Sparse Bayesian Learning of Explicit Algebraic Reynolds-Stress models for turbulent separated flows

Abstract

A novel Sparse Bayesian Learning (SBL) framework is introduced for generating parsimonious stochastic algebraic stress closures for the Reynolds-Averaged Navier–Stokes (RANS) equations from high-fidelity data. The models are formulated as physically-interpretable frame-invariant tensor polynomials and built from a library of candidate functions. By their stochastic formulation, the learned model coefficients are described by probability distributions and are therefore equipped with an intrinsic measure of uncertainty. The SBL framework is used to derive customized stochastic closure models for three separated flow configurations, characterized by different geometries but similar Reynolds number. The resulting SBL models are then propagated through a CFD solver for all three configurations. The results show significantly improved predictions of velocity profiles and friction coefficient in the separation / reattachment region in comparison with a baseline LEVM (namely, k-ω SST model), for training as well as for test cases. In all cases, the computed uncertainty intervals encompass reasonably well the reference data. Furthermore, the stochastic outputs enable a global sensitivity analysis with respect to the model terms selected by the algorithm, thus providing insights in view of further improvements of EARSM-type corrections.