Optimal Flow Control and Topology Optimization Using the Continuous Adjoint Method in Unsteady Flows

This paper presents the development and application of the unsteady continuous adjoint method to the incompressible Navier-Stokes equations and its use in two different optimization problems. The first is the computation of the optimal setting of a flow control system, based on pulsating jets located along the surface of a square cylinder, in order to minimize the time-averaged drag. The second is dealing with unsteady topology optimization of a duct system with four fixed inlets and a single outlet, with periodic in time inlet velocity profiles, where the target is to minimize the time-averaged viscous losses. The presentation of the adjoint formulation is kept as general as possible and can thus be used to other optimization problems governed by the unsteady Navier-Stokes equations. Though in the examined problems the flow is laminar, the extension to turbulent flows is doable.