Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics
Room: Exhibit Hall A
E'Aysha C.Y. Scaife - Virginia State University
In this project, we study the uniform stabilization of a nonlinear fluid-structure interaction (FSI) via interior feedback control. The underlying system of PDEs that governs the dynamical behavior of FSI consists of the Navier-Stokes equation and the wave equation. Feedback mechanism must be applied to the coupled system to achieve uniform stability. The coupled system of FSI and its constitutive equations have a wide range of real life applications: for example, the Navier-Stokes equation is used to model weather, ocean currents, water flow in a pipe, and airflow around a wing. Unfortunately, the theoretical understanding of the solutions to the Navier-Stokes equation is incomplete. Fluid-structure interaction is important in the engineering of aircraft, spacecraft, engines, and bridges. Our goal is to verify uniform stability of the coupled system when it is subject to some feedback mechanism by running numerical simulation. The feedback mechanism is interior only. The numerical simulation is based on the method of finite element. Time is discretized using the discontinuous Galerkin method. As a comparison, we also simulate the energy functional of the system when the system is not subject to any feedback mechanism. Our numerical simulation results show that (a) the energy of the coupled system won?t decay uniformly if there is no feedback mechanism; (b) the interior feedback on the fluid equation must be large enough for the energy of the coupled system to decay exponentially. As a direction for future research, we would like to figure out a quantitative relationship between the decay rate of the energy functional and the strength of the interior feedback. This will provide valuable insights to apply the feedback in a real world situation.
Funder Acknowledgement(s): Funder Acknowledgement(s): Proudly supported by NSF Grant No. 1601127
Faculty Advisor: Yongjin Lu, firstname.lastname@example.org
Role: I learned and research the essential topics of this subject. I also submitted codes and generated reports to conduct further research in this subject area.