The past few years have witnessed a renewed blossoming of data-driven turbulence models. Quantification of the concomitant modeling uncertainty, however, has been mostly omitted, and the generalization performance of the data-driven models is still facing great challenges when predicting complex flows with different flow physics not seen during training. A robust data-driven Reynolds-averaged turbulence model with uncertainty quantification and non-linear correction is proposed in this work with the Bayesian deep neural network. In this model, the Reynolds stress tensor is decomposed into linear and non-linear parts. The linear part is taken as the usual linear eddy viscosity model while the non-linear counterpart is learned by a Bayesian deep neural network. Independent tensor bases of invariants and tensors constituted by mean strain rate tensor and rotation rate tensor are embedded into the neural network to effectively consider key turbulence features in different flows. The proposed model is well validated through numerical simulations of four canonical flows that significantly deviate in geometrical configurations and/or Reynolds numbers from those in the training data. With the non-linear corrections of embedded invariants and tensors representing key features of turbulence, the proposed model not only improves the predictive capabilities of Reynolds-averaged turbulence models on the same mesh but also has better generalization performance when simulating complex turbulent flows with large scale separation. In addition, this model allows to quantitatively demonstrate the confidence interval of the predicted flow quantities that are originated from the model itself.

The paper is available at https://pubs.aip.org/aip/pof/article/35/5/055119/2889073/Data-driven-Reynolds-averaged-turbulence-modeling

The framework utilized in the present work for formulating data-driven turbulence model is shown below:

It is shown that the built model can improve the RANS predictions:

Ubuntu 20.04, OpenFOAM-7, Python 3.7, PyTorch 1.7, libtorch 1.7

See this file for using PyTorch neural network model with OpenFOAM, please.

I have prepared a docker image with all libraries and solvers installed. You can download it here. For the usage of docker, you can get some something useful here.

Note: I changed the OpenFOAM source code when doing this work. The best way is to leave the OpenFOAM source code as it is and compile the source files as user libraries and solvers.

This work is based on rans-uncertainty. Thank Dr. Nicholas Geneva for sharing the code and data.

Dr. Andre Weiner has written very good tutorials for using OpenFOAM with PyTorch and Docker.

If you encounter problems, feel free to open an issue. You can also email me ([email protected], Hongwei Tang).

If you find this work useful for your research, please consider citing our work

@article{10.1063/5.0149547,
    author = {Tang, Hongwei and Wang, Yan and Wang, Tongguang and Tian, Linlin and Qian, Yaoru},
    title = "{Data-driven Reynolds-averaged turbulence modeling with generalizable non-linear correction and uncertainty quantification using Bayesian deep learning}",
    journal = {Physics of Fluids},
    volume = {35},
    number = {5},
    year = {2023},
    month = {05},
    issn = {1070-6631},
    doi = {10.1063/5.0149547},
    url = {https://doi.org/10.1063/5.0149547},
    note = {055119}
}