A data-driven approach for the closure of RANS models by the divergence of the Reynolds Stress Tensor

Abstract

In the present paper a new data-driven model is proposed to close and increase accuracy of RANS equations. The divergence of the Reynolds Stress Tensor (RST) is obtained through a Neural Network (NN) whose architecture and input choice guarantee both Galilean and coordinates-frame rotation. The former derives from the input choice of the NN while the latter from the expansion of the divergence of the RST into a vector basis. This approach has been widely used for data-driven models for the anisotropic RST or the RST discrepancies and it is here proposed for the divergence of the RST. Hence, a constitutive relation of the divergence of the RST from mean quantities is proposed to obtain such expansion. Moreover, once the proposed data-driven approach is trained, there is no need to run any classic turbulence model to close the equations. The well-known tests of flow in a square duct and over periodic hills are used to show advantages of the present method compared to standard turbulence models.

arXiv comment26 pages, 13 figures

References in corpus (13)

• Adam: A Method for Stochastic Optimization
• Machine Learning for Fluid Mechanics
• Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)
• Turbulence Modeling in the Age of Data
• A Physics Informed Machine Learning Approach for Reconstructing Reynolds Stress Modeling Discrepancies Based on DNS Data
• A Comprehensive Physics-Informed Machine Learning Framework for Predictive Turbulence Modeling
• Physics-Informed Machine Learning Approach for Augmenting Turbulence Models: A Comprehensive Framework
• RANS Equations with Explicit Data-Driven Reynolds Stress Closure Can Be Ill-Conditioned
• Turbulence and secondary motions in square duct flow
• Physics-guided deep learning framework for predictive modeling of the Reynolds stress anisotropy
• One-point statistics for turbulent pipe flow up to $R{e}_{\tau }\approx 6000$
• Turbulent scalar flux in inclined jets in crossflow: counter gradient transport and deep learning modelling
• Neural Network Models for the Anisotropic Reynolds Stress Tensor in Turbulent Channel Flow

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