Modeling of transitional channel flow using balanced proper orthogonal decomposition

By Milovs Ilak, Clarence W. Rowley. 2007

196 citations recorded by the source corpus.

We study reduced-order models of three-dimensional perturbations in linearized channel flow using balanced proper orthogonal decomposition (BPOD). The models are obtained from three-dimensional simulations in physical space as opposed to the traditional single-wavenumber approach, and are therefore better able to capture the effects of localized disturbances or localized actuators. In order to assess the performance of the models, we consider the impulse response and frequency response, and variation of the Reynolds number as a model parameter. We show that the BPOD procedure yields models that capture the transient growth well at a low order, whereas standard POD does not capture the growth unless a considerably larger number of modes is included, and even then can be inaccurate. In the case of a localized actuator, we show that POD modes which are not energetically significant can be very important for capturing the energy growth. In addition, a comparison of the subspaces resulting from the two methods...

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/51bd2cca0bd991b8950b6fd5723ece646a55f33a

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In Computational Mechanics

In Statistical and Nonlinear Physics

Citations in the corpus

Feedback control of unstable steady states of flow past a flat plate using reduced-order estimators (2009, methodology): “Finally, we point out that while the balanced modelling procedure pursued in this paper works well, and often substantially outperforms simpler approaches using POD (e.g. as shown in Ilak & Rowley 2008), the overall procedure is admittedly complex.”
Closed-loop control of an open cavity flow using reduced-order models (2009, methodology): “Comparisons made in Rowley (2005), Ilak & Rowley (2008) and Bagheri et al. (2009b) suggest that the error committed by approximating the true Gramians by a series of discrete-time snapshots is very close to balanced truncation.”
Generalizing Koopman Theory to Allow for Inputs and Control (2016, methodology): “The method, however, requires a linear adjoint calculation [28, 49, 40, 20], which is not possible in typical data-driven experiments.”
Input–output analysis, model reduction and control of the flat-plate boundary layer (2009, methodology): “Therefore, the controllable modes can be regarded as POD modes (Ilak & Rowley 2008; Bagheri et al. 2008).”
Dynamic Mode Decomposition with Control (2014, methodology): “Generalizations of this scheme which combine balanced truncation with the SVD on empirical data, such as the balanced proper orthogonal decomposition, have already been shown to overcome some of the computational difficulties associated with the high-dimension of complex systems, but still requires ”
Dynamics and Control of Global Instabilities in Open-Flows: A Linearized Approach (2010, background): “[104] studied a channel flow; Bagheri et al.”
Model Reduction for Flow Analysis and Control (2017, unknown): “…nl y. Table 1 Examples of the use of balanced proper orthogonal decomposition (BPOD) for fluid systems Study Applications, findings, and variants Ilak & Rowley (2008) Three-dimensional channel flow; BPOD models outperform POD models due to dynamically important, low-energy POD modes, and…”
Optimal mode decomposition for unsteady flows (2013, background): “Such nonlinearities are commonly found in fluid systems, particularly those with high acoustic emissions or with transient growth (Ilak & Rowley 2008).”
Constrained sparse Galerkin regression (2016, methodology): “Control-theoretic extensions, such as balanced POD (BPOD) (Willcox & Peraire 2002; Rowley 2005), have also been widely applied for closed-loop flow control (Ilak & Rowley 2008; Bagheri, Brandt & Henningson 2009; Illingworth, Morgans & Rowley 2010).”
Machine Learning Control – Taming Nonlinear Dynamics and Turbulence (2016, background): “For example, in fluid dynamics there are numerous success stories of linear model-based flow control, including transition delay in a spatially developing boundary layer on a flat plate and in channel flow [29, 136, 135, 63, 142, 13, 11, 12, 244, 245, 101], reducing skinfriction drag in wall turbule”