A PDE-free, neural network-based eddy viscosity model coupled with RANS equations

TL;DR

This paper introduces a PDE-free, neural network-based eddy viscosity model that, when coupled with RANS equations, offers a robust and stable alternative to traditional turbulence models, demonstrated on flow over periodic hills.

Contribution

The paper presents a novel neural network approach to model turbulence transport physics, replacing PDE-based models in RANS simulations, enhancing robustness and stability.

Findings

Successfully coupled neural network model with RANS solver

Demonstrated robustness on flow over periodic hills

Paves way for neural network emulation of Reynolds stress models

Abstract

Most turbulence models used in Reynolds-averaged Navier-Stokes (RANS) simulations are partial differential equations (PDE) that describe the transport of turbulent quantities. Such quantities include turbulent kinetic energy for eddy viscosity models and the Reynolds stress tensor (or its anisotropy) in differential stress models. However, such models all have limitations in their robustness and accuracy. Inspired by the successes of machine learning in other scientific fields, researchers have developed data-driven turbulence models. Recently, a nonlocal vector-cloud neural network with embedded invariance was proposed, with its capability demonstrated in emulating passive tracer transport in laminar flows. Building upon this success, we use nonlocal neural network mapping to model the transport physics in the k-epsilon model and couple it to RANS solvers, leading to a PDE-free eddy-viscosity model. We demonstrate the robustness and stability of the RANS solver with a neural network-based turbulence model on flows over periodic hills of parameterized geometries. Our work serves as a proof of concept for using a vector-cloud neural network as an alternative to traditional turbulence models in coupled RANS simulations. The success of the coupling paves the way for neural network-based emulation of Reynolds stress transport models.