Efficient One-Shot Technique for Adjoint-Based Unsteady Optimization

Abstract

A computationally efficient one-shot approach with a low memory footprint is presented for unsteady optimization. The proposed technique is based on a novel and unique approach that combines local-in-time and fixed-point iteration methods to advance the unconverged primal and adjoint solutions forward and backward in time to evaluate the sensitivity of the globally time-integrated objective function. This is in some ways similar to the piggyback iterations in which primal and adjoint solutions are evaluated at a frozen design. During each cycle, the primal, adjoint, and design update problems are solved to advance the optimization problem. This new coupled approach is shown to provide significant savings in the memory footprint while reducing the computational cost of primal and adjoint evaluations per design cycle. The method is first applied to an inverse design problem for the unsteady lid-driven cavity. Following this, vortex suppression and mean drag reduction for a circular cylinder in crossflow is considered. Both of these objectives are achieved by optimizing the rotational speeds for steady or periodically oscillating excitations. For all cases presented in this work, the proposed technique is shown to provide significant reductions in memory as well as computational time. It is also shown that the unsteady optimization problem converges to the same optimal solution obtained using a conventional approach.