Self-scaling tensor basis neural network for Reynolds stress modeling of wall-bounded turbulence
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917397848391680 |
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| author | Yuan, Zelong Li, Yuzhu Pearl |
| author_facet | Yuan, Zelong Li, Yuzhu Pearl |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29659 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Self-scaling tensor basis neural network for Reynolds stress modeling of wall-bounded turbulence Yuan, Zelong Li, Yuzhu Pearl Fluid Dynamics 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. |
| title | Self-scaling tensor basis neural network for Reynolds stress modeling of wall-bounded turbulence |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2603.29659 |