Self-scaling tensor basis neural network for Reynolds stress modeling of wall-bounded turbulence

TL;DR

The paper introduces a self-scaling tensor basis neural network (STBNN) that enhances Reynolds-stress modeling in wall-bounded turbulence by incorporating an intrinsic, geometry-independent normalization, improving robustness and generalization across Reynolds numbers and geometries.

Contribution

It proposes a novel self-scaling tensor basis neural network that maintains physical invariance and generalizes well for Reynolds-stress modeling in wall-bounded turbulence.

Findings

STBNN accurately reproduces Reynolds-stress anisotropy with over 99% correlation.

The model predicts mean velocity profiles closely matching DNS data.

It generalizes from low to high Reynolds numbers and unseen geometries.

Abstract

Recent advances in data-driven turbulence modeling have established tensor basis neural networks (TBNN) as a physically grounded framework for Reynolds-stress closure in Reynolds-averaged Navier-Stokes (RANS) simulations. However, their robustness in wall-bounded turbulent flows remains limited across Reynolds numbers and geometries due to the lack of an intrinsic scaling mechanism. In this work, we propose a self-scaling tensor basis neural network (STBNN) for Reynolds-stress modeling of wall-bounded turbulence. The model incorporates an invariant velocity-gradient normalization derived from the first two invariants of the velocity-gradient tensor, providing an intrinsic and geometry-independent scale that balances strain and rotation effects without relying on empirical coefficients or wall-distance inputs. Owing to its frame-indifferent formulation, the approach preserves Galilean and rotational invariance while maintaining a physically interpretable representation of Reynolds-stress anisotropy. STBNN is evaluated through a priori and a posteriori studies using direct numerical simulation (DNS) data of canonical wall-bounded flows, including plane channel and periodic hill flows. In a priori tests, the model accurately reproduces Reynolds-stress anisotropy, with correlation coefficients exceeding 99% and relative errors below 10%, while capturing near-wall scaling and logarithmic-layer behavior. In a posteriori RANS simulations, STBNN predicts mean velocity profiles in close agreement with DNS and improves prediction of separation and reattachment compared with linear and quadratic eddy-viscosity models and the baseline TBNN. Notably, a model trained at low Reynolds numbers generalizes to higher Reynolds numbers and unseen geometries. These results demonstrate the effectiveness of the proposed framework for data-driven Reynolds-stress modeling in wall-bounded turbulent flows.