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- Laurent Cordier, Bernd R. Noack, +5 authors Robert K. Niven
- 2013

A reduced-order modelling (ROM) strategy is crucial to achieve model-based control in a wide class of flow configurations. In turbulence, ROMs are mostly derived by Galerkin projection of first-principles equations onto the proper orthogonal decomposition (POD) modes. These POD ROMs are known to be relatively fragile when used for control design. To… (More)

The Finite-time Lyapunov Exponent (FTLE) is a measure for the rate of separation of particles in time-dependent flow fields. It provides a valuable tool for the analysis of unsteady flows. Commonly it is defined based on the flow map, analyzing the separation of trajectories of nearby particles over a finite-time span. This paper proposes a localized… (More)

This paper proposes a Galilean invariant generalization of critical points of vector field topology for 2D time-dependent flows. The approach is based upon a Lagrangian consideration of fluid particle motion. It extracts long-living features, like saddles and centers, and filters out short-living local structures. This is well suited for analysis of… (More)

We generalize the POD-based Galerkin method for post-transient flow data by incorporating Navier–Stokes equation constraints. In this method, the derived Galerkin expansion minimizes the residual like POD, but with the power balance equation for the resolved turbulent kinetic energy as an additional optimization constraint. Thus, the projection of the… (More)

— A representation of actuation effects is developed for low-order empirical Galerkin models of incompressible fluid flows. These actuation models fill a missing link and, indeed, provide a key enabler towards feedback design in flow control utilizing empirical Galerkin models. A flow control strategy is proposed based on the extended flow models and on the… (More)

- Bernd R. Noack, Robert K. Niven
- Computers & Mathematics with Applications
- 2013

- Gilead Tadmor, Daniel Bissex, Bernd R. Noack, Marek Morzyński, Tim Colonius, Kunihiko Taira
- 2007

While POD / PCA / KL approximations are statistically energetically optimal, statistical optimality is indeed the sole consideration these (equivalent) methods invoke. This type of approximation is neither geared for, nor is it optimized to extract modes based on their significance to an underlying system dynamics. Furthermore, as computational… (More)

- Gilead Tadmor, Oliver Lehmann, +4 authors Marek Morzyński
- Philosophical transactions. Series A…
- 2011

We review a strategy for low- and least-order Galerkin models suitable for the design of closed-loop stabilization of wakes. These low-order models are based on a fixed set of dominant coherent structures and tend to be incurably fragile owing to two challenges. Firstly, they miss the important stabilizing effects of interactions with the base flow and… (More)

- Michael Schlegel, Bernd R. Noack, +7 authors Gilead Tadmor
- 2012

We propose a generalization of proper orthogonal decomposition (POD) for optimal flow resolution of linearly related observables. This Galerkin expansion, termed 'observable inferred decomposition' (OID), addresses a need in aerodynamic and aeroacoustic applications by identifying the modes contributing most to these observables. Thus, OID constitutes a… (More)

- Markus Quade, Markus Abel, Kamran Shafi, Robert K Niven, Bernd R Noack
- Physical review. E
- 2016

We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or simplified models need to be found. We focus on symbolic regression methods as a part of machine learning. These… (More)