Feature-Guided Sampling Strategy for Adaptive Model Order Reduction of Convection-Dominated Problems

Abstract

Though high-performance computing enables high-fidelity simulations of complex engineering systems, accurately resolving multi-scale physics for real-world problems remains computationally prohibitive, particularly in many-query applications such as optimization and uncertainty quantification. Projection-based model order reduction (MOR) has demonstrated significant potential for reducing computational costs by orders of magnitude through the creation of reduced-order models (ROMs). However, physical problems featuring strong convection, such as hypersonic flows and detonations, pose significant challenges to conventional MOR techniques due to the slow decay of Kolmogorov N-width present in these problems. In the past few years various approaches have been proposed to address this challenge; one of the promising methods is the adaptive MOR. In this work, we introduce a feature-guided adaptive projection-based MOR framework tailored for convection-dominated problems involving flames and shocks. This approach dynamically updates the ROM subspace and incorporates a feature-guided sampling method that strategically selects sampling points to capture prominent convective features, ensuring accurate predictions of crucial dynamics in the target problems. We evaluate the proposed methodology using a suite of challenging convection-dominated test problems, including shocks, flames, and detonations. The results demonstrate the feature-guided adaptive ROM's capability in producing efficient and reliable predictions of the nonlinear convection-dominated physical phenomena in the selected test suite, which are well recognized to be challenging for conventional ROM methods.