Model Order Reduction for Reacting Flows: Laminar Gaussian Flame Applications

Abstract

A model reduction technique based on Galerkin projection, proper orthogonal decomposition (POD), and the discrete empirical interpolation method (DEIM) is developed for chemically reacting flow applications. These applications are challenging problems which involve a strong coupling between fluid dynamics and chemical kinetics, a wide range of temporal and spatial scales, and highly nonlinear chemical kinetics. These problems often require a very long simulation time. In this study, the POD technique combined with Galerkin projection reduces the dimension of unknown chemical concentrations over the spatial domain, while the DEIM approximates the nonlinear chemical source term at interpolation points. The combined method provides an efficient offline–online solution strategy that enables rapid solution of the reduced-order model. Application of the technique to a premixed Gaussian flame leads to a reduced-order model with state dimension several orders of magnitude smaller than the original system. In this case, a reduced-order model with state dimension of 60 accurately approximates a full model with a dimension of about 100,000. This accelerates the simulation of the chemical kinetics by more than two orders of magnitude. The reduced-order model is used to analyse the sensitivity of outputs of interest with respect to uncertain input parameters describing the reaction kinetics.