Modal decomposition‐based global stability analysis for reduced order modeling of 2D and 3D wake flows

Stankiewicz, Witold; Morzyński, Marek; Kotecki, Krzysztof; Roszak, Robert; Nowak, Michał

doi:10.1002/fld.4181

Cited by 9 publications

(5 citation statements)

References 39 publications

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“…A more recent alternative is the dynamic mode decomposition (DMD) [39,42] and its variants like oscillation pattern decomposition (OPD) [56], multi-resolution DMD [23] and recursive DMD [33]. DMD can approximate stability eigenmodes from transient data [45] and Fourier modes from post-transient data. In this method, the unsteady data are represented by a time-resolved sequence of n snapshots V 0...n = {q 0 , q 1 , q 2 , .…”

Section: Model Order Reduction Based On Dynamic Mode Decomposition (Dmd)mentioning

confidence: 99%

“…While DMD modes yield the same subspace as POD modes, they point in different directions-what is observed as the rotation of the modes around x-axis. More details on the relationship between POD and DMD might be found in a paper by Tu et al [55], and the comparison of Galerkin models of 2D cylinder wake, based on POD and DMD modes, might be found in [45].…”

Section: Reduced-order Model For the Periodic Flowmentioning

confidence: 99%

See 1 more Smart Citation

On the need of mode interpolation for data-driven Galerkin models of a transient flow around a sphere

Stankiewicz

Morzyński

Kotecki

et al. 2016

Theor. Comput. Fluid Dyn.

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We present a low-dimensional Galerkin model with state-dependent modes capturing linear and nonlinear dynamics. Departure point is a direct numerical simulation of the three-dimensional incompressible flow around a sphere at Reynolds numbers 400. This solution starts near the unstable steady Navier-Stokes solution and converges to a periodic limit cycle. The investigated Galerkin models are based on the dynamic mode decomposition (DMD) and derive the dynamical system from first principles, the Navier-Stokes equations. A DMD model with training data from the initial linear transient fails to predict the limit cycle. Conversely, a model from limit-cycle data underpredicts the initial growth rate roughly by a factor 5. Key enablers for uniform accuracy throughout the transient are a continuous mode interpolation between both oscillatory fluctuations and the addition of a shift mode. This interpolated model is shown to capture both the transient growth of the oscillation and the limit cycle.

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Section: Model Order Reduction Based On Dynamic Mode Decomposition (Dmd)mentioning

confidence: 99%

Section: Reduced-order Model For the Periodic Flowmentioning

confidence: 99%

On the need of mode interpolation for data-driven Galerkin models of a transient flow around a sphere

Stankiewicz

Morzyński

Kotecki

et al. 2016

Theor. Comput. Fluid Dyn.

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“…The dynamic mode decomposition (DMD) method proposed by Schmid (2010) provides a means to decompose the original flow into a series of modes, with each mode containing a single characteristic frequency and growth rate. Thus, it is suitable for the identification of the spatiotemporal coherent structures in periodic flows and has been used in the analyses of cavity flows (Seena & Sung 2011;Guéniat, Pastur & Lusseyran 2014), backward-facing step flows (Sampath & Chakravarthy 2014) and flows around cylinders (Thompson et al 2014;Zhang, Liu & Wang 2014;Stankiewicz et al 2016;Li et al 2019) and cantilever beams (Cesur et al 2014). More recently, the dynamic pressure field over a finite-height prism immersed in a boundary layer flow has been examined using DMD (Luo & Kareem 2021).…”

Section: Introductionmentioning

confidence: 99%

“…2014; Zhang, Liu & Wang 2014; Stankiewicz et al. 2016; Li et al. 2019) and cantilever beams (Cesur et al.…”

Section: Introductionmentioning

confidence: 99%

Global instability and mode selection in flow fields around rectangular prisms

et al. 2023

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Large-eddy simulations of the unsteady flows around rectangular prisms with chord-to-depth ratios (B/D) ranging from 3 to 12 are carried out at a Reynolds number of 1000. A particular focus of the study is the physical mechanisms governing the global instability of the flow. The coherent structures and velocity spectra reveal that large-scale leading-edge vortices (L vortices) are formed by the coalescence of Kelvin–Helmholtz rollers. Based on dynamic mode decomposition, the interactions between the L vortex and the trailing-edge vortex (T vortex) at different B/D values are revealed. It is found that the phase difference between the L and T vortices is the critical factor promoting a stepwise increase in the Strouhal number with increasing B/D. According to the phase analysis, there are two types of pressure feedback-loop mechanisms maintaining the self-sustained oscillations. When B/D = 4–5, the feedback loop covers the separation region, and the global instability is controlled by the impinging shear-layer instability. When B/D = 3 and 6–12, the feedback loop covers the entire chord, and the global instability is controlled by the impinging leading-edge vortex shedding instability. Self-sustained oscillations of the shear layer still exist after a splitter plate is placed in the near wake, indicating that the T vortex shedding is not essential in triggering the global instability. Nevertheless, with the participation of the T vortex, the primary instability mode may be reselected due to the upper and lower limits of the shedding frequency imposed by the T vortex.

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“…It means that they are difficult to reduce to a low-dimensional subspace without losing at least some of these scales. During the last three decades, several efforts in theoretical foundations, numerical investigations, and methodological improvements have made it possible to develop general ideas in reduced order modeling and to tackle several problems arising in fluid dynamics [2][3][4]. Proper orthogonal decomposition (POD) [5,6], dynamic mode decomposition (DMD) [7], and Koopman analysis [8] are some of the well-known reduced order methods (ROMs) in the field of fluid dynamics.…”

Section: Introductionmentioning

confidence: 99%

Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flows

Eivazi,

Veisi,

Naderi

et al. 2020

Preprint

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Unsteady fluid systems are nonlinear high-dimensional dynamical systems that may exhibit multiple complex phenomena both in time and space. Reduced order modeling (ROM) of fluid flows has been an active research topic in the recent decade with the primary goal to decompose complex flows to a set of features most important for future state prediction and control, typically using a dimensionality reduction technique. In this work, a novel data-driven technique based on the power of deep neural networks for reduced order modeling of the unsteady fluid flows is introduced. An autoencoder network is used for nonlinear dimension reduction and feature extraction as an alternative for singular value decomposition (SVD). Then, the extracted features are used as an input for long short-term memory network (LSTM) to predict the velocity field at future time instances. The proposed autoencoder-LSTM method is compared with dynamic mode decomposition (DMD) as the data-driven base method. Moreover, an autoencoder-DMD algorithm is introduced for reduced order modeling, which uses the autoencoder network for dimensionality reduction rather than SVD rank truncation. Results show that the autoencoder-LSTM method is considerably capable of predicting the fluid flow evolution, where higher values for coefficient of determination R 2 are obtained using autoencoder-LSTM comparing to DMD.

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Modal decomposition‐based global stability analysis for reduced order modeling of 2D and 3D wake flows

Cited by 9 publications

References 39 publications

On the need of mode interpolation for data-driven Galerkin models of a transient flow around a sphere

On the need of mode interpolation for data-driven Galerkin models of a transient flow around a sphere

Global instability and mode selection in flow fields around rectangular prisms

Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flows

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