Model Reduction of Hypersonic Aerodynamics with Residual Minimization Techniques

High-fidelity hypersonic aerodynamic simulations require extensive computational resources, hindering their usage in hypersonic vehicle design and uncertainty quantification. Projection-based reduced-order models (ROMs) are a computationally cheaper alternative to full-order simulations that can provide major speedup with marginal loss of accuracy when solving many-query problems such as design optimization and uncertainty propagation. However, ROMs can present robustness and convergence issues, especially when trained over large ranges of input parameters and/or with few training samples. This paper presents the application of several different residual minimization-based ROMs to hypersonic flows around flight vehicles using less training data than in previous work. The ROM demonstrations are accompanied by a comparison to fully data-driven approaches including kriging and radial basis function interpolation. Results are presented for three test cases including one three-dimensional flight vehicle. We show that registration-based ROMs trained on grid-tailored solutions can compute quantities of interest more accurately than data driven approaches for a given sparse training set. We also find that the classic L2 state error metric is not particularly useful when comparing different model reduction techniques on sparse training data sets.