Windowing Regularization Techniques for Unsteady Aerodynamic Shape Optimization

TL;DR

This paper introduces windowing regularization techniques for unsteady aerodynamic shape optimization, improving robustness by stabilizing sensitivity analysis of periodic, time-dependent functions governed by URANS equations.

Contribution

It develops and embeds windowing regularizers into the adjoint solver for URANS-based optimization, enhancing stability and robustness of the process.

Findings

Regularized optimization is more robust than classical methods.

Windowing techniques improve sensitivity analysis of periodic flows.

Enhanced methods show better convergence in shape optimization.

Abstract

Unsteady Aerodynamic Shape Optimization presents new challenges in terms of sensitivity analysis of time-dependent objective functions. In this work, we consider periodic unsteady flows governed by the URANS equations. Hence, the resulting output functions acting as objective or constraint functions of the optimization are themselves periodic with unknown period length, that may depend on the design parameter of said optimization. Sensitivity Analysis on the time-average of a function with these properties turns out to be difficult. Therefore, we explore methods to regularize the time average of such a function with the so called windowing-approach. Furthermore, we embed these regularizers into the discrete adjoint solver for the URANS equations of the multi-physics and optimization software SU2. Finally, we exhibit a comparison study between the classical non regularized optimization procedure and the ones enhanced with regularizers of different smoothness and show that the latter result in a more robust optimization.