dynamics) and noise amplifiers, such as boundary layers, jets or in some cases the separated flows, which are characterized by wider spectrum bands that depend essentially on the external noise (dynamic extrinsic). Previous studies have shown that separated flows are subject to self-induced oscillations of low frequency in incompressible regime. These studies have revealed links between the interaction of non-normal modes and low oscillations in an incompressible boundary-layer separation and it will be to establish the validity of this interpretation in a compressible regime. In this regard, non-reflecting boundary conditions have been developed to solve the eigenvalue problem formed by linearised Navier-Stokes equations. An absorbing region known as Perfectly Matched Layer has been implemented in order to damp acoustic perturbations which are generated when the compressibility of the flow is considered. A multi-domain approach using spectral collocation discretisation has also been developed in order to study the influence of this absorbing region on the stability analysis of an open cavity flow which is known to generate acoustic perturbations. Finally, we focused on separated boundary layer induced by a bump geometry in order to understand what are the effects of compressibility on the bidimensional low frequency phenomenon and also on transverse instabilities which are known to be unstable for a lots of separated flows
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Nazaikinskii, Vladimir, Anton Savin, Bert-Wolfgang Schulze, and Boris Sternin. "Elliptic theory on manifolds with nonisolated singularities : III. The spectral flow of families of conormal symbols." Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2638/.
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When studyind elliptic operators on manifolds with nonisolated singularities one naturally encounters families of conormal symbols (i.e. operators elliptic with parameter p ∈ IR in the sense of Agranovich-Vishik) parametrized by the set of singular points. For homotopies of such families we define the notion of spectral flow, which in this case is an element of the K-group of the parameter space. We prove that the spectral flow is equal to the index of some family of operators on the infinite cone.
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Mählmann, Stefan [Verfasser]. "Spectral Simulation of Leading-Edge Receptivity in Supersonic Flow over a Blunt Flat Plate / Stefan Mählmann." Aachen : Shaker, 2005. http://d-nb.info/1186580534/34.
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Buggisch, Lukas Werner [Verfasser], and Johannes [Akademischer Betreuer] Ebert. "The spectral flow theorem for families of twisted Dirac operators / Lukas Werner Buggisch ; Betreuer: Johannes Ebert." Münster : Universitäts- und Landesbibliothek Münster, 2019. http://d-nb.info/1190724960/34.
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Bouzarth, Elizabeth L. Minion Michael L. "Regularized singularities and spectral deferred correction methods a mathematical study of numerically modeling Stokes fluid flow /." Chapel Hill, N.C. : University of North Carolina at Chapel Hill, 2008. http://dc.lib.unc.edu/u?/etd,1917.
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Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2008.Title from electronic title page (viewed Dec. 11, 2008). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics." Discipline: Mathematics; Department/School: Mathematics.
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Graça, Cristo dos Santos Lopes Ruano Maria da. "Investigation of real-time spectral analysis techniques for use with pulsed ultrasonic Doppler blood flow detectors." Thesis, Bangor University, 1992. https://research.bangor.ac.uk/portal/en/theses/investigation-of-realtime-spectral-analysis-techniques-for-use-with-pulsed-ultrasonic-doppler-blood-flow-detectors(f184d2a8-bde7-492a-b487-438704d3ea04).html.
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The goals of the work described here were the development of a method of selection of spectral estimation for use with pulsed Doppler ultrasonic blood flow instruments, and the use of this method to select an estimator and its implementation in a form suitable for real-time applications. A study of estimation accuracy of the mean frequency and bandwidth using a number of spectral estimators was carried out. Fourier based, parametric, and, minimum variance estimators were considered. A Doppler signal simulator was developed to allow the accuracy tests required. A method of selection of spectral estimators based on the accuracy of estimation of decisive signal parameters, under the constraint of low computational complexity has been proposed. This novel cost/benefit criterion, allows the possibility of weighting appropriate to estimator (mean frequency and bandwidth) and signal frequency importance (across the range of signal characteristics). For parametric spectral estimators, this criterion may also be used to select model order, leading to lower orders than FPE, AIC and CAT criteria. Its use led to the selection of a 4t' order modified covariance parametric method. A new version of the modified covariance method for spectral estimation of real signals was developed. This was created with a view to the parallel partitioning of the algorithm for parallel implementation on a transputer-based system, using OCCAM. A number of parallel topologies were implemented. Their performance was evaluated considering estimation of a single, and a sequence of Doppler signal segments, revealing the feasibility of these parallel implementations to be achieved in real-time.
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Vadsola, Mayank. "High-Order Spectral Element Method Simulation of Flow Past a 30P30N Three-Element High Lift Wing." Thesis, Université d'Ottawa / University of Ottawa, 2020. http://hdl.handle.net/10393/40964.
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The purpose of a multi-element high lift device is to increase lift dramatically
while controlling the stall limit. The fluid flow over a multi-element high lift device
has been explored widely both experimentally and numerically at high Reynolds
numbers (O(10^6 )). The numerical simulations use turbulence models and hence
details of the flow are not yet available. Low Reynolds number (O(10^4 )) flows
over high lift devices have not been explored until recently. These lower Reynolds
number flows have applications in the development of small aerial vehicles. The
present work discusses both two-dimensional and three-dimensional direct numer-
ical simulations of fluid flow over a 30P30N three-element high lift system using a
high-order spectral element method code, Nek5000, that solves the incompressible
Navier-Stokes equations. The intricate geometry of the multi-element device poses
a challenge for the high-order spectral element method. We study the complex
flow physics in the slat cove region and the wake/shear layer interaction over a
30P30N three-element high lift device. The targeted cases are at Reynolds num-
bers based on stowed chord lengths (Rec ) of 8.32 × 10^3 , 1.27 × 10^4 , and 1.83 × 10^4 at angle of attack of 4. A critical interval for Rec has previously been found
between 1.27 × 10^4 and 1.38 × 10^4 in experiments. This divides the flow into
two types: when Rec is below the critical interval, no roll-up is observed in the
slat cove and Görtler vortices dominate the slat wake; however when the Rec is
above the critical interval, a roll-up is observed in the slat cove and co-existence
of streamwise and spanwise vortices is confirmed in the slat wake. We confirm
the presence of the critical interval from the simulations performed at three values of Rec . Lift and drag analysis is provided along with pressure coefficient plots
for each element of the multi-element airfoil. Different vortical structures are also
identified in the transition of flow from two dimensions to three dimensions. The
relevant validation is performed with the available experimental data.
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Nath, Subhra K. "Spectral estimates and flow characteristics from non-uniformly sampled LDV data in a turbulent junction vortex." Diss., Virginia Polytechnic Institute and State University, 1989. http://hdl.handle.net/10919/54395.
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The strongly time variant flow in an incompressible, turbulent junction vortex formed at the base of a streamlined cylinder with a circular leading edge placed normal to a flat surface was investigated. The investigation centered around spectral analysis and time resolved measurements of the velocity fluctuations to characterize the time variant flow on the plane of symmetry. All the measurements were performed with a two-color, two-component, frequency shifted laser Doppler velocimeter.
Spectral analysis methods for randomly sampled data occurring from the LDV were evaluated under various simulated and real flow situations. The real flow situations studied were the vortex shedding flow behind a cylinder and the two-dimensional turbulent boundary layer. The spectral estimates obtained from the discretized lag product method were found to be better than those obtained from the direct transform method. It was found that the exact lag product method does not offer significant improvements in the spectral estimates to offset its computational slowness.
The mean velocity vectors in the junction vortex showed a single vortex on the plane of symmetry and a singular separation point upstream of the cylinder.
The time resolved measurements showed the instantaneous separation point on the plane of symmetry to be randomly oscillating between two limits. Maximum possible excursions of the junction vortex position and size were also obtained form the time resolved measurements.
The turbulence intensities in the junction vortex were found to be at least two to three times higher than typical two-dimensional boundary layer values. The histograms of instantaneous velocity fluctuations deviated from the expected Gaussian distributions and were found to have multiple peaks.
The spectral content of the junction vortex flow was investigated. The overall character of the junction vortex flow was found to be similar to a two-dimensional turbulent boundary layer, with greater amplification perceived in the lower frequencies relative to the higher frequencies. The spectra at locations above the time mean center of the junction vortex showed distinct peaks around 20-30 Hz, unlike boundary layer flows.Ph. D.
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Mekonnen, Muluneh Admass. "Modeling flow and sediment transport in water bodies and watersheds." Doctoral thesis, KTH, Vattendragsteknik, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4703.
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The research focus is on the various modeling aspects of flow and sediment transport in water bodies and watersheds. The interaction of flow with a mobile bed involves a complex process in which various turbulent scales characterized by coherent structures cause a chaotic sediment motion. In many rivers and natural waterways secondary flows that are dominating flow struc-tures bring about more complications. In estuaries and open waterbodies thermal stratification and internal mixing control the flow structure besides the flow interaction with the mobile bed. To adequately model these processes 3D coupled flow and transport models are needed. The research is based on use and adaptation of open source codes for 3D hydrodynamic and sediment transport model known as Estuarine Coastal Ocean Model (ECOMSED) and the Soil and Water Assessment Tool (SWAT) model. A bed load transport model was developed and coupled to ECOMSED. The flow and sediment transport characteristics in a curved channel and a river reach were successfully captured by the model. Improvements in ECOMSED were made to study the effect of wind and basin bathymetry on mixing and flow exchange between two estuaries. Using spectral analysis the hydrological component of SWAT model was investigated for its applicability under limited data conditions in three Ethiopian catchments.QC 20100827
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Dao, Xuan Quy. "Fluid flow control by visual servoing." Thesis, Rennes 1, 2014. http://www.theses.fr/2014REN1S053/document.
Full textAbstract:
Cette thèse a pour but l'étude de la mise en œuvre de commandes par asservissement visuel pour le contrôle actif d'un écoulement de Poiseuille. D'un point de vue général, le contrôle d'écoulements vise à modifier ou à maintenir l'état de l'écoulement, malgré une éventuelle perturbation extérieure. Une des situations d'intérêt concerne par exemple la transition vers la turbulence où l'écoulement peut devenir turbulent avec la croissance de sa densité d'énergie cinétique. La réduction de la traînée est également une application potentielle dans des problèmes d'ingénierie. Un des buts applicatifs de cette thèse cherchera ainsi à minimiser à la fois la densité d'énergie cinétique et la traînée. Des modèles numériques peuvent être utilisés pour générer un modèle d'état des équations aux dérivées partielles d'un écoulement de Poiseuille. Le modèle d'état considéré dans cette thèse s'appuie sur une représentation spectrale afin de transformer les équations aux dérivées partielles originelles en un système d'équations différentielles ordinaires. Le vecteur d'état rassemble dans notre cas la vitesse et la vorticité. Les signaux de commande dépendent eux de conditions aux limites de type Dirichlet non homogènes qui correspondent à des actions de soufflage/aspiration. Le nombre de degrés de liberté commandé du problème correspond à la dimension du signal de commande. La densité d'énergie cinétique et la traînée sont modélisées en fonction du vecteur d'état et du signal de commande. Dans cette thèse nous avons plus particulièrement considéré un asservissement visuel partitionné. Celui-ci est appliqué au modèle d'état de l'écoulement avec deux degrés de liberté afin de minimiser simultanément la densité d'énergie cinétique et la traînée. La traînée, contrairement à l'énergie cinétique, diminue de façon monotone en fonction du temps. Une augmentation du nombre de degrés de liberté permet d'améliorer la décroissance de la densité d'énergie cinétique. Lorsque le nombre de degré de liberté correspond à la dimension du vecteur d'état, et en s'appuyant sur une commande par asservissement visuel, nous montrons que la densité d'énergie cinétique décroit de façon monotone au cours du temps. Le modèle d'état de l'écoulement de Poiseuille vit dans un espace de très grande dimension. Par conséquent, il est nécessaire d'un point de vue pratique de réduire la dimension du contrôleur. Nous démontrons que la loi de commande s'appuyant sur un modèle réduit peut être appliquée au système complet. Dans ce cas la densité d'énergie cinétique décroit presque de façon monotone au cours du temps en utilisant une commande par asservissement visuel à deux degrés de libertéThe visual servoing control approach is formulated for the flow control of the plane Poiseuille flow. Generally, the flow control can lead the flow from its current state to a desired state. In transition to turbulence, the growth of kinetic energy density can lead the flow to turbulence. Moreover, the drag reduction is a potential application in the engineering applications. Therefore, this thesis aims to minimize the kinetic energy density and the skin friction drag. The governing equations of the plane Poiseuille flow are modeled to a standard form in the automatic control. More precisely, the partial differential equations of the plane Poiseuille flow are transformed to a state space representation by using the spectral method. The streamwise and spanwise directions are discretized based on the Fourier series while the wall-normal direction is discretized based on the Chebyshev polynomials. The state vector involves the wall-normal velocity and vorticity. The control signals depend on the inhomogeneous Dirichlet boundary conditions which correspond to blowing/suction boundary control. The number of independent control signals is called the number of the degree of freedom. Moreover, the skin-friction drag and the kinetic energy density are modeled as a function of the state vector. The goal is to minimize both the skin-friction drag and the kinetic energy density by appropriate methods. The partitioned visual servoing control is used to minimize, simultaneously, the skin-friction drag and the kinetic energy density with two degrees of freedom. As a result, the behavior of the skin-friction drag monotonically decreases in time. However, the behavior of the kinetic energy density does not monotonically decrease in time, the similar results from the other methods such as: PID and LQR controls. Therefore, the number of the degree of freedom increases, which leads to the improvement of the kinetic energy density. In addition, when the number of the degree of freedom equals the number of state vector, the kinetic energy density monotonically decreases in time by using the visual servoing control. The dimension of linearized plane Poiseuille flow is large, therefore, we need to reduce the order of controller. We demonstrate that the control law based on a mode reduction can be applied for the full system. Moreover, the kinetic energy density almost will monotonically decreases in time even using two degrees of freedom when the visual servoing control is designed based on the model order reduction
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Liefvendahl, Mattias. "Stability results for viscous shock waves and plane Couette flow." Doctoral thesis, Stockholm, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3241.
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Nazaikinskii, Vladimir, Anton Savin, Bert-Wolfgang Schulze, and Boris Sternin. "Differential operators on manifolds with singularities : analysis and topology : Chapter 3: Eta invariant and the spectral flow." Universität Potsdam, 2003. http://opus.kobv.de/ubp/volltexte/2008/2659/.
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Contents:
Chapter 3: Eta Invariant and the Spectral Flow
3.1. Introduction
3.2. The Classical Spectral Flow
3.2.1. Definition and main properties
3.2.2. The spectral flow formula for periodic families
3.3. The Atiyah–Patodi–Singer Eta Invariant
3.3.1. Definition of the eta invariant
3.3.2. Variation under deformations of the operator
3.3.3. Homotopy invariance. Examples
3.4. The Eta Invariant of Families with Parameter (Melrose’s Theory)
3.4.1. A trace on the algebra of parameter-dependent operators
3.4.2. Definition of the Melrose eta invariant
3.4.3. Relationship with the Atiyah–Patodi–Singer eta invariant
3.4.4. Locality of the derivative of the eta invariant. Examples
3.5. The Spectral Flow of Families of Parameter-Dependent Operators
3.5.1. Meromorphic operator functions. Multiplicities of singular points
3.5.2. Definition of the spectral flow
3.6. Higher Spectral Flows
3.6.1. Spectral sections
3.6.2. Spectral flow of homotopies of families of self-adjoint operators
3.6.3. Spectral flow of homotopies of families of parameter-dependent operators
3.7. Bibliographical Remarks
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Cardoso, Jose Carlos Silva. "Investigation and implementation of real-time spectral estimation techniques for use with pulsed Doppler blood flow detectors." Thesis, Bangor University, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.389743.
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Marklund, Lars. "Topographic Control of Groundwater Flow." Doctoral thesis, KTH, Mark- och vattenteknik, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-11153.
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Gravity is the main driving force for groundwater flow, and both landscape topography and geology distribute the effects of gravity on groundwater flow. The groundwater table defines the distribution of the potential energy of the water. In humid regions where the bedrock permeability is relatively low and the soil depth is sufficiently shallow, the groundwater table closely follows the landscape topography and, thus, the topography controls the groundwater circulation in these regions. In this thesis, I investigate multi-scale topography-controlled groundwater flow, with the goal of systematizing the spatial distribution of groundwater flow and assessing geological parameters of importance for groundwater circulation. Both exact solutions and numerical models are utilized for analyzing topography-controlled groundwater flow. The more complex numerical models are used to explore the importance of various simplifications of the exact solutions. The exact solutions are based on spectral representation of the topography and superpositioning of unit solutions to the groundwater flow field. This approach is an efficient way to analyze multi-scaled topography-controlled groundwater flow because the impact of individual topographic scales on the groundwater flow can be analyzed separately. The results presented here indicate that topography is fractal and affects groundwater flow cells at wide range of spatial scales. We show that the fractal nature of the land surface produces fractal distributions of the subsurface flow patterns. This underlying similarity in hydrological processes also yields a single scale-independent distribution of subsurface water residence times which have been found in distributions of solute efflux from watersheds. Geological trends modify the topographic control of the groundwater circulation pattern and this thesis presents exact solutions explaining the impact of geological layering, depth-decaying and anisotropic hydraulic conductivity on the groundwater flow field. For instance, layers of Quaternary deposits and decaying permeability with depth both increase the importance of smaller topographic scales and creates groundwater flow fields where a larger portion of the water occupies smaller and shallower circulation cells, in comparison to homogeneous systems.Gravitationen är den mest betydelsefulla drivkraften för grundvattenströmning. Topografin och geologin fördelar vattnets potentiella energi i landskapet. Grundvattenytans läge definierar vattnets potentiella energi, vilket är ett randvillkor för grundvattnets strömningsfält. I humida områden med en relativt tät berggrund och tillräckligt tunna jordlager, följer grundvattenytan landskapets topografi. Därav följer att grundvattenströmningen är styrd av topografin i dessa områden. I denna avhandling belyser jag den flerskaliga topografistyrda grundvattenströmningen. Min målsättning har varit att kvantitativt bestämma grundvattenströmningens rumsliga fördelning samt att undersöka hur olika geologiska parametrar påverkar grundvattencirkulationen. Jag har använt såväl numeriska modeller som analytiska lösningar, för att undersöka hur topografin styr grundvattenströmningen. De numeriska modellerna är mer komplexa än de analytiska lösningarna och kan därför användas för att undersöka betydelserna av olika förenklingar som finns i de analytiska lösningarna. De analytiska lösningarna är baserade på spektralanalys av topografin, samt superponering av enhetslösningar, där varje enhetslösning beskriver hur en specifik topografisk skala påverkar grundvattnets strömningsfält. Detta är ett effektivt tillvägagångssätt för att undersöka flerskaliga effekter av topografin, eftersom påverkan av varje enskild topografisk skala kan studeras separat. Resultaten som presenteras indikerar att topografin är fraktal och att den ger upphov till cirkulationsceller av varierande storlek som även dessa är av en fraktal natur. Denna grundläggande fördelning i grundvattnets strömningsfält ger upphov till att grundvattnets uppehållstid i marken följer ett självlikformigt mönster och kan förklara uppmätta tidsvariationer av lösta ämnens koncentrationer i vattendrag efter regn. Geologiska trender påverkar hur grundvattenströmningen styrs av topografin. De exakta lösningar som presenteras här, beskriver hur geologiska lager samt djupavtagande och anisotropisk hydraulisk konduktivitet påvekar grundvattnets strömning. Exempelvis är betydelsen av mindre topografiska skalor viktigare i områden med kvartära avlagringar och en berggrund med djupavtagande konduktivitet, än i områden med homogen bergrund utan kvartära avlagringar. Dessutom är en större andel strömmande vatten belägen närmare markytan i de förstnämnda områdena.
QC 20100802
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Dines, Nicoleta, X. Liu, and Bert-Wolfgang Schulze. "Edge quantisation of elliptic operators." Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2008/2683/.
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The ellipticity of operators on a manifold with edge is defined as the bijectivity of the components of a principal symbolic hierarchy σ = (σψ, σ∧), where the second component takes value in operators on the infinite model cone of the local wedges. In general understanding of edge problems there are two basic aspects: Quantisation of edge-degenerate operators in weighted Sobolev spaces, and verifying the elliptcity of the principal edge symbol σ∧ which includes the (in general not explicitly known) number of additional conditions on the edge of trace and potential type. We focus here on these queations and give explicit answers for a wide class of elliptic operators that are connected with the ellipticity of edge boundary value problems and reductions to the boundary. In particular, we study the edge quantisation and ellipticity for Dirichlet-Neumann operators with respect to interfaces of some codimension on a boundary. We show analogues of the Agranovich-Dynin formula for edge boundary value problems, and we establish relations of elliptic operators for different weights, via the spectral flow of the underlying conormal symbols.
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Li, Zhaobin. "Two-phase spectral wave explicit Navier-Stokes equations method for wave-structure interactions." Thesis, Ecole centrale de Nantes, 2018. http://www.theses.fr/2018ECDN0041/document.
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Cette thèse propose un algorithme efficace pour la simulation numérique des interactions houle-structure avec des solveurs CFD bi-phasiques. L'algorithme est basé sur le couplage de la théorie potentielle et des équations bi-phasiques de Navier-Stokes. C'est une extension de la méthode Spectral Wave Explicit Navier-Stokes Equations (SWENSE) pour les solveurs CFD bi-phasiques avec une technique de capture d'interface. Dans cet algorithme, la solution totale est décomposée en une composante incidente et une composante complémentaire. La partie incidente est explicitement obtenue avec des méthodes spectrales basées sur la théorie des écoulements potentiels ; seule la partie complémentaire est résolue avec des solveurs CFD, représentant l'influence de la structure sur les houles incidentes. La décomposition assure la précision de la cinématique des houles incidentes quel que soit le maillage utilisé parles solveurs CFD. Une réduction significative de la taille du maillage est attendue dans les problèmes typiques des interactions houle structure. Les équations sont présentées sous trois formes : la forme conservative, la forme non conservative et la forme Ghost of Fluid Method. Les trois versions d'équations sont implémentées dans OpenFOAM et validées par une série de cas de test. Une technique d'interpolation efficace pour reconstruire la solution des houles irrégulières donnée par la méthode Higher-Order Spectral (HOS) sur le maillage CFD est également proposéeThis thesis proposes an efficient algorithm for simulating wave-structure interaction with two-phase Computational Fluid Dynamics (CFD) solvers. The algorithm is based on the coupling of potential wave theory and two phase Navier-Stokes equations. It is an extension of the Spectral Wave Explicit Navier-Stokes Equations (SWENSE) method for generalized two-phase CFD solvers with interface capturing techniques. In this algorithm, the total solution isdecomposed into an incident and acomplementary component. The incident solution is explicitly obtained with spectral wave models based on potential flow theory; only the complementary solution is solved with CFD solvers, representing the influence of the structure on the incident waves. The decomposition ensures the accuracy of the incident wave’s kinematics regardless of the mesh in CFD solvers. A significant reduction of the mesh size is expected in typical wave structure interaction problems. The governing equations are given in three forms: the conservative form, the non conservative form, and the Ghost of Fluid Method (GFM) form. The three sets of governing equations are implemented in OpenFOAM and validated by a series of wave-structure interaction cases. An efficient interpolation technique to map the irregular wave solution from a Higher-Order Spectral (HOS) Method onto the CFD grid is also proposed
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Komminaho, Jukka. "Direct numerical simulation of turbulent flow in plane and cylindrical geometries." Doctoral thesis, Stockholm, 2000. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3054.
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Piatkowski, Stephan-Marian [Verfasser], and Peter [Akademischer Betreuer] Bastian. "A Spectral Discontinuous Galerkin method for incompressible flow with Applications to turbulence / Stephan-Marian Piatkowski ; Betreuer: Peter Bastian." Heidelberg : Universitätsbibliothek Heidelberg, 2019. http://d-nb.info/1191760529/34.
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Rahimian, Abtin. "Parallel algorithms for direct blood flow simulations." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/43611.
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Fluid mechanics of blood can be well approximated by a mixture model of a Newtonian fluid and deformable particles representing the red blood cells. Experimental and theoretical evidence suggests that the deformation and rheology of red blood cells is similar to that of phospholipid vesicles. Vesicles and red blood cells are both area preserving closed membranes that resist bending. Beyond red blood cells, vesicles can be used to investigate the behavior of cell membranes, intracellular organelles, and viral particles. Given the importance of vesicle flows, in this thesis we focus in efficient numerical methods for such problems: we present computationally scalable algorithms for the simulation of dilute suspension of deformable vesicles in two and three dimensions. Our method is based on the boundary integral formulation of Stokes flow. We present new schemes for simulating the three-dimensional hydrodynamic interactions of large number of vesicles with viscosity contrast. The algorithms incorporate a stable time-stepping scheme, high-order spatiotemporal discretizations, spectral preconditioners, and a reparametrization scheme capable of resolving extreme mesh distortions in dynamic simulations. The associated linear systems are solved in optimal time using spectral preconditioners. The highlights of our numerical scheme are that (i) the physics of vesicles is faithfully represented by using nonlinear solid mechanics to capture the deformations of each cell, (ii) the long-range, N-body, hydrodynamic interactions between vesicles are accurately resolved using the fast multipole method (FMM), and (iii) our time stepping scheme is unconditionally stable for the flow of single and multiple vesicles with viscosity contrast and its computational cost-per-simulation-unit-time is comparable to or less than that of an explicit scheme. We report scaling of our algorithms to simulations with millions of vesicles on thousands of computational cores.
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McKernan, John. "Control of plane poiseuille flow : a theoretical and computational investigation." Thesis, Cranfield University, 2006. http://hdl.handle.net/1826/1431.
Full textAbstract:
Control of the transition of laminar flow to turbulence would result in lower drag and reduced energy consumption in many engineering applications. A spectral state-space model of linearised plane Poiseuille flow with wall transpiration ac¬tuation and wall shear measurements is developed from the Navier-Stokes and continuity equations, and optimal controllers are synthesized and assessed in sim¬ulations of the flow. The polynomial-form collocation model with control by rate of change of wall-normal velocity is shown to be consistent with previous interpo¬lating models with control by wall-normal velocity. Previous methods of applying the Dirichlet and Neumann boundary conditions to Chebyshev series are shown to be not strictly valid. A partly novel method provides the best numerical behaviour after preconditioning.
Two test cases representing the earliest stages of the transition are consid¬ered, and linear quadratic regulators (LQR) and estimators (LQE) are synthesized. Finer discretisation is required for convergence of estimators. A novel estimator covariance weighting improves estimator transient convergence. Initial conditions which generate the highest subsequent transient energy are calculated. Non-linear open- and closed-loop simulations, using an independently derived finite-volume Navier-Stokes solver modified to work in terms of perturbations, agree with linear simulations for small perturbations. Although the transpiration considered is zero net mass flow, large amounts of fluid are required locally. At larger perturbations the flow saturates. State feedback controllers continue to stabilise the flow, but estimators may overshoot and occasionally output feedback destabilises the flow.
Actuation by simultaneous wall-normal and tangential transpiration is derived. There are indications that control via tangential actuation produces lower highest transient energy, although requiring larger control effort. State feedback controllers are also synthesized which minimise upper bounds on the highest transient energy and control effort. The performance of these controllers is similar to that of the optimal controllers.
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Zhu, Lailai. "Simulation of individual cells in flow." Doctoral thesis, KTH, Stabilitet, Transition, Kontroll, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-142557.
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In this thesis, simulations are performed to study the motion ofindividual cells in flow, focusing on the hydrodynamics of actively swimming cells likethe self-propelling microorganisms, and of passively advected objects like the red bloodcells. In particular, we develop numerical tools to address the locomotion ofmicroswimmers in viscoelastic fluids and complex geometries, as well as the motion ofdeformable capsules in micro-fluidic flows. For the active movement, the squirmer is used as our model microswimmer. The finiteelement method is employed to study the influence of the viscoelasticity of fluid on theperformance of locomotion. A boundary element method is implemented to study swimmingcells inside a tube. For the passive counterpart, the deformable capsule is chosen as the modelcell. An accelerated boundary integral method code is developed to solve thefluid-structure interaction, and a global spectral method is incorporated to handle theevolving cell surface and its corresponding membrane dynamics. We study the locomotion of a neutral squirmer with anemphasis on the change of swimming kinematics, energetics, and flowdisturbance from Newtonian to viscoelastic fluid. We also examine the dynamics of differentswimming gaits resulting in different patterns of polymer deformation, as well as theirinfluence on the swimming performance. We correlate the change of swimming speed withthe extensional viscosity and that of power consumption with the phase delay of viscoelasticfluids. Moreover, we utilise the boundary element method to simulate the swimming cells in astraight and torus-like bent tube, where the tube radius is a few times the cell radius. Weinvestigate the effect of tube confinement to the swimming speed and power consumption. Weanalyse the motions of squirmers with different gaits, which significantly affect thestability of the motion. Helical trajectories are produced for a neutralsquirmer swimming, in qualitative agreement with experimental observations, which can beexplained by hydrodynamic interactions alone. We perform simulations of a deformable capsule in micro-fluidic flows. We look atthe trajectory and deformation of a capsule through a channel/duct with a corner. Thevelocity of capsule displays an overshoot as passing around the corner, indicating apparentviscoelasticity induced by the interaction between the deformable membrane and viscousflow. A curved corner is found to deform the capsule less than the straight one. In addition, we propose a new cell sorting device based on the deformability of cells. Weintroduce carefully-designed geometric features into the flow to excite thehydrodynamic interactions between the cell and device. This interaction varies andclosely depends on the cell deformability, the resultant difference scatters the cellsonto different trajectories. Our high-fidelity computations show that the new strategy achievesa clear and robust separation of cells. We finally investigate the motion of capsule in awall-bounded oscillating shear flow, to understand the effect of physiological pulsation to thedeformation and lateral migration of cells. We observe the lateral migration velocity of a cellvaries non-monotonically with its deformability.QC 20140313
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Reich, Wieland. "Spectral, Combinatorial, and Probabilistic Methods in Analyzing and Visualizing Vector Fields and Their Associated Flows." Doctoral thesis, Universitätsbibliothek Leipzig, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-222643.
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In this thesis, we introduce several tools, each coming from a different branch of mathematics, for analyzing real vector fields and their associated flows.
Beginning with a discussion about generalized vector field decompositions, that mainly have been derived from the classical Helmholtz-Hodge-decomposition, we decompose a field into a kernel and a rest respectively to an arbitrary vector-valued linear differential operator that allows us to construct decompositions of either toroidal flows or flows obeying differential equations of second (or even fractional) order and a rest. The algorithm is based on the fast Fourier transform and guarantees a rapid processing and an implementation that can be directly derived from the spectral simplifications concerning differentiation used in mathematics.
Moreover, we present two combinatorial methods to process 3D steady vector fields, which both use
graph algorithms to extract features from the underlying vector field. Combinatorial approaches are known to be less sensitive to noise than extracting individual trajectories. Both of the methods are extensions of an existing 2D technique to 3D fields.
We observed that the first technique can generate overly coarse results and therefore we present a second method that works using the same concepts but produces more detailed results. Finally, we discuss several possibilities for categorizing the invariant sets with respect to the flow.
Existing methods for analyzing separation of streamlines are often restricted to a finite time or a local area. In the frame of this work, we introduce a new method that complements them by allowing an infinite-time-evaluation of steady planar vector fields. Our algorithm unifies combinatorial and probabilistic methods and introduces the concept of separation in time-discrete Markov chains. We compute particle distributions instead of the streamlines of single particles. We encode the flow into a map and then into a transition matrix for each time direction. Finally, we compare the results of our grid-independent algorithm to the popular Finite-Time-Lyapunov-Exponents and discuss the discrepancies.
Gauss\' theorem, which relates the flow through a surface to the vector field inside the surface, is an important tool in flow visualization. We are exploiting the fact that the theorem can be further refined on polygonal cells and construct a process that encodes the particle movement through the boundary facets of these cells using transition matrices. By pure power iteration of transition matrices, various topological features, such as separation and invariant sets, can be extracted without having to rely on the classical techniques, e.g., interpolation, differentiation and numerical streamline integration.