General-purpose Data-driven Wall Model for Low-speed Flows Part I: Baseline Model

Abstract

We present a general-purpose wall model for large-eddy simulation. The model builds on the building-block flow principle, leveraging essential physics from simple flows to train a generalizable model applicable across complex geometries and flow conditions. The model addresses key limitations of traditional equilibrium wall models (EQWM) and improves upon shortcomings of earlier building-block-based approaches. The model comprises four components: (i) a baseline wall model, (ii) an error model, (iii) a classifier, and (iv) a confidence score. The baseline model predicts the wall-shear stress, while the error model estimates epistemic errors and aleatoric errors, both used for uncertainty quantification. In Part I of this work, we present the baseline model, while the remaining three components are introduced in Part II. The baseline model is designed to capture a broad range of flow phenomena, including turbulence over curved walls and zero, adverse, and favorable mean pressure gradients, as well as flow separation and laminar flow. The problem is formulated as a regression task to predict wall shear stress using a neural network. Model inputs are localized in space and dimensionless, with their selection guided by information-theoretic criteria. Training data include, among other cases, a newly generated direct numerical simulation dataset of turbulent boundary layers under favorable and adverse PG conditions. Validation is carried out through both a priori and a posteriori tests. The a priori evaluation spans 140 diverse high-fidelity numerical datasets and experiments (67 training cases included), covering turbulent boundary layers, airfoils, Gaussian bumps, and full aircraft geometries, among others. We demonstrate that the baseline wall model outperforms the EQWM in 90% of test scenarios, while maintaining errors below 20% for 98% of the cases.