When simulating fluids the industry standard is Reynolds averaged Navier-Stokes (RANS). However, the results for certain flows are inaccurate. The main source of error in popular RANS turbulence models is the Boussinesq approximation, assuming a linear relationship between the Reynolds stress anisotropy and the mean rate of strain. Experiments show this is simply not correct. Most state of the art research in data driven turbulence modelling is focused on replacing or augmenting this linear relationship.

The research presented in this report implements two corrections, one to the Reynolds stress anisotropy and another to account for the modified production of turbulent kinetic energy by the modified anisotropy tensor. The magnitude of the required corrections is found by comparing RANS simulations to more detailed CFD algorithms such as large eddy simulation and direct numerical simulation.

A state of the art symbolic regressions framework named deep symbolic regression (DSR) is used to find explicit algebraic Reynolds stress models. DSR uses a recurrent neural network to create expressions and is able to find complex expressions that fit the data very well.

The expressions found with DSR are implemented in a custom k-omega SST turbulence model and validated in CFD. Large improvements over the standard turbulence model are achieved. The results are compared to results of the SpaRTA framework where the same method of corrections is applied. DSR is able to produce better fitting expressions and these result in improved flow fields over the best models found with SpaRTA.

The best model is also tested in a true prediction of a flow at a Reynolds number that is roughly three times as large as values encountered during training. The results are good, showing generalisability of the model outside training conditions.