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

Saleh Nabi, Piyush Grover, Colm P Caulfield

Abstract: We compare the performance of direct-adjoint-looping (DAL) and one-shot algorithms in a design optimization task involving turbulent flow modeled using the 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 preconditioned one-shot algorithms can solve the PDE-constrained optimization problem with a cost of computation comparable (i.e. typically a single digit multiple greater) to that of the simulation run alone. This cost is substantially less than that of DAL, which requires $\mathcal{O}(10)$ 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.