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.

翻译：非定常气动外形优化在时间依赖目标函数的灵敏度分析方面提出了新的挑战。在本工作中，我们考虑由非定常雷诺平均纳维-斯托克斯（URANS）方程控制的周期性非定常流动。因此，作为优化目标函数或约束函数的输出函数本身也是周期性的，其周期长度未知，并且可能依赖于所述优化的设计参数。对具有此类性质的函数进行时间平均的灵敏度分析被证明是困难的。为此，我们探索了采用所谓窗函数方法来正则化此类函数时间平均的技术。此外，我们将这些正则化器嵌入到多物理场及优化软件SU2的URANS方程离散伴随求解器中。最后，我们展示了经典的非正则化优化流程与采用不同光滑度正则化器增强的优化流程之间的对比研究，结果表明后者能实现更稳健的优化。