Structure-preserving reduced-order models of thin panels in supersonic and hypersonic flow

Miguel A. Aguilo

We build structure-preserving reduced-order models for both challenge problems of the AePW-4 High-Speed Working Group. They are a clamped thin panel at Mach 1.92 (RC-19) and a cantilever plate at Mach 5.85 (HyMAX). The published data for each case hold no time-resolved response and no repeated runs. The physics must therefore be carried by the form of the model. One construction gives two models per problem. A Ritz-Galerkin reference model describes the plate. A learned model keeps the reference model's exact potential, fits the remaining generalized forces, and trains only a dissipation that cannot add energy. Its energy balance holds for any weights by construction. On the trained model the worst relative residual is 2.2e-15. On RC-19, shock relations predict a pressure ratio of 1.521 across the panel. Pressure-sensitive paint measured the same value. Thirty runs of the learned model place the mean dominant frequency within 1.0% of the measured 236 Hz. At one periodic and one chaotic condition, the learned model reproduces the response regime of a published reduced-order model in all sixteen runs. It does so without that model's 113 Hz spectral peak, which the measurements do…