A symbolic regression-based implicit algebraic stress turbulence model: Incorporating the production of Reynolds stress anisotropy tensor

Turbulence constitutes an exceptionally complex and irregular flow phenomenon that manifests in liquids, gases, and plasma, making it ubiquitous in both natural processes and engineering applications. Given the relatively modest advancements in classical turbulence models over the past half-century, data-driven approaches, such as machine learning, have recently gained considerable traction in turbulence model research. In this study, we introduce a symbolic regression-based implicit algebraic stress turbulence model that incorporates the production of the Reynolds stress anisotropy tensor, thereby capturing the contribution of the shape of local turbulence produced by the mean flow field. We rigorously evaluate our model across five distinct characteristic flow cases and benchmark it against three alternative turbulence models. Our comprehensive analysis demonstrates that the proposed model exhibits robust performance and substantial generalizability across all test cases while manifesting notable advantages when compared with the reference turbulence models.