Relevant bibliographies by topics / Spectral Proper Orthogonal Decomposition

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Academic literature on the topic 'Spectral Proper Orthogonal Decomposition'

Author: Grafiati
Published: 6 September 2023
Last updated: 7 September 2023

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Journal articles on the topic "Spectral Proper Orthogonal Decomposition"

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Sieber, Moritz, C. Oliver Paschereit, and Kilian Oberleithner. "Spectral proper orthogonal decomposition." Journal of Fluid Mechanics 792 (March 4, 2016): 798–828. http://dx.doi.org/10.1017/jfm.2016.103.

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The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures the dominant flow structures. The most prominent candidates are the energy-ranked proper orthogonal decomposition (POD) and the frequency-ranked Fourier decomposition and dynamic mode decomposition (DMD). However, these methods are not suitable when the relevant coherent structures occur at low energies or at multiple frequencies, which is often the case. To overcome the deficit of these ‘rigid’ approaches, we propose a new method termed spectral proper orthogonal decomposition (SPOD). It is based on classical POD and it can be applied to spatially and temporally resolved data. The new method involves an additional temporal constraint that enables a clear separation of phenomena that occur at multiple frequencies and energies. SPOD allows for a continuous shifting from the energetically optimal POD to the spectrally pure Fourier decomposition by changing a single parameter. In this article, SPOD is motivated from phenomenological considerations of the POD autocorrelation matrix and justified from dynamical systems theory. The new method is further applied to three sets of PIV measurements of flows from very different engineering problems. We consider the flow of a swirl-stabilized combustor, the wake of an airfoil with a Gurney flap and the flow field of the sweeping jet behind a fluidic oscillator. For these examples, the commonly used methods fail to assign the relevant coherent structures to single modes. The SPOD, however, achieves a proper separation of spatially and temporally coherent structures, which are either hidden in stochastic turbulent fluctuations or spread over a wide frequency range. The SPOD requires only one additional parameter, which can be estimated from the basic time scales of the flow. In spite of all these benefits, the algorithmic complexity and computational cost of the SPOD are only marginally greater than those of the snapshot POD.
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Schmidt, Oliver T., and Tim Colonius. "Guide to Spectral Proper Orthogonal Decomposition." AIAA Journal 58, no. 3 (March 2020): 1023–33. http://dx.doi.org/10.2514/1.j058809.

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He, Xiao, Zhou Fang, Georgios Rigas, and Mehdi Vahdati. "Spectral proper orthogonal decomposition of compressor tip leakage flow." Physics of Fluids 33, no. 10 (October 2021): 105105. http://dx.doi.org/10.1063/5.0065929.

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Baars, Woutijn J., and Charles E. Tinney. "Proper orthogonal decomposition-based spectral higher-order stochastic estimation." Physics of Fluids 26, no. 5 (May 2014): 055112. http://dx.doi.org/10.1063/1.4879255.

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Schmidt, Oliver T., and Aaron Towne. "An efficient streaming algorithm for spectral proper orthogonal decomposition." Computer Physics Communications 237 (April 2019): 98–109. http://dx.doi.org/10.1016/j.cpc.2018.11.009.

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Mendez, M. A., M. Balabane, and J. M. Buchlin. "Multi-scale proper orthogonal decomposition of complex fluid flows." Journal of Fluid Mechanics 870 (May 15, 2019): 988–1036. http://dx.doi.org/10.1017/jfm.2019.212.

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Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low-order models of complex phenomena. In this work, we analyse the main limits of two popular decompositions, namely the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), and we propose a novel decomposition which allows for enhanced feature detection capabilities. This novel decomposition is referred to as multi-scale proper orthogonal decomposition (mPOD) and combines multi-resolution analysis (MRA) with a standard POD. Using MRA, the mPOD splits the correlation matrix into the contribution of different scales, retaining non-overlapping portions of the correlation spectra; using the standard POD, the mPOD extracts the optimal basis from each scale. After introducing a matrix factorization framework for data-driven decompositions, the MRA is formulated via one- and two-dimensional filter banks for the dataset and the correlation matrix respectively. The validation of the mPOD, and a comparison with the discrete Fourier transform (DFT), DMD and POD are provided in three test cases. These include a synthetic test case, a numerical simulation of a nonlinear advection–diffusion problem and an experimental dataset obtained by the time-resolved particle image velocimetry (TR-PIV) of an impinging gas jet. For each of these examples, the decompositions are compared in terms of convergence, feature detection capabilities and time–frequency localization.
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Mengaldo, Gianmarco, and Romit Maulik. "PySPOD: A Python package for Spectral Proper Orthogonal Decomposition (SPOD)." Journal of Open Source Software 6, no. 60 (April 16, 2021): 2862. http://dx.doi.org/10.21105/joss.02862.

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Gambassi, Henrique, Paul Ziadé, and Chris Morton. "Sparse sensor-based flow estimation with spectral proper orthogonal decomposition." AIP Advances 12, no. 8 (August 1, 2022): 085208. http://dx.doi.org/10.1063/5.0094874.

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The application of Artificial Neural Networks (ANNs) in developing sensor-based estimators for unsteady flows has become an active area of research over the last decade. One of the challenges in this area is the selection of a low-dimensional subspace that enables the ANN to reconstruct relevant spatiotemporal dynamics in the flow, as both sparsity and interpretability are simultaneously desired. The present study demonstrates the use of a flow-estimation framework based on Long Short-Term Memory (LSTM) neural networks and the time-domain Spectral Proper Orthogonal Decomposition (SPOD) [Sieber et al., “Spectral proper orthogonal decomposition,” J. Fluid Mech. 792, 798–828 (2016)], which was proposed as an extension to the traditional POD. The two-cylinder flow selected for analysis in this study is referred to as the “flip-flop” regime for exhibiting intermittent changes in the phase alignment of the vortices shed by the two cylinders. This flow has dynamics occurring over a wide range of frequencies, and it was selected to demonstrate the usefulness of SPOD in characterizing the wake dynamics of periodic wake flows and to determine if it can provide a better subspace for training and estimation when compared to POD. It was found that a particular SPOD basis obtained with an empirically determined filter length completely separated the frequency centered phenomena present in the spectrum of the most energetic POD modes into different modes. These new SPOD modes were observed to have a direct relationship with the vortex dynamics in the flow, providing direct access to the antiphase and in-phase flow states. The LSTM neural networks estimation capacities were very similar across all the modal spaces investigated, performing well regardless of whether the frequency content of the modal space used for training and estimation was found superimposed in the spectrum of the most energetic modes (POD) or separated into different modes (SPOD). Further investigation is required to determine if this result holds for turbulent flows.
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Cho, Woon, Samir Sahyoun, Seddik M. Djouadi, Andreas Koschan, and Mongi A. Abidi. "Reduced-order spectral data modeling based on local proper orthogonal decomposition." Journal of the Optical Society of America A 32, no. 5 (April 9, 2015): 733. http://dx.doi.org/10.1364/josaa.32.000733.

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Towne, Aaron, Oliver T. Schmidt, and Tim Colonius. "Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis." Journal of Fluid Mechanics 847 (May 29, 2018): 821–67. http://dx.doi.org/10.1017/jfm.2018.283.

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We consider the frequency domain form of proper orthogonal decomposition (POD), called spectral proper orthogonal decomposition (SPOD). Spectral POD is derived from a space–time POD problem for statistically stationary flows and leads to modes that each oscillate at a single frequency. This form of POD goes back to the original work of Lumley (Stochastic Tools in Turbulence, Academic Press, 1970), but has been overshadowed by a space-only form of POD since the 1990s. We clarify the relationship between these two forms of POD and show that SPOD modes represent structures that evolve coherently in space and time, while space-only POD modes in general do not. We also establish a relationship between SPOD and dynamic mode decomposition (DMD); we show that SPOD modes are in fact optimally averaged DMD modes obtained from an ensemble DMD problem for stationary flows. Accordingly, SPOD modes represent structures that are dynamic in the same sense as DMD modes but also optimally account for the statistical variability of turbulent flows. Finally, we establish a connection between SPOD and resolvent analysis. The key observation is that the resolvent-mode expansion coefficients must be regarded as statistical quantities to ensure convergent approximations of the flow statistics. When the expansion coefficients are uncorrelated, we show that SPOD and resolvent modes are identical. Our theoretical results and the overall utility of SPOD are demonstrated using two example problems: the complex Ginzburg–Landau equation and a turbulent jet.
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Dissertations / Theses on the topic "Spectral Proper Orthogonal Decomposition"

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Le, Thai Hoa. "UNSTEADY BUFFETING FORCES AND GUST RESPONSE OF BRIDGES WITH PROPER ORTHOGONAL DECOMPOSITION APPLICATIONS." 京都大学 (Kyoto University), 2007. http://hdl.handle.net/2433/49126.

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学位授与大学：京都大学 ; 取得学位: 博士(工学) ; 学位授与年月日: 2007-09-25 ; 学位の種類: 新制・課程博士 ; 学位記番号: 工博第2843号 ; 請求記号: 新制/工/1418 ; 整理番号: 25528
The unsteady buffeting forces and the gust response prediction of bridges in the atmospheric turbulent flows is recently attracted more attention due to uncertainties in both experiment and analytical theory. The correction functions such as the aerodynamic admittance function and the spatial coherence function have been supplemented to cope with limitations of the quasi-steady theory and strip one so far. Concretely, so-called single-variate quasi-steady aerodynamic admittance functions as the transfer functions between the wind turbulence and induced buffeting forces, as well as coherence of wind turbulence has been widely applied for the gust response prediction. Recent literatures, however, pointed out that the coherence of force exhibits higher than that of turbulence. These correction functions, in the other words, contain their uncertainties which are required to be more understanding. Proper orthogonal decomposition (POD), known as the Karhunen-Loeve decomposition has been applied popularly in many engineering fields. Main advantage of the POD is that the multi-variate correlated random fields/processes can be decomposed and described in such simplified way as a combination of limited number of orthogonally low-order dominant eigenvectors (or turbulent modes) which is convenient and applicable for order-reduced representation, simulation of the random fields/processes such as the turbulent fields, turbulent-induced force fields and stochastic response prediction as well. The POD and its proper transformations based on either zero-time-lag covariance matrix or cross spectral one of random fields/processes have been branched by either the covariance proper transformation (CPT) in the time domain or the spectral proper transformation (SPT) in the frequency domain. So far, the covariance matrix-based POD and its covariance proper transformation in the time domain has been used almost in the wind engineering topics due to its simplification in computation and interpretation. In this research, the unsteady buffeting forces and the gust response prediction of bridges with emphasis on the POD applications have been discussed. Investigations on the admittance function of turbulent-induced buffeting forces and the coherence one of the surface pressure as well as the spatial distribution and correlation of the unsteady pressure fields around some typically rectangular cylinders in the different unsteady flows have been carried out thanks to physical measurements in the wind tunnel. This research indicated effect of the bluff body flow and the wind-structure interaction on the higher coherence of buffeting forces than the coherence of turbulence, thus this effect should be accounted and undated for recent empirical formulae of the coherence function of the unsteady buffeting forces. Especially, the multi-variate nonlinear aerodynamic admittance function has been proposed in this research, as well as the temporo-spectral structure of the coherence functions of the wind turbulence and the buffeting forces has been firstly here using the wavelet transform-based coherence in order to detect intermittent characteristics and temporal correspondence of these coherence functions. In POD applications, three potential topics in the wind engineering field have been discussed in the research: (i) analysis and identification, modeling of unsteady pressure fields around model sections; (ii) representation and simulation of multi-variate correlated turbulent fields and (iii) stochastic response prediction of structures and bridges. Especially, both POD branches and their proper transformations in the time domain and the frequency one have been used in these applications. It found from these studies that only few low-order orthogonal dominant modes are enough accuracy for representing, modeling, simulating the correlated random fields (turbulence and unsteady surface pressure, unsteady buffeting forces), as well as predicting stochastic response of bridges in the time and frequency domains. The gust response prediction of bridges has been formulated in the time domain at the first time in this research using the covariance matrix-based POD and its covariance proper transformation which is very promising to solve the problems of the nonlinear and unsteady aerodynamics. Furthermore, the physical linkage between these low-order modes and physical causes occurring on physical models has been interpreted in some investigated cases.
Kyoto University (京都大学)
0048
新制・課程博士
博士(工学)
甲第13372号
工博第2843号
新制||工||1418(附属図書館)
25528
UT51-2007-Q773
京都大学大学院工学研究科社会基盤工学専攻
(主査)教授 松本 勝, 教授 河井 宏允, 准教授 白土 博通
学位規則第4条第1項該当
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Malm, Johan. "Spectral-element simulations of turbulent wall-bounded flows including transition and separation." Doctoral thesis, KTH, Stabilitet, Transition, Kontroll, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-50294.

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The spectral-element method (SEM) is used to study wall-bounded turbulent flowsin moderately complex geometries. The first part of the thesis is devoted to simulations of canonical flow cases, such as temporal K-type transitionand turbulent channel flow, to investigate general resolution requirements and computational efficiency of the numerical code nek5000. Large-eddy simulation (LES) is further performed of a plane asymmetric diffuser flow with an opening angle of 8.5 degrees, featuring turbulent flow separation. Good agreement with numerical studies of Herbst (2007) is obtained, and it is concluded that the use of a high-order method is advantageous for flows featuring pressure-induced separation. Moreover, it is shown, both a priori on simpler model problems and a posteriori using the full Navier--Stokes equations, that the numerical instability associated with SEM at high Reynolds numbers is cured either by employing over-integration (dealiasing) or a filter-based stabilisation, thus rendering simulations of moderate to high Reynolds number flows possible. The second part of the thesis is devoted to the first direct numerical simulation (DNS) of a truly three-dimensional, turbulent and separated diffuser flow at Re = 10 000 (based on bulk velocity and inflow-duct height), experimentally investigated by Cherry et al. (2008). The massively parallel capabilities of the spectral-element method are exploited by running the simulations on up to 32 768 processors. Very good agreement with experimental mean flow data is obtained and it is thus shown that well-resolved simulations of complex turbulent flows with high accuracy are possible at realistic Reynolds numberseven in complicated geometries. An explanation for the discovered asymmetry of the mean separated flow is provided and itis demonstrated that a large-scale quasi-periodic motion is present in the diffuser. In addition, a new diagnostic measure, based on the maximum vorticity stretching component in every spatial point, is designed and tested in a number of turbulent and transitional flows. Finally, Koopman mode decomposition is performed of a minimal channel flow and compared to classical proper orthogonal decomposition (POD).
QC 20111206
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Spitz, Nicolas. "Prediction of Trailing Edge Noise from Two-Point Velocity Correlations." Thesis, Virginia Tech, 2005. http://hdl.handle.net/10919/32637.

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This thesis presents the implementation and validation of a new methodology developed by Glegg et al. (2004) for solving the trailing edge noise problem. This method is based on the premises that the noise produced by a surface can be computed by the integral of the cross product between the velocity and vorticity fields, of the boundary layer and shed vorticity (Howe (1978)). To extract the source terms, proper orthogonal decomposition is applied to the velocity cross spectrum to extract modes of the unsteady velocity and vorticity. The new formulation of the trailing edge noise problem by Glegg et al. (2004) is attractive because it applies to the high frequencies of interest but does not require an excessive computational effort. Also, the nature of the formulation permits the identification of the modes producing the noise and their associated velocity fluctuations as well as the regions of the boundary layer responsible for the noise production. The source terms were obtained using the direct numerical simulation of a turbulent channel flow by Moser et al. (1998). Two-point velocity and vorticity statistics of this data set were obtained by averaging 41 instantaneous fields. For comparisons purposes, experimental boundary layer data by Adrian et al. (2000) was chosen. Statistical reduction of 50 velocity fields obtained by particle image velocimetry was performed and analysis of the two-point correlation function showed features similar to the DNS data case. Also, proper orthogonal decomposition revealed identical dominant modes and eddy structures in the flow, therefore justifying considering the channel flow as an external boundary layer for noise calculations. Comparison of noise predictions with experimental data from Brooks et al. (1989) showed realistic results with the largest discrepancies, on the order of 5 dB, occurring at the lowest frequencies. The DNS results are least applicable at these frequencies, since these correspond to the longest streamwise lengthscales, which are the most affected by the periodicity conditions used in the DNS and also are the least representative of the turbulence in an external boundary layer flow. Most of the noise was shown to be produced by low-frequency streamwise velocity modes in the bottom 10% of the boundary layer and locations closest to the wall. Only 6 modes were required to obtain noise levels within 1 dB of the total noise. Finally, the method for predicting spatial velocity correlation from Reynolds stress data in wake flows, originally developed by Devenport et al. (1999, 2001) and Devenport and Glegg (2001), was adapted to boundary-layer type flows. This method, using Reynolds stresses and the prescription of a lengthscale to extrapolate the full two-point correlation, was shown to produce best results for a lengthscale prescribed as proportional to the turbulent macroscale. Noise predictions using modeled two-point statistics showed good agreement with the DNS inferred data in all but frequency magnitude, a probable consequence of the modeling of the correlation function in the streamwise direction. Other quantities associated to noise were seen to be similar to the ones obtained using the DNS.
Master of Science
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Di, Donfrancesco Fabrizio. "Reduced Order Models for the Navier-Stokes equations for aeroelasticity." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS603.

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Le coût d’une simulation numérique aéroélastique peut devenir trop onéreuse lorsque une analyse paramétrique à haut fidélité est requise. Dans ce contexte, des Modèles d'Ordre Réduit (MOR) ont été développés en vue de réduire le coût de calcul des simulations numériques en préservant un haut niveau de précision. Ce travail de thèse porte sur la construction d'un MOR pour les équations de Navier-Stokes en tenant compte d'un maillage déformable dans le cas d'une application aéroélastique. Une base modale pour l'écoulement est obtenue via la Décomposition Orthogonale aux valeurs propres et une projection Galerkin est utilisée pour réduire le système d'équations de la mécanique des fluides. Pour pouvoir prendre en compte les non-linéarités des équation de Navier-Stokes une méthode de projection masquée est mise en œuvre et évaluée pour différent cas test avec maillage fixe. Le MOR est ensuite adapté pour prendre en compte des maillages déformables. Finalement, une méthode réduite spectrale en temps (ROTSM) a été formulée afin de répondre aux problèmes de stabilité qui concernent le MORs avec projection dans le domaine de la mécanique des fluides. Une évaluation du MOR obtenu est ensuite menée sur des études paramétriques pour des applications aéroélastiques
The numerical prediction of aeroelastic systems responses becomes unaffordable when parametric analyses with high-fidelity CFD are required. Reduced order modeling (ROM) methods have therefore been developed in view of reducing the costs of the numerical simulations while preserving a high level of accuracy. The present thesis focuses on the family of projection based methods for the compressible Navier-Stokes equations involving deforming meshes in the case of aeroelastic applications. A vector basis obtained by Proper Orthogonal Decomposition (POD) combined to a Galerkin projection of the system equations is used in order to build a ROM for fluid mechanics. Masked projection approaches are therefore implemented and assessed for different test cases with fixed boundaries in order to provide a fully nonlinear formulation for the projection-based ROMs. Then, the ROM is adapted in the case of deforming boundaries and aeroelastic applications in a parametric context. Finally, a Reduced Order Time Spectral Method (ROTSM) is formulated in order to address the stability issues which involve the projection-based ROMs for fluid mechanics applications
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Allison, Timothy Charles. "System Identification via the Proper Orthogonal Decomposition." Diss., Virginia Tech, 2007. http://hdl.handle.net/10919/29424.

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Although the finite element method is often applied to analyze the dynamics of structures, its application to large, complex structures can be time-consuming and errors in the modeling process may negatively affect the accuracy of analyses based on the model. System identification techniques attempt to circumvent these problems by using experimental response data to characterize or identify a system. However, identification of structures that are time-varying or nonlinear is problematic because the available methods generally require prior understanding about the equations of motion for the system. Nonlinear system identification techniques are generally only applicable to nonlinearities where the functional form of the nonlinearity is known and a general nonlinear system identification theory is not available as is the case with linear theory. Linear time-varying identification methods have been proposed for application to nonlinear systems, but methods for general time-varying systems where the form of the time variance is unknown have only been available for single-input single-output models. This dissertation presents several general linear time-varying methods for multiple-input multiple-output systems where the form of the time variance is entirely unknown. The methods use the proper orthogonal decomposition of measured response data combined with linear system theory to construct a model for predicting the response of an arbitrary linear or nonlinear system without any knowledge of the equations of motion. Separate methods are derived for predicting responses to initial displacements, initial velocities, and forcing functions. Some methods require only one data set but only promise accurate solutions for linear, time-invariant systems that are lightly damped and have a mass matrix proportional to the identity matrix. Other methods use multiple data sets and are valid for general time-varying systems. The proposed methods are applied to linear time-invariant, time-varying, and nonlinear systems via numerical examples and experiments and the factors affecting the accuracy of the methods are discussed.
Ph. D.
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Omar, Ahmed F. "Calibrating pressure sensitive paints using proper orthogonal decomposition." [Gainesville, Fla.] : University of Florida, 2006. http://purl.fcla.edu/fcla/etd/UFE0013431.

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Toal, David J. J. "Proper orthogonal decomposition & kriging strategies for design." Thesis, University of Southampton, 2009. https://eprints.soton.ac.uk/72023/.

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The proliferation of surrogate modelling techniques have facilitated the application of expensive, high fidelity simulations within design optimisation. Taking considerably fewer function evaluations than direct global optimisation techniques, such as genetic algorithms, surrogate models attempt to construct a surrogate of an objective function from an initial sampling of the design space. These surrogates can then be explored and updated in regions of interest. Kriging is a particularly popular method of constructing a surrogate model due to its ability to accurately represent complicated responses whilst providing an error estimate of the predictor. However, it can be prohibitively expensive to construct a kriging model at high dimensions with a large number of sample points due to the cost associated with the maximum likelihood optimisation. The following thesis aims to address this by reducing the total likelihood optimisation cost through the application of an adjoint of the likelihood function within a hybridised optimisation algorithm and the development of a novel optimisation strategy employing a reparameterisation of the original design problem through proper orthogonal decomposition.
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DOLCI, VALENTINA. "Proper Orthogonal Decomposition for Surrogate Models in Aerodynamics." Doctoral thesis, Politecnico di Torino, 2017. http://hdl.handle.net/11583/2678186.

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This study describes the design and implementation of surrogate models for aerodynamic optimization or database generations. Two different methods are presented: the first one follows the classical methodology: a parametric POD is applied to a set of initial solutions or snapshots obtained with an high fidelity CFD model. With respect to approaches presented in literature, in this research work no truncation of the POD modes is performed and they are all used to construct the surrogate model. Several applications are presented: a backward facing step case, the analysis of the flow around a NACA 0012 airfoil and a RAE 2822 supercritical airfoil, the optimization of an automotive external shape and a database generation of a three-dimensional aircraft.
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Akkari, Nissrine. "Etude mathématique de la sensibilité POD (Proper orthogonal decomposition)." Phd thesis, Université de La Rochelle, 2012. http://tel.archives-ouvertes.fr/tel-01066073.

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Dans cette thèse, nous nous sommes intéressés à l'étude mathématique de la sensibilité paramétrique de la méthode de réduction de modèles par projection connue sous le nom de POD pour Proper Orthogonal Decomposition. Dans beaucoup d'applications de la mécanique des fluides,la base de projection (base POD) calculée à un paramètre caractéristique fixe du problème de Navier-Stokes, est utilisée à la suite pour construire des modèles d'ordre réduit ROM-POD pour d'autres valeurs du paramètre caractéristique. Alors, la prédiction du comportement de ce ROM-POD vis-à-vis du problème initial est devenue cruciale. Pour cela, nous avons discuté cette problématique d'un point de vue mathématique. Nous avons établi des résultats mathématiques de sensibilité paramétrique des erreurs induites par application de la méthode ROM-POD. Plus précisément, notre approche est basée sur l'établissement d'estimations a priori de ces erreurs paramétriques, en utilisant les méthodes énergétiques classiques. Nos résultats sont démontrés pour les deux problèmes de type Burgers et Navier-Stokes. Des validations numériques de ces résultats mathématiques ont été faites uniquement pour le problème de type Burgers.
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Behzad, Fariduddin. "Proper Orthogonal Decomposition Based Reduced Order Modeling for Fluid Flow." Thesis, Clarkson University, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3682451.

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Proper orthogonal decomposition-based reduced order modeling is a technique that can be used to develop low dimensional models of fluid flow. In this technique, the Navier-Stokes equations are projected onto a finite number of POD basis functions resulting in a system of ODEs that model the system. The overarching goal of this work is to determine the best methods of applying this technique to generate reliable models of fluid flow. The first chapter investigates some basic characteristics of the proper orthogonal decomposition using the Burgers equation as a surrogate model problem. In applying the POD to this problem, we found that the eigenvalue spectrum is affected by machine precision and this leads to non-phsical negative eigenvalues in the POD. To avoid this, we introduced a new method called deflation that gives positive eigenvalues, but has the disadvantage that the orthogonality of the POD modes is more affected by numerical precision errors. To reduce the size of eigenproblem of POD process, the well-known snapshot method was tested. It was found that the number of snapshots required to obtain an accurate eigenvalue spectrum was determined by the smallest time scale of the phenomenon. After resolving this time scale, the errors in the eigenvalues and modes drop rapidly then converge with second-order accuracy. After obtaing POD modes, the ROM error was assessed using two errors, the error of projection of the problem onto the POD modes (the out-plane error) and the error of the ROM in the space spanned by POD modes (the in-plane error). The numerical results showed not only is the in-plane error bounded by the out-plane error (in agreement with theory) but it actually converges faster than the out-of-plane error. The second chapter is dedicated to building a robust POD-ROM for long term simulation of Navier-Stokes equation. The ability of the POD method to decompose the simulation and the capability of POD-ROM to simulate a low and high Reynolds flow over a NACA0015 airfoil was studied. We observed that POD can be applied for low Reynolds flows successfully if a proper stabilization method is used. For the high Reynolds case, the convergence of the eigenvalues spectrum with respect to duration of time window from we observed that the number of modes needed to simulate a certain time window increases almost linearly with the length of the time window. So, generating a POD-ROM for high Reynolds flow that reproduced the correct long-term limit cycle behavior needs many more modes than has been usually used in the literature. In the last chapter, we address the problem that the standard method of generating POD modes may be inaccurate when used "off-design" (at parameter values not used to generate the POD). We tested some of the popular methods developed to remedy that problem. The accuracy of these methods was in direct relation with the amount of data provided for those methods. So, in order to generate appropriate POD modes, very large POD problems must be solved. To avoid this, a new multi-level method, called recursive POD, for enriching the POD modes is introduced that mathematically provides optimal POD modes while reducing the computational size of problem to a manageable degrees. A low Reynolds flow over NACA 0015, actuated with constant suction/blowing of a fluidic jet located on top surface of airfoil is used as benchmark to test the technique. The flow is shifted from one periodic state to another periodic state due to fluidic jet effect. It was found that the modes extracted with the recursive POD method are as accurate as the modes of the best known method, global POD, while the computational effort is lower.

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Books on the topic "Spectral Proper Orthogonal Decomposition"

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Center, Langley Research, ed. Proper orthogonal decomposition in optimal control of fluids. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1999.

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Arian, Eyal. Trust-region proper orthogonal decomposition for flow control. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 2000.

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Inverse analyses with model reduction: Proper orthogonal decomposition in structural mechanics. Berlin: Springer, 2012.

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Proper Orthogonal Decomposition Methods for Partial Differential Equations. Elsevier, 2019. http://dx.doi.org/10.1016/c2017-0-04826-7.

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Proper Orthogonal Decomposition Methods for Partial Differential Equations. Academic Press, 2018.

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National Aeronautics and Space Administration (NASA) Staff. Proper Orthogonal Decomposition in Optimal Control of Fluids. Independently Published, 2018.

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Luo, Zhendong, and Goong Chen. Proper Orthogonal Decomposition Methods for Partial Differential Equations. Elsevier Science & Technology Books, 2018.

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Buljak, Vladimir. Inverse Analyses with Model Reduction: Proper Orthogonal Decomposition in Structural Mechanics. Springer, 2014.

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Buljak, Vladimir. Inverse Analyses with Model Reduction: Proper Orthogonal Decomposition in Structural Mechanics. Springer, 2011.

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Azam, Saeed Eftekhar. Online Damage Detection in Structural Systems: Applications of Proper Orthogonal Decomposition, and Kalman and Particle Filters. Springer London, Limited, 2014.

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Book chapters on the topic "Spectral Proper Orthogonal Decomposition"

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Gatski, T. B., and M. N. Glauser. "Proper Orthogonal Decomposition Based Turbulence Modeling." In Instability, Transition, and Turbulence, 498–510. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-2956-8_48.

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Silva, José P., E. Jan W. ter Maten, Michael Günther, and Matthias Ehrhardt. "Proper Orthogonal Decomposition in Option Pricing." In Novel Methods in Computational Finance, 441–52. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-61282-9_24.

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Berkooz, Gal. "Observations on the Proper Orthogonal Decomposition." In Studies in Turbulence, 229–47. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4612-2792-2_16.

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Pinnau, René. "Model Reduction via Proper Orthogonal Decomposition." In Mathematics in Industry, 95–109. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-78841-6_5.

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Alfonsi, Giancarlo, Leonardo Primavera, Giuseppe Passoni, and Carlo Restano. "Proper Orthogonal Decomposition of Turbulent Channel Flow." In Computational Fluid Dynamics 2000, 473–78. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56535-9_71.

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Keuzer, E., and O. Kust. "Controlling Torsional Vibrations Through Proper Orthogonal Decomposition." In Solid Mechanics and Its Applications, 207–14. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5778-0_26.

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Cueto, Elías, Francisco Chinesta, and Antonio Huerta. "Model Order Reduction based on Proper Orthogonal Decomposition." In Separated Representations and PGD-Based Model Reduction, 1–26. Vienna: Springer Vienna, 2014. http://dx.doi.org/10.1007/978-3-7091-1794-1_1.

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Awrejcewicz, Jan, Vadim A. Krys’ko, and Alexander F. Vakakis. "Order Reduction by Proper Orthogonal Decomposition (POD) Analysis." In Nonlinear Dynamics of Continuous Elastic Systems, 177–238. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-08992-7_3.

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Du, Qiang, and Max D. Gunzburger. "Centroidal Voronoi Tessellation Based Proper Orthogonal Decomposition Analysis." In Control and Estimation of Distributed Parameter Systems, 137–50. Basel: Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-8001-5_9.

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Pham, Toan, and Damien Tromeur-Dervout. "Proper Orthogonal Decomposition In Decoupling Large Dynamical Systems." In Lecture Notes in Computational Science and Engineering, 193–202. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14438-7_20.

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Conference papers on the topic "Spectral Proper Orthogonal Decomposition"

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He, Xiao, Fang Zhou, Georgios Rigas, and Mehdi Vahdati. "Spectral Proper Orthogonal Decomposition of Compressor Tip Leakage Flow." In European Conference on Turbomachinery Fluid Dynamics and Thermodynamics. European Turbomachinery Society, 2021. http://dx.doi.org/10.29008/etc2021-491.

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Sieber, Moritz, Alexander Kuhn, Hans-Christian Hege, C. Oliver Paschereit, and Kilian Oberleithner. "Poster: A graphical representation of the spectral proper orthogonal decomposition." In 68th Annual Meeting of the APS Division of Fluid Dynamics. American Physical Society, 2015. http://dx.doi.org/10.1103/aps.dfd.2015.gfm.p0007.

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Cottier, Stephanie, Christopher S. Combs, and Leon Vanstone. "Spectral Proper Orthogonal Decomposition Analysis of Shock-Wave/Boundary-Layer Interactions." In AIAA Aviation 2019 Forum. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2019. http://dx.doi.org/10.2514/6.2019-3331.

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Acharya, Adit, Todd Lowe, and Wing Ng. "Spectral Proper Orthogonal Decomposition Downstream of a Vortex Tube Separator Array." In AIAA SCITECH 2023 Forum. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2023. http://dx.doi.org/10.2514/6.2023-2354.

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Towne, Aaron. "Space-time Galerkin projection via spectral proper orthogonal decomposition and resolvent modes." In AIAA Scitech 2021 Forum. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2021. http://dx.doi.org/10.2514/6.2021-1676.

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Eppink, Jenna L. "Three-Dimensional Instantaneous Flow-field Reconstruction Using Planar Spectral Proper Orthogonal Decomposition." In AIAA SCITECH 2022 Forum. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2022. http://dx.doi.org/10.2514/6.2022-2430.

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Heidt, Liam, Tim Colonius, Akhil Nekkanti, Oliver Schmdit, Igor Maia, and Peter Jordan. "Analysis of forced subsonic jets using spectral proper orthogonal decomposition and resolvent analysis." In AIAA AVIATION 2021 FORUM. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2021. http://dx.doi.org/10.2514/6.2021-2108.

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Georgiou, Ioannis T., and Christos I. Papadopoulos. "A Novel Vibration Analysis of Stiff-Soft Structural Systems by the Method of Spectral Proper Orthogonal Decomposition." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85296.

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We have analyzed the computational dynamics of a complex one-dimensional structural system consisting of a number of alternating stiff and soft subsystems. In particular, the method of Proper Orthogonal Decomposition (POD) in the frequency domain has been applied to analyze the (single-frequency) steady state dynamics in terms of spectral amplitudes and spatial shapes of proper orthogonal modes. It is shown that the dominant POD modes of such a multi-body system are sensitive to imperfections. The processing of the computational dynamics by the spectral-POD method leads to a novel computation of the transfer function of the system.
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Witte, Matthias, Benjamin Torner, and Frank-Hendrik Wurm. "Analysis of Unsteady Flow Structures in a Radial Turbomachine by Using Proper Orthogonal Decomposition." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-76596.

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Tonalities in hydro and airborne noise emission are a known problem of turbomachines, wherein the tonalities in the noise spectrum are associated with the different orders of the blade passing frequency (BPF). The proper orthogonal decomposition (POD) method was utilized to find the relationship between the fluctuations in the pressure field at the BPF orders which are the origin of the noise emission and the correlated fluctuations in the turbulent velocity field in terms of coherent, periodic flow structures. In order the provide the input data for the POD analysis, a URANS k-ω-SST scale adaptive simulation (SAS) of the turbulent flow field in a single stage radial pump under part load conditions was performed. Compared to traditional two equation turbulence models this approach is less dissipative and allows the development of small scale turbulence structures and is therefore an appropriate method for this study. In order to compute the POD correlation matrix Sirovich’s “Methods of Snapshots” was applied to the unsteady pressure and velocity fields from the CFD simulation. The discrimination of coherent, periodic flow structures and the incoherent, chaotic turbulence was carried out by analyzing the POD eigenvalue distributions, the POD mode shapes and the spectral properties of the POD time coefficients. Five coupled POD mode pairs were identified in total, which were strictly correlated with the 1st, 2nd, 3rd, 4th and 5th order of the BPF and therefore responsible for the noise emission at these discrete frequencies. The coherent structures were explored on the basis of the spatial POD velocity und pressure mode shapes and in terms of vortical structures after an additional phase averaging. The scope of this study is to introduce an enhanced collection of post processing techniques which are capable of analyzing highly unsteady flow fields from numerical simulations in a better way than is possible by just using traditional techniques like the evaluation of integral or time averaged quantities. The identified coherent flow structures and their associated pressure fluctuations are key elements for a proper comprehension of the internal dynamics of the turbulent flow field in a turbomachine and therefore essential for the understanding of the noise generation processes and the optimization of such machines.
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Rosafio, Nicola, Giove De Cosmo, Simone Salvadori, Mauro Carnevale, and Daniela Anna Misul. "Identification of Fluctuation Modes for a Cylindrical Film Cooling Hole Using the Spectral Proper Orthogonal Decomposition Method." In ASME Turbo Expo 2022: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/gt2022-79528.

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Abstract Film cooling is the main technology adopted to guarantee safe working conditions of vanes and blades in high-pressure turbine stages. Recent experimental investigations highlighted that unsteady interaction between the coolant jet and the hot gas contributes to the lateral dispersion of cold flow over the cooled surface. Hence, considering the harsh working environment of these devices, a fair prediction of their thermal performance requires accurate modelling of the interaction between cold and hot gases. In this paper, an experimental setup originally studied at the University of Karlsruhe during the EU-funded TATEF project is numerically investigated to determine the influence of high-frequency unsteady fluctuations on the thermal performance of the cooling device. The case study consists of a film cooling hole positioned on a flat plate, working at engine-like conditions. Unsteady Reynolds-Averaged Navier-Stokes equations are solved for a compressible flow in transonic regime on a hybrid mesh. Turbulence is modelled using the Scale-Adaptive Simulation method to correctly predict the interaction between the coolant and the main flow. Three different sets of conditions are analyzed by varying the blowing ratio from 0.5 to 1.5, aiming at highlighting the unsteady mechanisms occurring for different penetrations of the coolant into the hot gas. Time-averaged unsteady results are compared with the available experimental data to determine to what extent hybrid modelling allows for correctly predicting film cooling performance at different blowing ratios. Instantaneous solutions are then analyzed to investigate the time-dependent flow field in the vicinity of the jet exit section and on the cooled surface. Spectral Proper Orthogonal Decomposition is enforced to identify the principal fluctuation modes associated with the time-dependent coolant penetration into the main flow.
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Reports on the topic "Spectral Proper Orthogonal Decomposition"

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Oxberry, Geoffrey M., Tanya Kostova-Vassilevska, Bill Arrighi, and Kyle Chand. Limited-memory adaptive snapshot selection for proper orthogonal decomposition. Office of Scientific and Technical Information (OSTI), April 2015. http://dx.doi.org/10.2172/1224940.

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Ly, Hung V., and Hien T. Tran. Modeling and Control of Physical Processes Using Proper Orthogonal Decomposition. Fort Belvoir, VA: Defense Technical Information Center, February 1999. http://dx.doi.org/10.21236/ada454477.

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Del Rosario, R. C., H. T. Tran, and H. T. Banks. Proper Orthogonal Decomposition Based Control of Transverse Beam Vibrations: Experimental Implementation. Fort Belvoir, VA: Defense Technical Information Center, January 1999. http://dx.doi.org/10.21236/ada454479.

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Narayanan, Vinod, and Benn Eilers. Identification of Coherent Structure Dynamics in Wall-Bounded Sprays using Proper Orthogonal Decomposition. Fort Belvoir, VA: Defense Technical Information Center, August 2010. http://dx.doi.org/10.21236/ada532067.

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Ly, Hung V., and Hien T. Tran. Proper Orthogonal Decomposition for Flow Calculations and Optimal Control in a Horizontal CVD Reactor. Fort Belvoir, VA: Defense Technical Information Center, March 1998. http://dx.doi.org/10.21236/ada451227.

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McDaniel, Dwayne, George Dulikravich, and Paul Cizmas. Development of a Reduced-Order Model for Reacting Gas-Solids Flow using Proper Orthogonal Decomposition. Office of Scientific and Technical Information (OSTI), November 2017. http://dx.doi.org/10.2172/1411716.

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Viggiano, Bianca. Reduced Order Description of Experimental Two-Phase Pipe Flows: Characterization of Flow Structures and Dynamics via Proper Orthogonal Decomposition. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.5723.

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