A Proper-Orthogonal Decomposition Variational Multiscale Approximation Method for a Generalized Oseen Problem

We introduce the variational multiscale (VMS) stabilization for the reduced-order modeling of incompressible flows. It is well known that the proper orthogonal decomposition (POD) technique in reduced-order modeling experiences numerical instability when applied to complex flow problems. In this case a POD discretization naturally separates out structures which corresponding to the energy cascade on large and small scales, in order, a VMS approach is natural. In this paper, we provide the mathematical background necessary for implementing VMS to a POD-Galerkin model of a generalized Oseen problem. We provide theoretical evidence which indicates the consistency of utilizing a VMS approach in the stabilization of reduced order flows. In addition we provide numerical experiments indicating that VMS improves fidelity in reproducing the qualitative properties of the flow.

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Reduced-Order Modeling for Complex Flow Emulation by Common Kernel-Smoothed Proper Orthogonal Decomposition

AIAA Journal ◽

10.2514/1.j060574 ◽

2021 ◽

pp. 1-13

Author(s):

Yu-Hung Chang ◽

Xingjian Wang ◽

Liwei Zhang ◽

Yixing Li ◽

Simon Mak ◽

...

Keyword(s):

Proper Orthogonal Decomposition ◽

Reduced Order Modeling ◽

Orthogonal Decomposition ◽

Complex Flow ◽

Reduced Order ◽

Proper Orthogonal

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Modeling the Turbulent Wake Behind a Wall-Mounted Square Cylinder

Logic Journal of IGPL ◽

10.1093/jigpal/jzaa060 ◽

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.

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Nonlinear Dynamic Analysis of a Simply Supported Beam with Breathing Crack Using Proper Orthogonal Decomposition Based Reduced-Order Modeling

Lecture Notes in Mechanical Engineering - Advances in Rotor Dynamics, Control, and Structural Health Monitoring ◽

10.1007/978-981-15-5693-7_22 ◽

2020 ◽

pp. 315-325

Author(s):

Vigneshwaran Krishnaswamy ◽

Manoj Pandey

Keyword(s):

Dynamic Analysis ◽

Proper Orthogonal Decomposition ◽

Nonlinear Dynamic ◽

Nonlinear Dynamic Analysis ◽

Reduced Order Modeling ◽

Orthogonal Decomposition ◽

Breathing Crack ◽

Reduced Order ◽

Simply Supported ◽

Proper Orthogonal

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Reduced-Order Modeling of the Upper Tropical Pacific Ocean Model using Proper Orthogonal Decomposition

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2006.11.012 ◽

2006 ◽

Vol 52 (8-9) ◽

pp. 1373-1386 ◽

Cited By ~ 78

Author(s):

Yanhua Cao ◽

Jiang Zhu ◽

Zhendong Luo ◽

I.M. Navon

Keyword(s):

Pacific Ocean ◽

Proper Orthogonal Decomposition ◽

Ocean Model ◽

Reduced Order Modeling ◽

Tropical Pacific ◽

Orthogonal Decomposition ◽

Tropical Pacific Ocean ◽

Reduced Order ◽

Proper Orthogonal

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Investigation of the Effects of Length to Depth Ratio on Open Supersonic Cavities Using CFD and Proper Orthogonal Decomposition

The Scientific World JOURNAL ◽

10.1155/2013/810175 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12 ◽

Cited By ~ 5

Author(s):

Ibrahim Yilmaz ◽

Ece Ayli ◽

Selin Aradag

Keyword(s):

Proper Orthogonal Decomposition ◽

Stokes Equations ◽

Reduced Order Modeling ◽

Orthogonal Decomposition ◽

Navier Stokes ◽

Reduced Order ◽

Modeling Approach ◽

Depth Ratio ◽

Minimum Number ◽

Proper Orthogonal

Simulations of supersonic turbulent flow over an open rectangular cavity are performed to observe the effects of length to depth ratio (L/D) of the cavity on the flow structure. Two-dimensional compressible time-dependent Reynolds-averaged Navier-Stokes equations with k-ωturbulence model are solved. A reduced order modeling approach, Proper Orthogonal Decomposition (POD) method, is used to further analyze the flow. Results are obtained for cavities with severalL/Dratios at a Mach number of 1.5. Mostly, sound pressure levels (SPL) are used for comparison. After a reduced order modeling approach, the number of modes necessary to represent the systems is observed for each case. The necessary minimum number of modes to define the system increases as the flow becomes more complex with the increase in theL/Dratio. This study provides a basis for the control of flow over supersonic open cavities by providing a reduced order model for flow control, and it also gives an insight to cavity flow physics by comparing several simulation results with different length to depth ratios.

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