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- W2997926708 abstract "Fluid dynamics has witnessed the evolution of a diverse collection of model reduction techniques for facilitating real-time optimization and control through the past few decades. The systematic grey-box nature of the projection-based Reduced-Order Models (ROMs) has provided a strong physics-based foundation for the study of the coherent structures, and online prediction of the true dynamics. Numerical properties of this class of ROMs however are significantly affected by the quality of the underlying subspace that is formed by compression of the high-dimensional snapshots and subsequent truncation of the modal information based on a certain metric, such as energy content in the Proper Orthogonal Decomposition (POD). Therefore, the choice of the inner product definition for mapping of the high-dimensional manifold to the low-dimensional space, and projection of the dynamics onto the subspace, influences stability and robustness of the model. Bounded operators in the symmetrized governing equations have inspired the use of a symmetry inner product in construction of the projection-based ROMs. Previous studies in the literature have shown that compressible flow ROMs based on the symmetry inner product have better stability properties compared to those based on the L2 inner product. POD-Galerkin ROMs in this study are created with the snapshots of supersonic flows with unsteady shock oscillations, and naturally exhibit large instabilities in the absence of the low-energy, high-frequency modes that are truncated before the Galerkin projection. Therefore, stabilization methods are applied to the constructed ROMs to facilitate study of the influence of the inner product definition on the control space of the stabilized ROMs. As a result, when the symmetry inner product is used, not only the bare bone original ROM is more stable, but it is considerably more controllable than the model generated based on the L2 inner product, and exhibits a robust performance when sub-optimal control laws are used for stabilization." @default.
- W2997926708 created "2020-01-10" @default.
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- W2997926708 date "2020-01-05" @default.
- W2997926708 modified "2023-10-16" @default.
- W2997926708 title "Impact of Symmetrization on the Robustness of POD-Galerkin ROMs for Compressible Flows" @default.
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- W2997926708 doi "https://doi.org/10.2514/6.2020-1318" @default.
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