# A data-driven approach for the closure of RANS models by the divergence of the Reynolds Stress Tensor

arXiv: https://arxiv.org/abs/2203.16944 · HTML: https://mlsanity.com/paper/2203.16944/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 40 references that are in the map.
- First posted on arXiv 31 Mar 2022.

## Builds on (most cited first, 4 of 4)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Turbulent scalar flux in inclined jets in crossflow: counter gradient transport and deep learning modelling](https://mlsanity.com/paper/2001.04600/) (2020)

## Built on by (most cited first, 1 of 1)

- [A Deep Learning algorithm to accelerate Algebraic Multigrid methods in Finite Element solvers of 3D elliptic PDEs](https://mlsanity.com/paper/2304.10832/) (2023)

## Abstract (arXiv)

In the present paper a new data-driven model is proposed to close and increase accuracy of RANS equations. The divergence of the Reynolds Stress Tensor (RST) is obtained through a Neural Network (NN) whose architecture and input choice guarantee both Galilean and coordinates-frame rotation. The former derives from the input choice of the NN while the latter from the expansion of the divergence of the RST into a vector basis. This approach has been widely used for data-driven models for the anisotropic RST or the RST discrepancies and it is here proposed for the divergence of the RST. Hence, a constitutive relation of the divergence of the RST from mean quantities is proposed to obtain such expansion. Moreover, once the proposed data-driven approach is trained, there is no need to run any classic turbulence model to close the equations. The well-known tests of flow in a square duct and over periodic hills are used to show advantages of the present method compared to standard turbulence models.