Unified LSPG Model Reduction Framework and Assessment for Hypersonic Computational Fluid Dynamics

Abstract

A unified least-squares Petrov–Galerkin (LSPG) framework for projection-based model order reduction featuring three different approximation manifolds [affine manifold, quadratic manifold, and nonlinear manifold built using a deep artificial neural network (ANN)] is presented. Its performance was assessed for a variable-speed version of the double-cone hypersonic benchmark problem. First, a high-dimensional viscous computational fluid dynamics model (HDM) was constructed, verified, and validated. The dimensionality of the HDM was then reduced using LSPG, each of the aforementioned approximation manifolds, and a global right reduced-order basis trained in the range 8≤M∞≤13. Each resulting global projection-based reduced-order model (PROM) was hyper-reduced and transformed into a hyper-reduced PROM (HPROM). The accuracy of each constructed HPROM was assessed for various quantities of interest and contrasted with that of snapshot interpolation. For this purpose, three different error measures were considered and discussed in the context of shock-dominated problems. Wall-clock and CPU time speedup factors are reported. Overall, it was shown that using a relatively small set of training data, all constructed LSPG HPROMs were nonlinearly stable, real-time capable, and highly predictive. The LSPG HPROM constructed using a nonlinear approximation manifold and an ANN was the most computationally efficient.