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

TL;DR

This paper introduces an on-the-fly reduced order modeling approach for passive and reactive species transport in turbulent flows, using time-dependent low-rank decompositions to significantly reduce computational costs without relying on full-dimensional data.

Contribution

The novel method directly extracts low-rank components from transport equations, enabling adaptive, on-the-fly reduced modeling without prior high-fidelity data generation.

Findings

Efficient reduction of computational cost in species transport simulations.

Adaptive low-rank decomposition captures transient species dynamics.

Demonstrated effectiveness on passive and reactive transport cases.

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.