Adaptive Projection-Based Reduced Order Modeling of Chemically Reacting Flows

Projection-based reduced-order modeling (ROM) offers a computationally efficient framework for high-fidelity simulation-based design studies. In this study, we examine the capabilities of Galerkin projection-based ROM techniques for simulating convection-dominated chemically reacting flows. Specifically, we evaluate the performance of an adaptive ROM technique in comparison to a classical projection-based ROM. In the classical approach, first, a reduced basis space is constructed using the proper orthogonal decomposition (POD) during an offline stage. Afterward, the governing system of equations is projected to the reduced space, leading to a low-dimensional dynamical system, which is evolved during the online stage. As chemically reacting flows are governed by a highly nonlinear system of equations, a hyper-reduction strategy is essential to fully realize the computational efficiency. We employ the QR factorization with column pivoting-based discrete empirical interpolation method (QDEIM) coupled with randomized and feature-based sampling for hyper-reduction, which identifies the sampling locations in the computational domain where the full-order model evaluations of nonlinear terms are performed. In the adaptive ROM, both the reduced basis space and the sampling locations are dynamically updated during simulation to enable accurate and efficient simulation of convection-dominated flows. We assess the capabilities of the classical and adaptive ROMs by simulating several representative chemically reacting flows, including a freely propagating turbulent premixed flame, a propagating detonation wave, and a temporally evolving non-premixed jet flame exhibiting the presence of local extinction and re-ignition.