Concurrent hpk-Mesh Adaptation and Shape Optimization of Complex Geometries through an Adjoint-Based Discontinuous Petrov-Galerkin Isogeometric Analysis

在过去的十年中，伴随优化框架已经应用于气动曲面的多学科设计以及网格自适应，以提高升力和阻力系数等综合函数的精度。伴随为基础的设计优化和网格自适应已独立推进，但没有同时进行研究。气动外形优化算法必须促进下一代商用飞机的设计，以满足未来航空环境影响的全球标准。欧盟的清洁天空和美国宇航局的环境责任航空（ERA）项目已经对未来飞机设计预期的性能改进类型进行了基准测试。因此，该社区正处于创新和开发全新飞机设计的关键时刻。计算工具使机体制造商既能设计出具有上级高升力气动性能的飞机，又能在一个数值框架内精确地求解远场声学特征，这是非常宝贵的。这种能力与目前采用多种数值工具的做法不同，这种做法只会延长设计周期并达到次优设计。 因此，该研究计划的长期愿景是建立一个通用的框架，使用高阶不连续Petrov-Galerkin格式进行并行网格自适应和形状优化，以提高气动表面的性能。该研究计划有可能对下一代商用飞机的设计产生变革性的影响。 研究培训将为研究生提供一个丰富的环境，以促进和定义一个新兴领域。学者将毕业于制定研究问题，交流他们的想法，接受批评，并接受下一代高性能计算的培训。这项研究计划的长期影响将产生高技能人才，并使加拿大能够保持目前飞机技术的领先地位。

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. 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. The European Union's Clean Sky and NASA's Environmentally Responsible Aviation (ERA) Project have placed benchmarks on the type of performance improvements that are expected on future aircraft designs. The community, therefore, is at a critical juncture to innovate and develop radically new aircraft designs. Computational tools that allow airframe manufacturers to both design aircraft with superior high-lift aerodynamic performance and accurately resolve far-field acoustic signatures within a single numerical framework are invaluable. Such capabilities are unlike the current practice of employing multiple numerical tools that only prolong the design cycle and arrive at sub-optimal designs. Thus, the long-term vision of the research program is to establish a common framework using a high-order discontinuous Petrov-Galerkin scheme for the concurrent mesh adaptation and shape optimization to increase the performance of aerodynamic surfaces. The research program has the potential to make a transformative impact on the design of the next generation of commercial aircraft. The research training will provide graduate students an enriching environment to contribute and define an emerging field. Scholars will graduate with skills in formulating research questions, communicating their ideas, receiving critiques, and being trained on the next-generation of high-performance computing. The long-term impact of this research program will produce highly skilled personnel and enable Canada to remain a leader in current aircraft technology.