Multilevel parameterizations and fast multigrid methods for aerodynamic shape optimization

流场数值模拟是商用飞机制造过程中不可缺少的一部分。由于计算能力的进步和仿真算法效率的提高，现在可以想象仅在计算机上设计飞机的零件甚至整个飞机。因此，数值形状优化将对未来的飞机设计和各自的行业发挥战略作用。目前数值优化方法在该领域的局限性主要是由于数值流模型的高度复杂性，如果将标准优化算法与流求解器相结合，则计算时间很长，可能需要数周甚至数月。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，计算机上形状的最佳表示主要是开放的，这导致了参数化和局部设计改进的问题。这两个问题都是空气动力学外形设计的基本问题，当然，它们是相互作用的。在这个应用中，我们建议通过利用形状和流动问题中出现的多层次结构来研究多层次形状参数化和快速优化算法。与传统的优化方法相比，最受青睐的算法范式是针对所有涉及的变量的整体多网格优化方法。这种方法范例将潜在地导致优化方法，这只需要相当于几次模拟运行的数值努力-无论离散化的分辨率如何。该项目的目标是以最好的方式探索这种潜力的利用。由于弹性效应在机翼设计中起着重要的作用，因此也将涉及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.