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Pixel Club: Modeling Fluid Flow on Inertial Manifolds: Physics, Geometry and the Challenge of Model Reduction
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Gilead Tadmor (Northeastern University, Boston)
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Tuesday, 2.8.2011, 11:30
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Room 337-8 Taub Bld.
Model order reduction is essential for feasible analysis, design, realtime control of distributed systems. Recent uses also include accelerating detailed simulations and the extraction of actionable meaning from large scale data streams. Alas, a mature and mathematically rigorous theory is largely limited to the linear case, and even there, the mere computational complexity its tools entail, restrict its use to relatively moderate dimensions. Heuristics fill in the gap, with successions of intuitive patches, with very mixed results.

Our motivation comes from active flow control (AFC), a field driven by needs of truly epic proportions: From energy efficiency of air, ground and maritime transportation, through clean and efficient combustion and wind energy, micro-fluidic, diagnostic chips, artificial hearts and other bio-engineering designs, to HVAC and bio-chem defense. Arguably, the lack of adequate low order models is a major impediment for real progress and transition to wide-range usage.

We present a rational approach to Galerkin-type model order reduction that tracks and addresses longstanding impediments at their first-principles roots - the Navier-Stokes equation. Embedding flow states in parameterized inertial manifolds, is used as to address difficult practical and conceptual problems, including unsteady boundaries (e.g., flapping wings), boundary actuation and transient deformation of coherent structures.
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