Modal Analysis of Fluid Flows: An Overview

Taira, Kunihiko; Brunton, Steven L.; Dawson, Scott T. M.; Rowley, Clarence W.; Colonius, Tim; McKeon, Beverley; Schmidt, Oliver T.; Gordeyev, Stanislav; Theofilis, Vassilios; Ukeiley, Lawrence

doi:10.2514/1.j056060

Cited by 1,226 publications

(651 citation statements)

References 198 publications

Supporting

Mentioning

649

Contrasting

Order By: Relevance

“…As an alternative to the existing techniques, the reduced order modeling (ROM) approach has quickly become a promising approach to reduce the computational burden of high-fidelity simulations. In general, ROM works in such a way that the high-dimensional complex dynamical systems will be represented with much lower-dimensional (but dense) systems while keeping the solution quality within the acceptable range [8,9]. An introduction to ROM methodologies can be found in recent review articles [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

et al. 2019

View full text Add to dashboard Cite

In this study, we present a non-intrusive reduced order modeling (ROM) framework for largescale quasi-stationary systems. The framework proposed herein exploits the time series prediction capability of long short-term memory (LSTM) recurrent neural network architecture such that: (i) in the training phase, the LSTM model is trained on the modal coefficients extracted from the highresolution data snapshots using proper orthogonal decomposition (POD) transform, and (ii) in the testing phase, the trained model predicts the modal coefficients for the total time recursively based on the initial time history. Hence, no prior information about the underlying governing equations is required to generate the ROM. To illustrate the predictive performance of the proposed framework, the mean flow fields and time series response of the field values are reconstructed from the predicted modal coefficients by using an inverse POD transform. As a representative benchmark test case, we consider a two-dimensional quasi-geostrophic (QG) ocean circulation model which, in general, displays an enormous range of fluctuating spatial and temporal scales. We first illustrate that the conventional Galerkin projection based reduced order modeling of such systems requires a high number of POD modes to obtain a stable flow physics. In addition, ROM-GP does not seem to capture the intermittent bursts appearing in the dynamics of the first few most energetic modes. However, the proposed non-intrusive ROM framework based on LSTM (ROM-LSTM) yields a stable solution even for a small number of POD modes. We also observe that the ROM-LSTM model is able to capture quasi-periodic intermittent bursts accurately, and yields a stable and accurate mean flow dynamics using the time history of a few previous time states, denoted as the lookback time-window in this paper. Throughout the paper, we demonstrate our findings in terms of time series evolution of the field values and mean flow patterns, which suggest that the proposed fully non-intrusive ROM framework is robust and capable of predicting noisy nonlinear fluid flows in an extremely efficient way compared to the conventional projection based ROM framework.

show abstract

Section: Introductionmentioning

confidence: 99%

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

et al. 2019

View full text Add to dashboard Cite

show abstract

“…To further examine the base flow, we perform dynamic mode decomposition (DMD) (Schmid 2010;Rowley et al 2009;Kutz 2013;Taira et al 2017) to identify the coherent structures associated with the detected frequencies. To conduct DMD of the threedimensional flow field, we collect 250 snapshots over eight periods for the frequency of f 1 = 0.27.…”

Section: Uncontrolled Flowmentioning

confidence: 99%

Active Flow Control of a Pump-Induced Wall-Normal Vortex With Steady Blowing

Liu

Nohmi

et al. 2020

Journal of Fluids Engineering

Self Cite

View full text Add to dashboard Cite

The emergence of a submerged vortex upstream of a pump can reduce pump intake efficiency and cause structural damage. In this study, we consider the use of active flow control with steady blowing to increase the pressure distribution within a single-phase pump-induced wall-normal vortex model, which is based on the Burgers vortex with a no-slip boundary condition prescribed along its symmetry plane. The goal of our control is to modify the vortex core velocity profile. These changes are sought to increase the core pressure such that detrimental effects on the pump are alleviated. Three-dimensional direct numerical simulations (DNS) are performed to examine the dynamics of the vortex with the application of axial momentum injection at and around the root of the vortex. We find that the active flow control approach can effectively modify the wall-normal vortical structure and significantly increase the low-core pressure by up to 81% compared to that of the uncontrolled case. The result shows that the control setup is also effective when it is introduced in an off-centered manner. Compared to the unsteady blowing and suction based actuation from our previous work , the current steady control technique offers an effective and simple flow control setup that can support robust operations of pumps.

show abstract

“…Benner et al [83], Taira et al [85], Surveys on reduced order modeling of dynamical systems Peherstorfer et al [84] Algorithms using meta models for the objective function Ong et al [112], Ray et al [113] Combination of RBF and MOEA Beermann et al [110,111] Combination of POD and set-oriented method…”

Section: Surveysmentioning

confidence: 99%

A Survey of Recent Trends in Multiobjective Optimal Control -- Surrogate Models, Feedback Control and Objective Reduction

Peitz¹,

Dellnitz²

2018

Preprint

View full text Add to dashboard Cite

Abstract:Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto optimal solutions have led to a wide range of new applications related to optimal and feedback control which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview over recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort.

show abstract

Modal Analysis of Fluid Flows: An Overview

Abstract: If the square matrix A is real, its eigenvalues are either real or come in complex conjugate pairs. c In such case, A is called diagonalizable or non-defective. If A is defective, we have A = V JV −1 with J being the canonical Jordan form [31,33].

Cited by 1,226 publications

References 198 publications

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

Active Flow Control of a Pump-Induced Wall-Normal Vortex With Steady Blowing

A Survey of Recent Trends in Multiobjective Optimal Control -- Surrogate Models, Feedback Control and Objective Reduction

Contact Info

Product

Resources

About