A New Paradigm for Computing Discrete Adjoint Sensitivities Based on Operator-Overloading and Its Application to Aerodynamic Design

未来风力涡轮机、飞机和涡轮机械的设计和开发需要广泛使用计算流体动力学(CFD)分析来模拟和理解复杂的流体现象。然而，这些分析本身并不能提供对当前和未来设计如何进行优化的洞察。与CFD分析相辅相成的是另一种称为伴随计算的计算方法。高保真伴随计算为空气动力学优化提供了令人兴奋的潜力，但由于手工编码伴随解算器所需的大量时间以及采用现有自动化方法所需的相当繁琐的调试过程，此类方法的广泛使用受到了阻碍。因此，该项目的主要目标是开发全自动的伴随灵敏度分析技术，不仅在计算和内存方面有效，而且能够很容易地集成到现有的CFD解算器中。成功完成这一项目将极大地推动空气动力学设计优化的最先进水平，并使下一代航空航天创新成为可能。这个项目将包括几个外展和教育活动，包括一个新的基于项目的研究生课程，一个针对对这项技术感兴趣的教师和工程专业人员的培训计划，以及为职前科学教师举办的动手研讨会，以促进课堂上相关活动的使用。这个项目的总体目标是引入一种新的伴随敏感性分析方法。这一新的范例将使用运算符重载(OO)，这是面向对象编程提供的一种能力，以自动计算任何目标函数对所有设计变量(可能是数千个)的敏感度。与传统的在伴随计算中使用面向对象的方法不同，该方法需要存储迭代过程中的任何中间变量，从而以指数级增加所需的内存，该方法将利用迭代过程的重复性来最小化内存占用。更具体地说，这些努力将集中在(I)开发一种基于CFD的新的、高效的方法来计算稳态、时间周期、时间精确的伴随灵敏度；(Ii)将该新技术与基于降阶模型的加速技术相结合，以进一步加快伴随计算；(Iii)将新技术应用于相关问题，包括优化风力机形状和设计新的自然层流翼型。这些活动将直接有助于从根本上了解复杂的流动特征如何影响未来飞机发动机以及飞机机翼和风力涡轮机叶片的设计和性能。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The design and development of future wind turbines, aircraft, and turbomachinery requires extensive use of computational fluid dynamic (CFD) analyses to model and understand complex fluid phenomena. However, these analyses alone do not provide insight into how current and future designs can be optimized. Complementary to CFD analyses is another computational method called adjoint computation. High-fidelity adjoint computations provide exciting potential for aerodynamic optimization, but widespread use of such methods is hindered due to the significant time required for hand-coding adjoint solvers and the substantially cumbersome debugging process needed to adopt existing automated approaches. Therefore, the principal aim of this project is to develop fully automated adjoint sensitivity analysis techniques that are not only computationally and memory efficient but also able to be readily integrated into existing CFD solvers. Successfully completing this project will significantly advance the state-of-the-art in aerodynamic design optimization and enable the next generation of aerospace innovation. This project will incorporate several outreach and educational activities, including a new project-based graduate course, a training program for faculty and engineering professionals interested in this technology, and hands-on workshops to pre-service science teachers to facilitate the use of related activities in the classroom.The overall goal of this project is to introduce a new approach for adjoint sensitivity analysis. This new paradigm will employ operator overloading (OO), a capability offered by object-oriented programming, to automatically compute the sensitivity of any objective function to all design variables (potentially thousands). Unlike the traditional use of OO in adjoint computations, which requires the storage of any intermediate variable in the iterative process, thereby exponentially increasing the memory needed, this method will take advantage of the repetitiveness of the iterative process to minimize the memory footprint. More specifically, the efforts will focus on (i) developing a novel and efficient CFD-based approach to calculate steady, time-periodic, time-accurate adjoint sensitivities; (ii) coupling this novel technique to a reduced-order-model-based acceleration technique to further speed up adjoint computations; (iii) applying the new technique to relevant problems including optimizing wind turbine shape and designing new natural-laminar flow airfoils. These activities will directly contribute to the fundamental understanding of how complex flow features affect design and performance of future aircraft engines, as well as aircraft wings and wind turbine blades.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.