Regularization for Adjoint-Based Unsteady Aerodynamic Optimization Using Windowing Techniques

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 unsteady Reynolds-averaged Navier–Stokes (URANS) equations. Hence, the resulting output functions acting as objective or constraint functions of the optimization are themselves periodic with unknown period length, which 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 multiphysics and optimization software SU2. Finally, we exhibit a comparison study between the classical nonregularized optimization procedure and the ones enhanced with regularizers of different smoothness, and we show that the latter result in a more robust optimization.