scholarly journals Proper orthogonal decomposition and low-dimensional models for driven cavity flows

1998 ◽  
Vol 10 (7) ◽  
pp. 1685-1699 ◽  
Author(s):  
W. Cazemier ◽  
R. W. C. P. Verstappen ◽  
A. E. P. Veldman
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Cavity Flows ◽  
Driven Cavity ◽  
Dimensional Models ◽  
Low Dimensional ◽  
Proper Orthogonal

Proper Orthogonal Decomposition for Time-Dependent Lid-Driven Cavity Flows

2002 ◽  
Vol 42 (4) ◽  
pp. 285-306 ◽  
Author(s):  
Daniel Ahlman ◽  
Fredrik Söderlund ◽  
Jelliffe Jackson ◽  
Andrew Kurdila ◽  
Wei Shyy
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Time Dependent ◽  
Cavity Flows ◽  
Driven Cavity ◽  
Proper Orthogonal

scholarly journals Local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition

2009 ◽  
Vol 629 ◽  
pp. 41-72 ◽  
Author(s):  
ALEXANDER HAY ◽  
JEFFREY T. BORGGAARD ◽  
DOMINIQUE PELLETIER
Keyword(s):  
Sensitivity Analysis ◽  
Proper Orthogonal Decomposition ◽  
Stokes Equations ◽  
Orthogonal Decomposition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Reduced Order ◽  
Selection Step ◽  
Low Dimensional ◽  
Proper Orthogonal

The proper orthogonal decomposition (POD) is the prevailing method for basis generation in the model reduction of fluids. A serious limitation of this method, however, is that it is empirical. In other words, this basis accurately represents the flow data used to generate it, but may not be accurate when applied ‘off-design’. Thus, the reduced-order model may lose accuracy for flow parameters (e.g. Reynolds number, initial or boundary conditions and forcing parameters) different from those used to generate the POD basis and generally does. This paper investigates the use of sensitivity analysis in the basis selection step to partially address this limitation. We examine two strategies that use the sensitivity of the POD modes with respect to the problem parameters. Numerical experiments performed on the flow past a square cylinder over a range of Reynolds numbers demonstrate the effectiveness of these strategies. The newly derived bases allow for a more accurate representation of the flows when exploring the parameter space. Expanding the POD basis built at one state with its sensitivity leads to low-dimensional dynamical systems having attractors that approximate fairly well the attractor of the full-order Navier–Stokes equations for large parameter changes.

Analysis of Particle Image Velocimetry Measurements of Natural Convection in an Enclosure Using Proper Orthogonal Decomposition

2015 ◽  
Vol 137 (12) ◽  
Author(s):  
Nirmalendu Biswas ◽  
Souvick Chatterjee ◽  
Mithun Das ◽  
Amlan Garai ◽  
Prokash C. Roy ◽  
...  
Keyword(s):  
Particle Image Velocimetry ◽  
Natural Convection ◽  
Velocity Field ◽  
Proper Orthogonal Decomposition ◽  
Particle Image ◽  
Field Measurements ◽  
Orthogonal Decomposition ◽  
Image Velocimetry ◽  
Low Dimensional ◽  
Proper Orthogonal

This work investigates natural convection in an enclosure with localized heating on the bottom wall with a flushed or protruded heat source and cooled on the top and the side walls. Velocity field measurements are done by using 2D particle image velocimetry (PIV) technique. Proper orthogonal decomposition (POD) has been used to create low dimensional approximations of the system for predicting the flow structures. The POD-based analysis reveals the modal structure of the flow field and also allows reconstruction of velocity field at conditions other than those used in PIV study.

Low-Dimensional Representations of Inflow Turbulence and Wind Turbine Response Using Proper Orthogonal Decomposition

2005 ◽  
Vol 127 (4) ◽  
pp. 553-562 ◽  
Author(s):  
Korn Saranyasoontorn ◽  
Lance Manuel
Keyword(s):  
Wind Turbine ◽  
Proper Orthogonal Decomposition ◽  
Low Frequency ◽  
Orthogonal Decomposition ◽  
Response Variance ◽  
Spectral Models ◽  
Inflow Turbulence ◽  
Using Data ◽  
Low Dimensional ◽  
Proper Orthogonal

A demonstration of the use of Proper Orthogonal Decomposition (POD) is presented for the identification of energetic modes that characterize the spatial random field describing the inflow turbulence experienced by a wind turbine. POD techniques are efficient because a limited number of such modes can often describe the preferred turbulence spatial patterns and they can be empirically developed using data from spatial arrays of sensed input/excitation. In this study, for demonstration purposes, rather than use field data, POD modes are derived by employing the covariance matrix estimated from simulations of the spatial inflow turbulence field based on standard spectral models. The efficiency of the method in deriving reduced-order representations of the along-wind turbulence field is investigated by studying the rate of convergence (to total energy in the turbulence field) that results from the use of different numbers of POD modes, and by comparing the frequency content of reconstructed fields derived from the modes. The National Wind Technology Center’s Advanced Research Turbine (ART) is employed in the examples presented, where both inflow turbulence and turbine response are studied with low-order representations based on a limited number of inflow POD modes. Results suggest that a small number of energetic modes can recover the low-frequency energy in the inflow turbulence field as well as in the turbine response measures studied. At higher frequencies, a larger number of modes are required to accurately describe the inflow turbulence. Blade turbine response variance and extremes, however, can be approximated by a comparably smaller number of modes due to diminished influence of higher frequencies.

scholarly journals The Proper Orthogonal Decomposition for Dimensionality Reduction in Mode-Locked Lasers and Optical Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Eli Shlizerman ◽  
Edwin Ding ◽  
Matthew O. Williams ◽  
J. Nathan Kutz
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Dimensional Space ◽  
Mode Locking ◽  
Maximum Energy ◽  
Orthogonal Decomposition ◽  
Optical Systems ◽  
Energy Output ◽  
Low Dimensional ◽  
Proper Orthogonal ◽  
Mode Locked Lasers

The onset of multipulsing, a ubiquitous phenomenon in laser cavities, imposes a fundamental limit on the maximum energy delivered per pulse. Managing the nonlinear penalties in the cavity becomes crucial for increasing the energy and suppressing the multipulsing instability. A proper orthogonal decomposition (POD) allows for the reduction of governing equations of a mode-locked laser onto a low-dimensional space. The resulting reduced system is able to capture correctly the experimentally observed pulse transitions. Analysis of these models is used to explain the sequence of bifurcations that are responsible for the multipulsing instability in the master mode-locking and the waveguide array mode-locking models. As a result, the POD reduction allows for a simple and efficient way to characterize and optimize the cavity parameters for achieving maximal energy output.

Model order reduction using sparse coding exemplified for the lid-driven cavity

2016 ◽  
Vol 808 ◽  
pp. 189-223 ◽  
Author(s):  
Rohit Deshmukh ◽  
Jack J. McNamara ◽  
Zongxian Liang ◽  
J. Zico Kolter ◽  
Abhijit Gogulapati
Keyword(s):  
Unsteady Flow ◽  
Proper Orthogonal Decomposition ◽  
Sparse Coding ◽  
Flow Fields ◽  
Orthogonal Decomposition ◽  
Driven Cavity ◽  
Reduced Order ◽  
Multi Scale ◽  
Small Set ◽  
Proper Orthogonal

Basis identification is a critical step in the construction of accurate reduced-order models using Galerkin projection. This is particularly challenging in unsteady flow fields due to the presence of multi-scale phenomena that cannot be ignored and may not be captured using a small set of modes extracted using the ubiquitous proper orthogonal decomposition. This study focuses on this issue by exploring an approach known as sparse coding for the basis identification problem. Compared with proper orthogonal decomposition, which seeks to truncate the basis spanning an observed data set into a small set of dominant modes, sparse coding is used to identify a compact representation that spans all scales of the observed data. As such, the inherently multi-scale bases may improve reduced-order modelling of unsteady flow fields. The approach is examined for a canonical problem of an incompressible flow inside a two-dimensional lid-driven cavity. The results demonstrate that Galerkin reduction of the governing equations using sparse modes yields a significantly improved predictive model of the fluid dynamics.

Low-dimensional characteristics of a transonic jet. Part 1. Proper orthogonal decomposition

2008 ◽  
Vol 612 ◽  
pp. 107-141 ◽  
Author(s):  
C. E. TINNEY ◽  
M. N. GLAUSER ◽  
L. S. UKEILEY
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Optical Measurement ◽  
Measurement Techniques ◽  
Sensitivity Study ◽  
Orthogonal Decomposition ◽  
Azimuthal Mode ◽  
Layer Width ◽  
Mode 2 ◽  
Low Dimensional ◽  
Proper Orthogonal

An experimental investigation concerning the most energetic turbulent features of the flow exiting from an axisymmetric converging nozzle at Mach 0.85 and ambient temperature is discussed using planar optical measurement techniques. The arrangement of the particle image velocimetry (PIV) system allows for all three components of the velocity field to be captured along the (r, θ)-plane of the jet at discrete streamwise locations between x/D=3.0 and 8.0 in 0.25 diameter increments. The ensemble-averaged (time-suppressed) two-point full Reynolds stress matrix is constructed from which the integral eigenvalue problem of the proper orthogonal decomposition (POD) is applied using both scalar and vector forms of the technique. A grid sensitivity study indicates that the POD eigenvalues converge safely to within 1% of their expected value when the discretization of the spatial grid is less than 30% of the integral length scale or 10% of the shear-layer width. The first POD eigenvalue from the scalar decomposition of the streamwise component is shown to agree with previous investigations for a range of Reynolds numbers and Mach numbers with a peak in azimuthal mode 5 at x/D=3.0, and a gradual shift to azimuthal mode 2 by x/D=8.0. The eigenvalues from the scalar POD of the radial and azimuthal components are shown to be much lower-dimensional with most of their energy residing in the first few azimuthal modes, that is modes 0, 1 and 2, with little change in the relative energies along the streamwise direction. From the vector decomposition, the azimuthal eigenspectra of the first two POD modes shift from a peak in azimuthal mode 5 at x/D=3.0, followed by a gradual decay to azimuthal mode 2 at x/D=8.0, the differences in the peak energies being very subtle. The conclusion from these findings is that when the Mach number is subsonic and the Reynolds number sufficiently large, the structure of the turbulent jet behaves independently of these factors.

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