Explorations on Reduced Order Model Development for 2D Detonation Wave

In recent years, pressure gain combustion systems, specifically rotating detonation engines (RDEs), have exhibited great potential as a viable alternative to traditional combustion in propulsion applications. Though high-fidelity simulations have become accessible for RDE modeling, they remain computationally expensive for practical engineering applications. Recent advancement in reduced-order model (ROM) development provides an avenue to address this challenge. The goal of this study is to develop a reduced-order modelling framework for RDE simulations via model-order reduction (MOR) techniques. However, it is well recognized that the conventional MOR methods exhibit difficulties in capturing problems with convection-dominated physics (e.g., shocks and chemical reactions). Therefore, this work focuses on developing an adaptive ROM method leveraging a recently developed formulation, model-form preserving least-squares projections with variable transformation (MP-LSVT). We will demonstrate the adaptive ROM method on a canonical two-dimensional RDE configuration with imposed periodic boundary conditions. Put simply, this framework will serve to make high-fidelity modeling of rotating detonation engines computationally efficient and aid in the design of future propulsive devices.