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

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.

Figures (15)

• Figure 1: Schematic diagram of the self-scaling tensor basis neural network (STBNN).
• Figure 2: Configurations of plane channel and periodic hill flows: (a) plane channel; and (b) periodic hill with varying hill steepness factor $\alpha$.
• Figure 3: Correlation coefficients of modeled deviatoric Reynolds stress components in plane channel flow across friction Reynolds numbers (${ Re}_\tau$): (a) $R_{11}^d$; (b) $R_{12}^d$; (c) $R_{22}^d$; (d) $R_{33}^d$.
• Figure 4: Relative errors of modeled deviatoric Reynolds stress components in plane channel flow across friction Reynolds numbers (${Re}_\tau$): (a) $R_{11}^d$; (b) $R_{12}^d$; (c) $R_{22}^d$; (d) $R_{33}^d$.
• Figure 5: Modeled deviatoric Reynolds stress components in plane channel flow at untrained friction Reynolds numbers ${Re}_\tau$. The rows correspond to ${Re}_\tau=550$, 5200, and 10000 (top to bottom), while the columns show $R_{11}^d$, $R_{22}^d$, and $R_{12}^d$ (left to right).