Finding Closure Terms Directly from Coarse Data for 2D Turbulent Flow

TL;DR

This paper employs machine learning to directly derive closure terms from coarse data for 2D turbulent flow, improving the accuracy of coarse-grained flow evolution predictions.

Contribution

It introduces a neural network-based method to compute closure terms directly from coarse data, enhancing flow modeling accuracy without relying on traditional turbulence models.

Findings

Predicted flow evolution aligns well with filtered high-resolution results.

Method generalizes to flows not used in training.

Smoothing the neural network output improves stability.

Abstract

Machine learning is used to develop closure terms for coarse grained model of two-dimensional turbulent flow directly from the coarse grained data by adding a source term to the Navier-Stokes equations to ensure that the coarse-grained flow evolves in the correct way. The source term is related to the average flow using a Neural Network with a relatively simple structure and smoothed slightly to prevent instabilities in a posteriori test. The time dependent coarse grained flow field is generated by filtering fully resolved results and the predicted coarse field evolution agrees well with the filtered results, both for the flow used to learn the closure terms and for flows not used for the learning.