Reduced Data-Driven Turbulence Closure for Capturing Long-Term Statistics

TL;DR

This paper presents a simplified, data-driven turbulence closure model that efficiently captures long-term statistical behavior of key quantities using a reduced scalar approach, outperforming traditional neural network methods in computational cost.

Contribution

The paper introduces a novel stochastic turbulence closure model based on a reduced scalar time series, simplifying the learning problem and improving computational efficiency.

Findings

The new model accurately captures long-term statistics of QoIs.

It is computationally cheaper than a-priori trained neural networks.

The approach effectively incorporates solver-surrogate interactions.

Abstract

We introduce a simple, stochastic, a-posteriori, turbulence closure model based on a reduced subgrid scale term. This subgrid scale term is tailor-made to capture the statistics of a small set of spatially-integrate quantities of interest (QoIs), with only one unresolved scalar time series per QoI. In contrast to other data-driven surrogates the dimension of the "learning problem" is reduced from an evolving field to one scalar time series per QoI. We use an a-posteriori, nudging approach to find the distribution of the scalar series over time. This approach has the advantage of taking the interaction between the solver and the surrogate into account. A stochastic surrogate parametrization is obtained by random sampling from the found distribution for the scalar time series. Compared to an a-priori trained convolutional neural network, evaluating the new method is computationally much cheaper and gives similar long-term statistics.