Elastoinertial turbulence: Data-driven reduced-order model based on manifold dynamics

TL;DR

This paper develops a data-driven reduced-order model for elastoinertial turbulence that captures complex flow dynamics with only 50 degrees of freedom, significantly reducing computational costs.

Contribution

It introduces a novel combination of viscoelastic POD, autoencoders, and neural ODEs to accurately model 2D EIT dynamics in a low-dimensional space.

Findings

Model accurately captures short- and long-time EIT dynamics

Reduces degrees of freedom from 10^6 to 50

Replicates self-similar traveling wave structures

Abstract

Elastoinertial turbulence (EIT) is a chaotic state that emerges in the flows of dilute polymer solutions. Direct numerical simulation (DNS) of EIT is highly computationally expensive due to the need to resolve the multi-scale nature of the system. While DNS of 2D EIT typically requires $O(10^6)$ degrees of freedom, we demonstrate here that a data-driven modeling framework allows for the construction of an accurate model with 50 degrees of freedom. We achieve a low-dimensional representation of the full state by first applying a viscoelastic variant of proper orthogonal decomposition to DNS results, and then using an autoencoder. The dynamics of this low-dimensional representation are learned using the neural ODE method, which approximates the vector field for the reduced dynamics as a neural network. The resulting low-dimensional data-driven model effectively captures short-time dynamics over the span of one correlation time, as well as long-time dynamics, particularly the self-similar, nested traveling wave structure of 2D EIT in the parameter range considered.