Self-Adaptive Model-Order Reduction for Shock-Dominated Problems

Abstract

Projection-based model-order reduction (MOR) offers a promising approach for accelerating expensive full-order model (FOM) by constructing reduced-order models (ROMs) that retain the majority of FOM accuracy while significantly reducing the computational cost. However, conventional static ROMs, often following offline/online training strategy, can exhibit limited predictive capability for convection-dominated problems featuring strongly evolving physics such as shocks. Adaptive ROMs emerge as a promising alternative and address such limitation by dynamically updating the low-dimensional subspace during online simulation to track locally evolving system dynamics, thereby enabling accurate predictions even for shock-dominated flows. However, such online adaptation introduces additional computational overhead, and frequent basis and sampling-point updates can substantially reduce their computational advantage relative to their static counterpart. To reconcile this tradeoff, the current work introduces a self-adaptive MOR framework that dynamically constructs and deploys the most appropriate ROM formulation (either adaptive or static) on the fly according to the evolving characteristics of the solution. to achieve optimal computational efficiency while maintaining high modeling accuracy of the local physics during the online model execution. In this regard, the proposed framework seeks to exploit the advantages of both adaptive- and static-ROM approaches to achieve an optimal computational efficiency and predictive accuracy while reducing reliance on extensive offline training. The framework is developed and evaluated for modeling rotating detonation engines (RDEs), which provide a challenging test environment involving strongly convection-dominated, transient, and multiscale reacting-flow dynamics.