A reduced‐order extrapolated Crank–Nicolson collocation spectral method based on proper orthogonal decomposition for the two‐dimensional viscoelastic wave equations

2019 ◽  
Vol 36 (1) ◽  
pp. 49-65 ◽  
Author(s):  
Zhendong Luo ◽  
Shiju Jin
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Spectral Method ◽  
Wave Equations ◽  
Orthogonal Decomposition ◽  
Two Dimensional ◽  
Reduced Order ◽  
Viscoelastic Wave ◽  
Collocation Spectral Method ◽  
Proper Orthogonal ◽  
Crank Nicolson

Developing a Reduced-Order Model of Nonsynchronous Vibration in Turbomachinery Using Proper-Orthogonal Decomposition Methods

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Stephen T. Clark ◽  
Fanny M. Besem ◽  
Robert E. Kielb ◽  
Jeffrey P. Thomas
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Cross Flow ◽  
Decomposition Methods ◽  
Initial Study ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Two Dimensional ◽  
Order Model ◽  
Reduced Order ◽  
Proper Orthogonal

The paper develops a reduced-order model of nonsynchronous vibration (NSV) using proper orthogonal decomposition (POD) methods. The approach was successfully developed and implemented, requiring between two and six POD modes to accurately predict computational fluid dynamics (CFD) solutions that are experiencing NSV. This POD method was first developed and demonstrated for a transversely moving, two-dimensional cylinder in cross-flow. Later, the method was used for the prediction of CFD solutions for a two-dimensional compressor blade. This research is the first to offer a POD approach to the reduced-order modeling of NSV in turbomachinery. Modeling NSV is especially challenging because NSV is caused by complicated, unsteady flow dynamics; this initial study helps researchers understand the causes of NSV, and aids in the future development of predictive tools for aeromechanical design engineers.

Developing a Reduced-Order Model of Non-Synchronous Vibration in Turbomachinery Using Proper Orthogonal Decomposition Methods

2014 ◽  
Author(s):  
Stephen T. Clark ◽  
Fanny M. Besem ◽  
Robert E. Kielb ◽  
Jeffrey P. Thomas
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Cross Flow ◽  
Initial Study ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Two Dimensional ◽  
Order Model ◽  
Decomposition Approach ◽  
Reduced Order ◽  
Proper Orthogonal

The paper develops a reduced-order model of non-synchronous vibration (NSV) using proper orthogonal decomposition (POD) methods. The approach was successfully developed and implemented, requiring between two and six POD modes to accurately predict CFD solutions that are experiencing non-synchronous vibration. This POD method was first developed and demonstrated for a transversely-moving, two-dimensional cylinder in cross-flow. Later, the method was used for the prediction of CFD solutions for a two-dimensional compressor blade. This research is the first to offer a proper orthogonal decomposition approach to the reduced-order modeling of non-synchronous vibration in turbomachinery. Modeling non-synchronous vibration is especially challenging because NSV is caused by complicated, unsteady flow dynamics; this initial study helps researchers understand the causes of NSV, and aids in the future development of predictive tools for aeromechanical design engineers.

Modeling the Turbulent Wake Behind a Wall-Mounted Square Cylinder

2020 ◽  
Author(s):  
Christian Amor ◽  
José M Pérez ◽  
Philipp Schlatter ◽  
Ricardo Vinuesa ◽  
Soledad Le Clainche
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Turbulent Wake ◽  
Orthogonal Decomposition ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Square Cylinder ◽  
Complex Flow ◽  
Reduced Order ◽  
Mode Decomposition ◽  
Proper Orthogonal

Abstract This article introduces some soft computing methods generally used for data analysis and flow pattern detection in fluid dynamics. These techniques decompose the original flow field as an expansion of modes, which can be either orthogonal in time (variants of dynamic mode decomposition), or in space (variants of proper orthogonal decomposition) or in time and space (spectral proper orthogonal decomposition), or they can simply be selected using some sophisticated statistical techniques (empirical mode decomposition). The performance of these methods is tested in the turbulent wake of a wall-mounted square cylinder. This highly complex flow is suitable to show the ability of the aforementioned methods to reduce the degrees of freedom of the original data by only retaining the large scales in the flow. The main result is a reduced-order model of the original flow case, based on a low number of modes. A deep discussion is carried out about how to choose the most computationally efficient method to obtain suitable reduced-order models of the flow. The techniques introduced in this article are data-driven methods that could be applied to model any type of non-linear dynamical system, including numerical and experimental databases.

Reduced-Order Model of a Bladed Rotor With Geometric Mistuning

2007 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Coordinate Measurement ◽  
Coordinate Measurement Machine ◽  
Bladed Disk ◽  
Bladed Rotor ◽  
Proper Orthogonal

This paper deals with the development of an accurate reduced-order model of a bladed disk with geometric mistuning. The method is based on vibratory modes of various tuned systems and proper orthogonal decomposition of coordinate measurement machine (CMM) data on blade geometries. Results for an academic rotor are presented to establish the validity of the technique.

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.

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