  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.
