Feature-Guided Adaptive Model Order Reduction for Convection-Dominated Problems*

Physical problems featuring strong convections (e.g., hypersonic flows and detonations) often present significant challenges and are well-recognized to be not amendable for conventional model-order reduction (MOR) methods. This can be mainly attributed to the well-known issues associated with the slow decay of Kolmogorov N-width. In literature, several remedies have been proposed to address this challenge via local subspaces, nonlinear manifolds, or adaptive MOR. In this work, we focus on formulating a feature-guided adaptive projection-based model order reduction (MOR) method to develop reduced-order model (ROM) for convection-dominated problems involving flames and shocks, which dynamically update the subspace during online execution to optimally capturing the crucial dynamics. Such adaptive ROM requires minimal offline training and inherently supports predictions of future states and parametric variations. To maximize efficiency and effectiveness, we develop a feature-guided sampling strategy that strategically populates sampling points to capture the prominent convective features with rigorous error controls, ensuring accurate prediction of the advection dynamics. A suite of challenging convection-dominated testing problems is used to assess the feature-guided sampling strategy, which includes sod shock tube, colliding shock waves, and detonation waves.