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

TL;DR

This work tackles the challenge of numerically consistent subgrid-scale closures for wall-modeled LES in flows with multiple inhomogeneous directions, specifically an adverse-pressure-gradient turbulent boundary layer. It introduces a non-Boussinesq tensorial SGS formulation whose closure coefficients are predicted by a dual-output ANN, with inputs derived from dimensionless invariants chosen via Buckingham-$\pi$, and trains the model using a data-assimilation framework based on statistical nudging that enforces solver-consistent forcing and dissipation. A key innovation is incorporating a dissipation-matching loss and a resolution-aware multi-task learning strategy to enforce monotonic convergence with grid refinement. The results show improved mean velocity and wall-shear predictions over Dynamic Smagorinsky and robust, monotonic grid convergence, demonstrating practical potential for WMLES in complex geometries and providing a path toward scalable, physics-informed ML closures.

Abstract

We extend the data-assimilation approach of Ling and Lozano-Durán (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.

Figures (8)

• Figure 1: The three main steps for constructing the numerically consistent BFM SGS model.
• Figure 2: Schematic of the DNS setup of the APG TBL.
• Figure 3: Some properties of the APG TBL computed by DNS are used for training and testing. (a) Clauser parameter $\beta$. (b) Momentum-thickness Reynolds number $Re_{\theta}$.
• Figure 4: Schematic of nudging. Compared to the unnudged trajectory, nudging pushes the system to better match the true trajectory. The red circles are observations that are assumed to be the truth. Adapted from aschDataAssimilationMethods2016.
• Figure 5: (a) The contour plot of the normalized instantaneous streamwise velocity at the center plane of the computational domain for the data generation of APG TBL case with a coarse grid. (b) The Voronoi grid in the black rectangular region shown in the left plot.