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Fourier Model Reduction for Large-Scale Applications in Computational Fluid Dynamics

By K. Willcox and A. Megretski


A new method, Fourier model reduction (FMR), for obtaining stable, accurate, low-order models of very large linear systems is presented. The technique draws on traditional control and dynamical system concepts and utilizes them in a way which is computationally very efficient. Discrete-time Fourier coefficients of the large system are calculated and used to construct a reduced-order model that preserves stability properties of the original system. Many coefficients can be calculated, which results in a very accurate representation of the system dynamics, but only a single inversion of the large system is required. The resulting system can be further reduced using explicit formulae for balanced truncation. The method is applied to a computational fluid dynamic system that models unsteady flow in a supersonic diffuser and the results are excellent. In comparison with other widely used reduction techniques, the new method is computationally efficient, preserves the stability of the original system, uses both input and output information, and is valid over a wide range of frequencies

Year: 2009
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