Leon Riccius presents his M.Sc. thesis on "Machine Learning Augmented Turbulence Modelling for the Reynolds Stress Closure Problem"

Abstract
The availability of high-performance computational resources have increased steadily, but
we are still far form the capacity to perform high-fidelity simulations for turbulent flows
in real-words applications. Thus, we still rely on computationally cheaper surrogates like
Reynolds-Averaged Navier-Stokes (RANS) turbulence modeling. The most commonly used
RANS models are the linear eddy viscosity models (LEVM), which rely on the turbulent vis-
cosity hypothesis for their Reynolds stress closure, a known source of structural uncertainty.
Despite the development of theoretically superior turbulence models such as algebraic mod-
els or Reynolds stress transport models, the LEVMs remain the most widely used class of
turbulence models due to their efficiency and stability. This work combined a nonlinear eddy
viscosity model with a deep neural network to yield improved predictions of the anisotropy
tensor on flow cases with surface curvature and flow separation traditionally challenging to
LEVMs. The neural network used an extensive set of rotationally invariant local flow fea-
tures for predictions and incorporates realizability constraints in the training process. Using
visualizations based on the barycentric map, our results indicate that the proposed machine
learning method’s predicted anisotropy tensor offers significant improvement over the best
performing LEVM (baseline) and compares very well with the DNS/LES (ground truth). The
predicted anisotropy tensor was able to uncover secondary flow information in some flow
cases. However, in a significant number of cases, the improved predictions did not translate
into an improvement of the mean velocity and pressure fields when measured against the
best-performing LEVM.