Optimal Control of Vortex Shedding Around Square Cylinder via Reduced Order Model

In this paper, optimal control of vortex shedding behind square cylinder in laminar flow regime (Re=200) has been investigated. When Navier-Stokes equations are used as state equations, the discretization of the optimality system leads to large scale discretized optimization problems that represent a tremendous computational task. In order to reduce the number of state variables during the optimization process, a Reduced-Order Model (ROM) based on POD modes is derived to be used as state equations. Then, these equations are modified by introducing a Control Function to ROM in order to gain equations which are suitable for optimal control. Optimal trajectory for control input has been found by employment of Quasi-linearization which is one of the numerical methods for solving optimal control equations. The flow is actuated via suction and blowing slots. The results have been investigated in Results Section.Keywords: Optimal Control- Vortex Shedding- Suction and blowing- Reduced Order Model- POD modes- Quasi-linearization method.