High-speed aerospace engineering applications rely heavily on computational fluid dynamics (CFD) models for design and analysis. This reliance on CFD models necessitates performing accurate and reliable uncertainty quantification (UQ) of the CFD models, which can be very expensive for hypersonic flows. Additionally, UQ approaches are many-query problems requiring many runs with a wide range of input parameters. One way to enable computationally expensive models to be used in such many-query problems is to employ projection-based reduced-order models (ROMs) in lieu of the (high-fidelity) full-order model (FOM). In particular, the least-squares Petrov–Galerkin (LSPG) ROM (equipped with hyper-reduction) has demonstrated the ability to significantly reduce simulation costs while retaining high levels of accuracy on a range of problems, including subsonic CFD applications. This allows LSPG ROM simulations to replace the FOM simulations in UQ studies, making UQ tractable even for large-scale CFD models. This work presents the first application of LSPG to a hypersonic CFD application, the Hypersonic International Flight Research Experimentation 1 (HIFiRE-1) in a three-dimensional, turbulent Mach 7.1 flow. This paper shows the ability of the ROM to significantly reduce computational costs while maintaining high levels of accuracy in computed quantities of interest.

高速航空工程应用程序严重依赖于计算流体动力学（CFD）模型进行设计和分析。这种对CFD模型的依赖使得必须对CFD模型执行准确而可靠的不确定性量化（UQ），这对于高超音速流而言可能是非常昂贵的。此外，UQ方法是很多查询问题，需要使用大量输入参数进行多次运行。使计算上昂贵的模型可以用于这种多查询问题的一种方法是采用基于投影的降阶模型（ROM）代替（高保真）全阶模型（FOM）。特别是，最小二乘的Petrov-Galerkin（LSPG）ROM（配备了超缩减功能）已证明能够显着降低仿真成本，同时在一系列问题上保持较高的准确性，包括亚音速CFD应用程序。这使得LSPG ROM模拟可以代替UQ研究中的FOM模拟，从而即使对于大规模CFD模型，UQ也易于处理。这项工作提出了LSPG在高超声速CFD应用中的第一个应用，即三维湍流Mach 7.1流中的高超声速国际飞行研究实验1（HIFiRE-1）。本文展示了ROM能够显着降低计算成本，同时在所关注的计算量中保持较高的准确性的能力。三维湍流Mach 7.1流中的Hypersonic国际飞行研究实验1（HIFiRE-1）。本文展示了ROM能够显着降低计算成本，同时在所关注的计算量中保持较高的准确性的能力。三维湍流Mach 7.1流中的Hypersonic国际飞行研究实验1（HIFiRE-1）。本文展示了ROM能够显着降低计算成本，同时在所关注的计算量中保持较高的准确性的能力。