Normalizing Flows as a Novel PDF Turbulence Model

TL;DR

This paper introduces normalizing flows as a new method for turbulence modeling within RANS equations, enabling direct sampling of turbulent quantities from learned PDFs, demonstrated on homogeneous shear turbulence.

Contribution

It presents a novel application of normalizing flows as a PDF turbulence model for RANS, offering a direct sampling approach for turbulent quantities.

Findings

Successful application to homogeneous shear turbulence

Enables direct sampling from turbulence PDFs

Uses DNS data for training

Abstract

In this paper, we propose normalizing flows (NF) as a novel probability density function (PDF) turbulence model (NF-PDF model) for the Reynolds-averaged Navier-Stokes (RANS) equations. We propose to use normalizing flows in two different ways: firstly, as a direct model for the Reynolds stress tensor, and secondly as a second-moment closure model, i.e. for modeling the pressure-strain and dissipation tensor in the Reynolds stress transport equation. In classical PDF closure models, a stochastic differential equation has to be modeled and solved to obtain samples of turbulent quantities. The NF-PDF closure model allows for direct sampling from the underlying probability density functions of fluctuating turbulent quantities, such that ensemble-averaged quantities can then be computed. To illustrate this approach we demonstrate an application for the canonical case of homogeneous shear turbulence. Training data are extracted from high-fidelity direct numerical simulations (DNS).