Multilevel parameterizations and fast multigrid methods for aerodynamic shape optimization

流动数值模拟是商用飞机制造过程中不可或缺的一部分。由于计算机计算能力的提高和仿真算法效率的提高，现在可以想象在计算机上设计飞机的部件甚至整个飞机。因此，数值形状优化将在未来的飞机设计和相应的行业中发挥战略作用。目前在这一领域的数值优化方法的局限性主要是由于数值流模型的高度复杂性，如果标准优化算法与流求解器相结合，则会导致数周和数月量级的长计算时间。此外，计算时间通常甚至取决于形状参数化。这就引出了高效优化算法的问题。此外，在计算机上的形状的最佳表示原则上是开放的，导致参数化和局部设计改进的问题。这两个问题都是气动外形设计的基本关注点，当然，是相互作用的。在这个应用程序中，我们建议调查多级形状参数化和快速优化算法，利用所产生的多级结构的形状和流动问题。算法的范例是一个整体的多重网格优化方法的所有变量，这是在传统的优化方法相反。这种方法范式将潜在地导致优化方法，其需要相当于仅几次模拟运行的数值工作-无论离散化的分辨率如何。该项目的目标是探索以最佳方式开发这种潜力。由于弹性效应在机翼设计中起着重要的作用，因此也将讨论多学科设计优化方面的问题。

Numerical flow simulation is an integral part of the construction process of commercial aircrafts. Due to the advance of computing power and improvements in the efficiency of simulation algorithms, it is nowadays conceivable to design parts of aircrafts or even whole aircrafts on the computer only. Therefore, numerical shape optimization will play a strategic role for future aircraft design and for the respective industry. Current limitations of numerical optimization methods in this field are mainly due to the high complexity of numerical flow models, resulting in long computation times in the order of weeks and months if a standard optimization algorithm is coupled with a flow solver. Additionally, the computation time typically even depends on the shape parameterization. That leads to questions of highly efficient optimization algorithms. Moreover, the optimal representation of shapes on the computer is principally open, resulting in questions of parameterizations and local design refinements. Both questions are of fundamental concern for aerodynamic shape design and, of course, are interacting.In this application, we propose to investigate multilevel shape parameterizations and fast optimization algorithms by exploiting the arising multilevel structures in the shape and in the flow problem. The algorithmic paradigm favored is that of an overall multigrid optimization method for all variables involved, which is in contrast to traditional optimization approaches. This methodological paradigm will potentially lead to optimization methods, which require a numerical effort equivalent to only a few simulation runs - regardless of the resolution of the discretizations. The goal of the project is to explore the exploitation of this potential in the best way. Because elastic effects play an important role in wing design, also aspects of multi-disciplinary design optimization will be addressed.