标题： 用于非定常空气动力学形状优化的窗口正则化技术 显示英文标题

标题： Windowing Regularization Techniques for Unsteady Aerodynamic Shape Optimization

摘要： 非定常气动外形优化在时间相关目标函数的敏感性分析方面提出了新的挑战。 在本工作中，我们考虑由URANS方程控制的周期性非定常流动。 因此，作为优化问题中的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，并可能依赖于所述优化的设计参数。 对具有这些特性的函数的时间平均值进行敏感性分析变得困难。 因此，我们探索了使用所谓的窗函数方法来对这类函数的时间平均值进行正则化。 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，我们进行了经典非正则化优化过程与不同平滑度正则化方法之间的比较研究，并表明后者能够实现更稳健的优化。 显示英文摘要

摘要： 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.