On Low-Dimensional Galerkin Models for Fluid Flow

By D. Rempfer. 2000

210 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5b713d785a7b891bb8d880be4ae110e159ded731

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Clarence W. Rowley
2. Steven L. Brunton
3. Bernd R. Noack
4. J. Nathan Kutz
5. Tim Colonius
6. Richard M. Murray
7. Scott T. M. Dawson
8. Marek Morzynski

In Statistical and Nonlinear Physics

1. Steven L. Brunton
2. Clarence W. Rowley
3. Bernd R. Noack
4. Tim Colonius
5. J. Nathan Kutz
6. Marek Morzynski
7. Laurent Cordier
8. Richard M. Murray

Citations in the corpus

• Enablers for robust POD models (2009, unknown): “method can first present a lack of inherent numerical stability even for very simple problems [10].”
• A hierarchy of low-dimensional models for the transient and post-transient cylinder wake (2003, result): “A similar result has been obtained by Rempfer (2000) in another dynamical system.”
• Calibration of POD reduced‐order models using Tikhonov regularization (2009, background): “i) the structural instability of the Galerkin projection [20, 21, 14], ii) the truncation of the POD basis (dissipative scales associated to higher POD modes are not sufficiently present in the model), iii) the fact that the set of data does not perfectly respect the weak formulation (5): inaccurate”
• Model reduction for compressible flows using POD and Galerkin projection (2004, background): “Possible reasons for this are illustrated with an elegant example in [5].”