An invariances-preserving vector basis neural network for the closure of Reynolds-averaged Navier–Stokes equations by the divergence of the Reynolds stress tensor

In the present paper, a new data-driven model is proposed to close and increase accuracy of Reynolds-averaged Navier–Stokes equations. Among variety turbulent quantities, it has been decided predict divergence Reynolds stress tensor (RST). Recent literature works highlighted potential this choice. The key novelty work obtain through neural network (NN) whose architecture input choice guarantee both Galilean coordinates-frame rotation. former derives from NN while latter expansion RST into vector basis. This approach widely used for models anisotropy or discrepancies but surprisingly not RST. paper tries fill gap. Hence, constitutive relation mean quantities such expansion. Moreover, once trained, there no need run any classic turbulence well-known tests flow in square duct over periodic hills are show advantages method compared standard models.