Abstract
A novel deterministic symbolic regression method SpaRTA (Sparse Regression of Turbulent Stress Anisotropy) is introduced to infer algebraic stress models for the closure of RANS equations directly from high-fidelity LES or DNS data. The models are written as tensor polynomials and are built from a library of candidate functions. The machine-learning method is based on elastic net regularisation which promotes sparsity of the inferred models. By being data-driven the method relaxes assumptions commonly made in the process of model development. Model-discovery and cross-validation is performed for three cases of separating flows, i.e. periodic hills (Re=10595), converging-diverging channel (Re=12600) and curved backward-facing step (Re=13700). The predictions of the discovered models are significantly improved over the k-ω SST also for a true prediction of the flow over periodic hills at Re=37000. This study shows a systematic assessment of SpaRTA for rapid machine-learning of robust corrections for standard RANS turbulence models.
Highlights
The capability of Computational Fluid Dynamics (CFD) to deliver reliable prediction is limited by the unsolved closure problem of turbulence modelling
The workhorse for turbulence modelling in industry are the Reynolds-Averaged Navier-Stokes (RANS) equations using linear eddy viscosity models (LEVM) [1]
Data-driven methods for turbulence modelling based on supervised machine learning have been introduced to leverage RANS for improved predictions [2,3,4]
Summary
Turbulence and Combustion (2020) 104:579–603 come at the price of uncertainty especially for flows with separation, adverse pressure gradients or high streamline curvature. The datadriven GEP method retains the input quantities used to derive EARSM, but replaces the commonly used projection method to find the formal structure of the model by an evolutionary process, which makes it an open-box machine learning approach The advantage of such a data-driven method is that instead of relying on assumptions made during the development of an EARSM, a model is inferred directly from data. While such a model might not provide an universal approach for all kinds of flows as commonly aimed for in physical modelling, it serves as a pragmatic tool to correct the flow at hand.
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