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Adaptive Model Reduction for High-Speed Flows

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DDEW03 - Computational Challenges and Emerging Tools

To avoid the fundamental linear reducibility limitation associated with high-speed fluid flows (or other convection-dominated problems), we construct a nonlinear approximation by composing a low-dimensional linear space with a parametrized domain mapping. The linear space is constructed using the method of snapshots and POD ; prior to compression, each snapshot is composed with a mapping that causes its local features to align (same spatial location) with the corresponding features in all other snapshots. The parametrized domain mapping is chosen such that the local features present in the linear space deform to the corresponding features in the solution being approximated, effectively removing the convection-dominated nature of the problem. The domain mapping is determined implicitly through the solution of a residual minimization problem, rather than relying on explicit sensing/detection.  We provide several numerical experiments to demonstrate the effectivity of the proposed method for high-speed aerodynamic flows, and discuss extensions to time-dependent problems with strong, propagating discontinuities.

This talk is part of the Isaac Newton Institute Seminar Series series.

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