An NN-improved SST turbulence model with varying Prt (turbulence heat flux term) and β (Reynolds stress term) was trained, and the NN-SST turbulence model is coupled with the HISA solver through the TensorFlow API

Environment configuration:

[1] The EnKF algorithm adopts the open-source data assimilation and field inversion framework DAFI, so the inversion environment needs to be configured first by following the instructions at: https://dafi.readthedocs.io/en/latest/install.html#

[2] This work uses TensorFlow 2.13.0, and the corresponding environment should be set up using pip install by installing the appropriate version and downloading the matching API libraries at: https://www.tensorflow.org/install/lang_c#.

[3] The HISA solver is a C++ based tool for computing compressible transonic and supersonic flow (https://hisa.gitlab.io/#). In this work, this solver is complined based on OpenFoam v2012 coupled with NN enhanced turbulence heat flux and Reynolds stress.

[4] Compile the compressible turbulence model by running wmake in the ./TurbulenceModels/turbulenceModels director, and then run wmake in the ./TurbulenceModels/compressible director.

[5] Compile the feature extraction program writeFieldsMLr4.C by running wmake, which is used to extract NN inputs during the training process.

Models training:

Once the above environment is installed, the training program can be executed by running: python /path/to/bin/dafi dafi.in, by running the pltmisfit.py to plot the convergence history

Models testing:

Enable fully coupled model evaluation by setting betannmodel 1; Prtnnmodel 1; in the constant/turbulenceProperties file, then run ./runsim in the case directory.