On-the-fly Reduced-Order Modeling of the Filter Density Function with Time-Dependent Subspaces

作     者：Aitzhan, Aidyn Givi, Peyman Babaee, Hessam 

作者机构：NVIDIA Corporation Santa ClaraCA95051 United States Mechanical Engineering and Materials Science University of Pittsburgh PittsburghPA15261 United States 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2025年

核心收录：

主　　题：Matrix factorization 

摘      要：A dynamical low-rank approximation is developed for reduced-order modeling (ROM) of the filtered density function (FDF) transport equation, which is utilized for large eddy simulation (LES) of turbulent reacting flows. In this methodology, the evolution of the composition matrix describing the FDF transport via a set of Langevin equations is constrained to a low-rank matrix manifold. The composition matrix is approximated using a low-rank factorization, which consists of two thin, time-dependent matrices representing spatial and composition bases, along with a small time-dependent coefficient matrix. The evolution equations for spatial and composition subspaces are derived by projecting the composition transport equation onto the tangent space of the low-rank matrix manifold. Unlike conventional ROMs, such as those based on principal component analysis, both subspaces are time-dependent and the ROM does not require any prior data to extract the low-dimensional subspaces. As a result, the constructed ROM adapts on the fly to changes in the dynamics. For demonstration, LES via the time-dependent bases (TDB) is conducted of the canonical configuration of a temporally developing planar CO/H2 jet flame. The flame is rich with strong flame-turbulence interactions resulting in local extinction followed by re-ignition. The combustion chemistry is modeled via the skeletal kinetics, containing 11 species with 21 reaction steps. It is shown that the FDF-TDB yields excellent predictions of various statistics of the thermochemistry variables, as compared to the full-order model (FOM). © 2025, CC BY-NC-ND.