Numerically Consistent Non-Boussinesq Subgrid-scale Stress Model with Enhanced Convergence

TL;DR

This paper introduces a machine-learning-based subgrid-scale stress model for large-eddy simulation that ensures numerical consistency, better captures complex flow features, and exhibits monotonic convergence with grid refinement.

Contribution

It develops a numerically consistent, non-Boussinesq SGS model with multi-task learning to improve LES accuracy and convergence in complex turbulent boundary layers.

Findings

Improved predictions of mean velocity and wall-shear stress.

Achieves monotonic convergence with grid refinement.

Outperforms the Dynamic Smagorinsky model in tests.

Abstract

We extend the data-assimilation approach of Ling and Lozano-Dur\'an (AIAA 2025-1280) to develop machine-learning-based subgrid-scale stress (SGS) models for large-eddy simulation (LES) that are consistent with the numerical scheme of the flow solver. The method accounts for configurations with two inhomogeneous directions and is applied to turbulent boundary layers (TBL) under adverse pressure gradients (APG). To overcome the limitations of linear eddy-viscosity closures in complex flows, we adopt a non-Boussinesq SGS formulation along with a dissipation-matching training loss. A second improvement is the integration of a multi-task learning strategy that explicitly promotes monotonic convergence with grid refinement, a property that is often absent in conventional SGS models. A posteriori tests show that the proposed model improves predictions of the mean velocity and wall-shear stress relative to the Dynamic Smagorinsky model (DSM), while also achieving monotonic convergence with grid refinement.