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

by   Donya Ramezanian, et al.

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.



There are no comments yet.


page 11

page 12

page 15

page 16


Reduced order modeling with time-dependent bases for PDEs with stochastic boundary conditions

Low-rank approximation using time-dependent bases (TDBs) has proven effe...

Scalable In Situ Compression of Transient Simulation Data Using Time-Dependent Bases

Large-scale simulations of time-dependent problems generate a massive am...

An asymptotic-preserving dynamical low-rank method for the multi-scale multi-dimensional linear transport equation

We introduce a dynamical low-rank method to reduce the computational com...

Implicit Methods with Reduced Memory for Thermal Radiative Transfer

This paper presents approximation methods for time-dependent thermal rad...

Tropical Abstraction of Biochemical Reaction Networks with Guarantees

Biochemical molecules interact through modification and binding reaction...

Time-dependent stochastic basis adaptation for uncertainty quantification

We extend stochastic basis adaptation and spatial domain decomposition m...

Prediction of magnetization dynamics in a reduced dimensional feature space setting utilizing a low-rank kernel method

We establish a machine learning model for the prediction of the magnetiz...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.