Robust preconditioned one-shot methods and direct-adjoint-looping for optimizing Reynolds-averaged turbulent flows

We compare the performance of direct-adjoint-looping (DAL) and one-shot methods in a design optimization task involving turbulent flow modeled using Reynolds-Averaged-Navier-Stokes equations. Two preconditioned variants of the one-shot algorithm are proposed and tested. The role of an approximate Hessian as a preconditioner for the one-shot method iterations is highlighted. We find that the preconditioned one-shot methods can solve the PDE-constrained optimization problem with the cost of computation comparable (about fourfold) to that of the simulation run alone. This cost is substantially less than that of DAL, which requires O(10) direct-adjoint loops to converge. The optimization results arising from the one-shot method can be used for optimal sensor/actuator placement tasks, or to provide a reference trajectory to be used for online feedback control applications.