In this paper, a computationally efficient multifidelity local search algorithm for aerodynamic design optimization is presented. In this paper’s approach, direct optimization of a computationally expensive model is replaced by an iterative updating and reoptimization of a fast multifidelity model constructed using a low-fidelity model adapted locally using manifold mapping (MM) to become a reliable representation of the high-fidelity one during the optimization process. Only one high-fidelity model evaluation is needed per design iteration, and no gradient information is used. The proposed method is validated and characterized by applying it to a few single- and multipoint optimization problems involving inviscid and viscous transonic flows. The proposed method is compared with the sequential least-squares programming (SLSQP) gradient-based approach with the gradients calculated based on adjoint sensitivities. In the inviscid single-point test case, a drag reduction of 410.8 counts was achieved by the MM algorithm while requiring approximately 1469 min on a high performance computing (HPC) with 32 processors. SLSQP with adjoints achieved a drag reduction of 425.9 counts, while requiring approximately 1536 min under the same HPC setup. For the viscous single-point test case, a 83.2 drag count reduction was reported for the MM compared to 83.4 for SLSQP with adjoints. In that case, the MM algorithm was around eight times faster in terms of computing time. In the multipoint design test case, the MM algorithm was computationally cheaper by at least an order of magnitude compared to SLSQP with adjoints, although the objective function value was around three drag counts higher. Furthermore, it was found that in the multipoint cases the MM algorithm scales favorably with the number of operational conditions considered compared to SLSQP with adjoints.

本文提出了一种用于空气动力学设计优化的计算有效的多保真度局部搜索算法。在本文的方法中，用迭代更新和重新优化快速多保真度模型代替了计算量大的模型的直接优化，该快速多保真度模型使用在本地使用流形映射（MM）适应的低保真度模型构建而成，成为高保真度的可靠表示一个在优化过程中。每次设计迭代仅需要进行一次高保真模型评估，并且不使用任何梯度信息。通过将该方法应用于涉及粘性和粘性跨音速流的一些单点和多点优化问题，对该方法进行了验证和表征。将所提出的方法与基于梯度最小二乘编程（SLSQP）的基于梯度的方法进行了比较，该方法具有基于伴随灵敏度计算的梯度。在无粘性的单点测试案例中，MM算法实现了410.8计数的减阻，同时在具有32个处理器的高性能计算（HPC）上大约需要1469分钟。带有附件的SLSQP减少了425.9的阻力，而在相同的HPC设置下大约需要1536分钟。对于粘性单点测试用例，据报道，MM的阻力数减少了83.2，相比之下，伴随着SLSQP的阻力数减少了83.4。在那种情况下，MM算法的计算时间快了大约八倍。在多点设计测试用例中，MM算法在计算上比带有伴奏的SLSQP便宜至少一个数量级，尽管目标函数值大约高三个阻力计数。此外，发现在多点情况下，MM算法与考虑的操作条件数量相比，具有伴随的SLSQP具有良好的伸缩性。