Optimal Force Control of the Flow Past Moving Cylinders with Adjoint-ROM Approach

It is usually difficult to perform optimal control of unsteady flow past a moving solid body, due to the huge control space that the problem usually has. In this work, the adjoint-based method is applied to the optimal control of flow past two-dimensional (2D) moving cylinders. Instead of performing control directly on the complex original flow system described by the incompressible Navier-Stokes equation, a Reduced-Order Model (ROM), which is constructed by global Proper Orthogonal Decomposition (POD)-Galerkin approach, is chosen as the surrogate model. The effectiveness of this approach has been demonstrated before by controlling the flow to match a prescribed velocity field. Here, the approach is further extended to control the aerodynamic forces. A ROM-switching strategy is implemented for the control, which is able to drastically reduce the online computational cost while keeping the accuracy of the adaptive ROMs during the optimization. The results of the numerical study demonstrate the effectiveness of the current approach to find the local optimum for aerodynamic forces, which is further validated against results from a parametric study based on direct numerical simulation (DNS). Lastly, an estimation of the reduction in computational cost by using ROM-based adjoint approach is made, which shows that the present approach takes 32 minutes while DNS-based approach may take dozens of hours to achieve the same optimal solutions.