2021/01/11 by Donya Ramezanian, Arash G. Nouri, Hessam Babaee · 45 citations
Chemistry · Computer Science · Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Artificial intelligence #Biological system #Chemistry #Combustion and flame dynamics #Computer science #Dimension (graph theory) #Dimensionality reduction #Eigenvalues and eigenvectors #Fluid Dynamics and Turbulent Flows #Intrinsic dimension #Manifold (fluid mechanics) #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Matrix decomposition #Model Reduction and Neural Networks #Orthonormal basis #Physics #Principal component analysis #Pure mathematics #Rank (graph theory) #Statistics #cs.CE
paper · pdf · doi:10.1016/j.cma.2021.113882
published in Computer Methods in Applied Mechanics and Engineering 382, 113882 (Elsevier BV)
arxiv created 2021/01/11 · openalex created_date 2021/01/18 · openalex publication_date 2021/05/04 · arxiv updated 2021/05/19 · openalex updated_date 2026/08/05
One of the principal barriers in developing accurate and tractable predictive models in turbulent flows with a large number of species is to track every species by solving a separate transport equation, which can be computationally impracticable. In this paper, we present an on-the-fly reduced order modeling of reactive as well as passive transport equations to reduce the computational cost. The presented approach seeks a low-rank decomposition of the species to three time-dependent components: (i) a set of orthonormal spatial modes, (ii) a low-rank factorization of the instantaneous species correlation matrix, and (iii) a set of orthonormal species modes, which represent a low-dimensional time-dependent manifold. Our approach bypasses the need to solve the full-dimensional species to generate high-fidelity data - as it is commonly performed in data-driven dimension reduction techniques such as the principle component analysis. Instead, the low-rank components are directly extracted from the species transport equation. The evolution equations for the three components are obtained from optimality conditions of a variational principle. The time-dependence of the three components enables an on-the-fly adaptation of the low-rank decomposition to transient changes in the species. Several demonstration cases of reduced order modeling of passive and reactive transport equations are presented.