The code in this repository features a Python implemention of Physics-informed neural networks (PINNs) for solving the Reynolds-averaged Navier–Stokes (RANs)equations for incompressible turbulent flows without any specific model or assumption for turbulence. The input data are spatial coordinates (x, y) only taken at the domain boundaries.

More details about the implementation and results from the training are available in "Physics-informed neural networks for solving Reynolds-averaged Navier–Stokes equations", Hamidreza Eivazi, Mojtaba Tahani, Philipp Schlatter, Ricardo Vinuesa(2022,Physics of Fluids)

The code was run successfully using Tensorflow>=2.6.0, using 1 GPU for training. In addition, scipy is necessary for implementing optimization algorithm

The dataset used for training and testing are available in order to ensure the reproducibility of the results.

In this repository, the database for zero-presure-gradient Boundary Layer and turbulent flows over NACA4412 airfoil are required to be downloaded manually.

The links of file have been provided in ZPG and NACA

Please, get in touch using the email address for correspondance in the paper to arrange the transfer.

The PINNs training and prediction can be performed after cloning the repository.

Take Falker-Skan(FS) Boundary Layer as example:

git clone  https://github.com/Fantasy98/Physics-informed-neural-networks-for-solving-Reynolds-averaged-Navier-Stokes-equations.git
cd FS
python train.py

All the training parameters are defined in the train_configs.py

For postprocessing the reults, it can be performed as follows:

python postprocessing.py

All cases follow the same file structure, take Falker-Skan(FS) Boundary Layer as example, the files follow structure below:

FS
├── data
├── pred
├── figs
├── models
├── train_configs.py
├── PINN.py
├── lbfgs.py
├── postprocessing.py
├── error.py
└── train.py

data: Folder to store the boundary layer data

pred: Folder to store the prediction results

models: Folder to store the trainede models

figs: Folder to store the postprocessed figures

train_configs.py: Definition of training parameters

PINN.py: class object of PINN

lbfgs.py: optimizer based on L-BFGS algorithm

postprocessing.py: script for postprocessing results.

error.py: function for error assessment used in paper.

train.py: script for training PINNs model