A highly accurate strategy for data-driven turbulence modeling

We develop a data-driven machine learning (ML) turbulence model and conduct a comparative study with representative approaches employed in the literature. The new approach is based on a recently proposed method to extract, from the mean velocity field high-fidelity data, the essential information to construct the Reynolds force vector (RFV). This quantity was shown to produce less error propagation, significantly enhancing the accuracy of the solution of Reynolds-averaged Navier–Stokes (RANS) equations, which were shown to be ill-conditioned. This fact motivates the use of the RFV as a target for ML techniques. Invariance is enforced by means of a procedure where vectorial and tensorial quantities are represented using an intrinsic local coordinate system associated with the eigenvectors of the rate-of-strain tensor of the baseline solution. The proposed hybrid method employs an implicit procedure for the linear part of the RFV. This structure is applied to two geometries analyzed in the literature, namely the square duct and the periodic hill flows, using direct numerical simulation (DNS) as the data source for learning and κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa $$\end{document}–ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document} RANS simulations as the baseline solution. A random-forest (RF) approach is employed for the machine learning process. When compared with other approaches, the new hybrid method shows lower error propagation from the predictions of the ML approach for both geometries, illustrating the potential of this model strategy.