On-the-fly Reduced Order Modeling of Passive and Reactive Species via Time-Dependent Manifolds

Abstract

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.

Skeletal Model Reduction with Forced Optimally Time Dependent Modes

“…The key characteristic of f-OTD is that both U (t) and Y (t) are time-dependent and they evolve based on closed form evolution equations extracted from the model, and are able to capture sudden transitions associated with the largest finite time Lyapunov exponents [33]. The time-dependent bases have also been used for the purpose of stochastic reduced order modeling [34][35][36][37][38] and recently for on the fly reduced order modeling of reactive species transport equation [39]. In a nutshell, f-OTD workflow i) is forward in time unlike AE, ii) bypasses the computational cost of solving FD and SE, or other data-driven reduction techniques, and iii) stores the modeled sensitivities in a reduced format unlike FD, SE and AE.…”