Comparison of different data-assimilation approaches to augment RANS turbulence models

Reynolds-averaged Navier-Stokes (RANS) simulations are the most widespread approach to predict turbulent flows typical of industrial problems. Despite its success, the inherent simplifications and assumptions used to model the unknown Reynolds stresses are sources of inaccuracies. With this in mind, data-assimilation (DA) techniques can be used to minimize errors between the predicted and the exact flow fields by optimizing a space-dependent correction term. This correction term can be subsequently fed into machine learning algorithms to enhance RANS turbulence models. The main objective of this work is to assess the performance of several correction terms to match a full mean-flow velocity field, provided by averaged DNS simulations, and analyze the pros and cons of each when used subsequently in a machine-learning based RANS framework. Three configurations were chosen to perform the analysis: the converging-diverging channel at Re = 12600, the flow over periodic hills at Re = 2800, and the square cylinder at Re = 22000. Six different correction terms were considered and discussed in this paper. Assimilations based on eddy-viscosity corrections, albeit constrained by the Boussinesq hypothesis, were able to correct the velocity field even for flows exhibiting large recirculation regions. However, the precise choice of the correction term employed has a major impact in the optimization process. On the other hand, when correction is applied as source terms in the momentum equations, better fit of the corrected mean-flow field is achieved.