Control of Fluid-Structure Interactions: Finite Dimensional Strategies for Flutter/Turbulence Suppression

点击翻译按钮获取中文摘要

The goal of this mathematical research project is to identify and construct physically implementable control strategies for suppression of turbulence, which is fluid motion characterized by chaotic changes in pressure and flow velocity, and control of flutter, which is sustained oscillation that may occur when a nonlinear body is subject to surrounding inviscid flow. The results are anticipated to inform several important application areas, including aerodynamic design and renewable energy systems in which harvesting flutter is a goal. The project involves collaboration with engineers and will train graduate students through research involvement in modeling, data assimilation, and scientific computing.The project studies questions in control theory and corresponding control strategies with focus on physical phenomena governed by three-dimensional (3D) fluids, flow/fluid-structure interactions which induce strong instabilities in their dynamics. The main goal is to establish flutter-suppression and turbulence-suppression by means of finite dimensional control strategies. The objectives of the project are: (i) finite dimensional attracting sets to capture flutter of the oscillating structure, (ii) finite dimensional boundary feedback stabilization of 3D fluids, and (iii) control theory for 3D fluid-structures with moving interface. The investigation of flutter will require the theory of non-dissipative dynamical systems and their attractors, along with microlocal analysis. In this project, investigation of turbulence in 3D will require Besov spaces of tight indices and maximal regularity (R-boundedness theory) of boundary-feedback partial differential equations. Quasilinear theory and sharp estimates for the hyperbolic Dirichlet-Neumann map will be essential tools in controlling bodies moving in a fluid, where global existence is still an open problem.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.