Applied Mathematics Colloquium: Dr. Michael Lee
NASA Langley
Friday, September 11, 2020 · 2 - 3 PM
Title: A Primer in Fluid Reduced-order Modeling
Abstract: Reduced-order modeling of nonlinear dynamical systems advertises both low computational cost and high simulation fidelity through the identification of a system’s most important characteristics and how they interact. From an analytical perspective, elucidating the coherent structures of a nonlinear system – those which define the attractor – is of fundamental interest. These normally manifest in the form of a modal basis of finite size; the fewer modes in the basis, the more reduced the model. From an applied perspective, the appeal of simulating very high-dimensional systems like turbulent fluid flows in orders of magnitude less time is readily apparent. The challenges of reduced-order modeling are as serious as the benefits, however: limited predictable accuracy, model stability, and application utility. In this talk, a survey of fluid reduced-order modeling approaches will be presented with an emphasis on how to understand their relative strengths and weaknesses. It will be argued that the method used to construct a modal basis is equally important as the method used to construct the model from the system’s governing equations. The spectrum of applications for reliable reduced-order models will also be explored.
Abstract: Reduced-order modeling of nonlinear dynamical systems advertises both low computational cost and high simulation fidelity through the identification of a system’s most important characteristics and how they interact. From an analytical perspective, elucidating the coherent structures of a nonlinear system – those which define the attractor – is of fundamental interest. These normally manifest in the form of a modal basis of finite size; the fewer modes in the basis, the more reduced the model. From an applied perspective, the appeal of simulating very high-dimensional systems like turbulent fluid flows in orders of magnitude less time is readily apparent. The challenges of reduced-order modeling are as serious as the benefits, however: limited predictable accuracy, model stability, and application utility. In this talk, a survey of fluid reduced-order modeling approaches will be presented with an emphasis on how to understand their relative strengths and weaknesses. It will be argued that the method used to construct a modal basis is equally important as the method used to construct the model from the system’s governing equations. The spectrum of applications for reliable reduced-order models will also be explored.
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