Adaptive High-Order Methods for the Concurrent Mesh and Shape Optimization of Aerodynamic Surfaces for the Design of Next-Generation Environmentally Responsible Aircraft

该研究计划的长期目标是建立一个使用自适应高阶方法的通用框架，用于并行网格适应和气动表面的形状优化。未来的气动外形优化算法必须促进下一代商用飞机的设计，以满足未来关于航空环境影响的全球标准。然而，目前的工业实践是使用多种数值工具来分析和设计飞机机翼，以改善气动性能和声学特征，这既延长了设计周期，又收敛于次优设计。例如，将使飞机制造商能够设计具有优越的高升力空气动力学性能的飞机，并在单个数值框架内准确地解析远场机身声学特征的方法，将是一种无价的计算工具。基于伴随的高阶气动外形优化框架有可能实现这一行业的变革性影响。在过去的十年里，基于伴随的优化框架应用于气动表面的多学科设计以及网格自适应，以提高诸如升力和阻力系数等综合函数的精度。基于伴随的设计优化和网格自适应都是独立推进的，但没有同时进行研究。研究目标需要两大努力。首先，开发基于伴随的hp适应的新技术，通过评估目标函数(例如积分量)相对于通过h适应或p适应增加的自由度的敏感性。该方法将允许自适应过程以最小的计算量实现解的误差的大幅减少。其次，发展了气动外形优化的高阶方法。这项工作的预期意义将是能够在真正的工业产能下使用伴随方法以高精度修改飞机的形状。这项研究将培养出高技能人才，并使加拿大在当前飞机技术方面保持领先地位。

The long-term objective of the research program is to establish a common framework using adaptive high-order methods for the concurrent mesh adaptation and shape optimization of aerodynamic surfaces. Future aerodynamic shape optimization algorithms must facilitate the design of the next generation of commercial aircraft to meet future global standards on the environmental impact of aviation. However, the current industry practice of employing multiple numerical tools to analyze and design aircraft wings for improved aerodynamic performance and acoustic signature, both prolongs the design cycle and converges to sub-optimal designs. Methodologies, for example, that will allow aircraft manufacturers to design aircraft with superior high-lift aerodynamic performance, and accurately resolve the far-field airframe acoustic signatures within a single numerical framework, would be an invaluable computational tool. An adjoint-based high-order aerodynamic shape optimization framework has the potential to realize this transformative impact on the industry. The past decade has seen the application of adjoint-based optimization frameworks for the multidisciplinary design of aerodynamic surfaces as well as mesh adaptation to increase the accuracy of integrated functions such as lift and drag coefficients. Both adjoint-based design optimization and mesh adaptation have been advanced independently but not investigated concurrently. The research objectives requires two major efforts. First, develop novel techniques for adjoint-based hp-adaptation, by evaluating the sensitivity of the objective function, such as integrated quantities, with respect to the addition of a degree of freedom either through h- or p-adaptation. The approach will allow the adaptation process to achieve a large reduction in the solution error for the least amount of computational cost. Second, develop high-order methods for aerodynamic shape optimization. The expected significance of the work will be the ability to modify the shape of the aircraft using the adjoint method with a high degree of accuracy in a truly industrial capacity. This research will produce highly skilled personnel and enable Canada to remain a leader in current aircraft technology.