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.

翻译：本文件建议采用新的数据驱动模型,以关闭和增加RANS方程式的准确性。Reynolds应激反应传感器(RST)的差异是通过神经网络(NN)获得的,该神经网络的架构和投入选择保证加利利安和坐标框架的旋转。前者来自NN的投入选择,而后者则来自RST差异扩大为矢量基础。这一方法被广泛用于由数据驱动的RST或RST差异的数据驱动模型,此处建议采用RST的差异。因此,建议采用RST与平均数量差异的构成关系,以获得这种扩展。此外,一旦对拟议的数据驱动方法进行了培训,就没有必要运行任何典型的波动模型来关闭方程式。众所周知的平方管和周期性山流测试被用来显示当前方法与标准波动模型相比的优势。