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如何优化当前和未来设计的见解。与CFD分析相辅相成的是另一种称为伴随计算的计算方法。高保真伴随计算为气动优化提供了令人兴奋的潜力，但由于手工编码伴随求解器需要大量时间，并且采用现有自动化方法需要大量繁琐的调试过程，因此这种方法的广泛使用受到阻碍。因此，该项目的主要目标是开发全自动伴随灵敏度分析技术，不仅计算和存储效率高，而且能够很容易地集成到现有的CFD求解器中。该项目的成功完成将极大地推动空气动力学设计优化的发展，并使下一代航空航天创新成为可能。该项目将包括一些推广和教育活动，包括一个新的基于项目的研究生课程，一个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提供的实践研讨会，以促进在课堂上使用相关活动。本课题的总体目标是引入伴随灵敏度分析的一种新方法。这个新范例将使用操作符重载（OO），这是面向对象编程提供的一种功能，可以自动计算任何目标函数对所有设计变量（可能有数千个）的敏感性。与伴随计算中OO的传统使用不同，伴随计算需要在迭代过程中存储任何中间变量，从而以指数方式增加所需的内存，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，工作将集中在：(1)开发一种新颖有效的基于cfd的方法来计算稳定的、时间周期的、时间精确的伴随灵敏度；（ii）将这种新技术与基于降阶模型的加速技术相结合，进一步加快伴随计算速度；(3)将新技术应用于相关问题，包括优化风力涡轮机形状和设计新的自然层流翼型。这些活动将直接有助于了解复杂的流动特征如何影响未来飞机发动机、飞机机翼和风力涡轮机叶片的设计和性能。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.