Tensor basis neural networks for unsteady turbulent flow prediction

Turbulence modeling remains a central challenge in computational fluid dynamics, particularly in unsteady flow regimes where traditional Reynolds-averaged Navier–Stokes (RANS) models exhibit limitations. Recent advances in data-driven turbulence modeling have demonstrated considerable potential, utilizing high-fidelity datasets derived from direct numerical simulations to improve predictive accuracy. Among these data-driven methodologies, tensor basis neural networks (TBNNs) stand out by embedding physics-informed constraints that respect fundamental turbulence properties, notably Galilean invariance. This study presents a novel extension of the TBNN approach to unsteady turbulent flows through integration with long short-term memory (LSTM) networks. The resulting TBNN–LSTM architecture leverages sequential modeling capabilities to ensure temporal coherence in predictions of the anisotropic Reynolds stress tensor. Furthermore, the model is integrated with the k-corrective frozen RANS approach, where k denotes the turbulent kinetic energy density. This integration addresses the persistent issue of ill-conditioning in data-driven RANS modeling, wherein even accurate Reynolds stress predictions may lead to substantial errors in the resulting mean velocity fields. The hybrid TBNN–LSTM and k-corrective frozen RANS framework introduced herein bridges the gap between traditional turbulence modeling methods and contemporary data-driven approaches, delivering substantial improvements in the accuracy and reliability of flow predictions. Particularly, this hybrid method demonstrates enhanced capability in capturing complex oscillatory boundary layer dynamics, which is especially relevant to coastal engineering applications. The current study validates the model within the interpolation range Reδ=846−1475. Results from this study underscore the method's efficacy, positioning it as a promising advancement toward robust, physically-consistent modeling of unsteady turbulent flows.