A realizable and scale-consistent data-driven non-linear eddy viscosity modeling framework for arbitrary regression algorithms

• Published in: The International journal of heat and fluid flow 2022-10, Vol.97, p.109018, Article 109018
• Main Authors: Mandler, Hannes, Weigand, Bernhard
• Format: Article
• Language: English
• Subjects: Data-driven turbulence modeling; Gene expression programming; Neural network; RANS closure; Univariate regression
• ISSN: 0142-727X; 1879-2278
• DOI: 10.1016/j.ijheatfluidflow.2022.109018

A data-driven modeling framework for non-linear eddy viscosity models is presented. In contrast to the majority of similar approaches, it splits the multivariate regression problem into a set of univariate problems and is, furthermore, independent of a specific machine learning algorithm. Instead of inferring the closure equation from high-fidelity data as a whole, the coefficients of the tensor polynomial are learned individually. The target variables are obtained from an efficient field inversion procedure by virtue of successive tensor projections. The hypotheses for each closure coefficient are then fitted separately by employing an arbitrary regression technique. Ordinary curve fitting, neural networks and gene expression programming are considered as examples. The robustness of the model against an extrapolation and the stability of the solver are promoted by coefficient limiters and a full barycentric realizability correction. Additionally, turbulent scale consistency is guaranteed by a k-corrective frozen-RANS method, which is the subject of a companion paper (Mandler and Weigand, 2022). The proposed strategy leads to models which are well suited for the application to the same class of flows they were inferred from, namely separated channel flows. As proven by an extensive extrapolation study, the resulting neuralSST model is robust against geometry and Reynolds number modifications provided the type of flow does not drastically change. It consistently outperforms both the shear stress transport (SST) and a more complex elliptic-blending model and agrees well with the reference data. •A data-driven non-linear eddy viscosity model with varying coefficients is proposed.•Field-inversion is efficiently solved by a series of successive tensor projections.•Inference is significantly simplified by physics-based data preparation.•The modeling strategy is independent of the regression algorithm.•The model is validated on test cases with different geometries and Reynolds numbers.