A priori screening of data-enabled turbulence models

Abstract

Assessing the compliance of a white-box turbulence model with known turbulent knowledge is straightforward. It enables users to screen conventional turbulence models and identify apparent inadequacies, thereby allowing for a more focused and fruitful validation and verification. However, comparing a black-box machine-learning model to known empirical scalings is not straightforward. Unless one implements and tests the model, it would not be clear if a machine-learning model, trained at finite Reynolds numbers preserves the known high Reynolds number limit. This is inconvenient, particularly because model implementation involves retraining and re-interfacing. This work attempts to address this issue, allowing fast a priori screening of machine-learning models that are based on feed-forward neural networks (FNN). The method leverages the mathematical theorems we present in the paper. These theorems offer estimates of a network's limits even when the exact weights and biases are unknown. For demonstration purposes, we screen existing machine-learning wall models and RANS models for their compliance with the log layer physics and the viscous layer physics in a priori manner. In addition, the theorems serve as essential guidelines for future machine-learning models.