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.

不稳定的空气动力学形状优化在随时间变化的目标函数的敏感性分析方面提出了新的挑战。在这项工作中，我们考虑由非稳态雷诺平均Navier–Stokes（URANS）方程控制的周期性非稳态流动。因此，用作优化的目标或约束函数的所得输出函数本身是周期性的，具有未知的周期长度，这可能取决于所述优化的设计参数。具有这些特性的函数的时间平均的灵敏度分析被证明是困难的。因此，我们探索了使用所谓的窗口化方法来规范该函数的时间平均的方法。此外，我们将这些正则化器嵌入到多物理场和优化软件SU2的URANS方程的离散伴随求解器中。最后，