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- Laurent Cordier, Bernd R. Noack, Gilles Tissot, Guillaume Lehnasch, Joël Delville, Maciej Balajewicz +2 others
- 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)

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)

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)

— 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)

- Michael Schlegel, Bernd R. Noack, Peter Jordan, Andreas Dillmann, Elmar Gröschel, Wolfgang Schröder +4 others
- 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)

A novel data-driven modal decomposition of fluid flow is proposed comprising key features of POD and DMD. The first mode is the normalized real or imaginary part of the DMD mode which minimizes the time-averaged residual. The N-th mode is defined recursively in an analogous manner based on the residual of an expansion using the first N −1 modes. The… (More)

A new approach to model order reduction of the Navier-Stokes equations at high Reynolds number is proposed. Unlike traditional approaches, this method does not rely on empirical turbulence modeling or modification of the Navier-Stokes equations. It provides spatial basis functions different from the usual proper orthogonal decomposition basis function in… (More)

— Reduced Galerkin models of fluid flows are traditionally obtained by the Galerkin projection of a low-dimensional flow expansion onto the the Navier-Stokes equation. A new approach in this application domain is the a posteriori model parameter estimation to correct for distortions due to the low dimensional compression. Preserving model structure, this… (More)