  A local artificial neural network (LANN) framework is developed for
turbulence modeling. The Reynolds-averaged Navier-Stokes (RANS) unclosed terms
are reconstructed by artificial neural network (ANN) based on the local
coordinate system which is orthogonal to the curved walls. We verify the
proposed model for the flows over periodic hills. The correlation coefficients
of the RANS unclosed terms predicted by the LANN model can be made larger than
0.96 in an a priori analysis, and the relative error of the unclosed terms can
be made smaller than 18%. In an a posteriori analysis, detailed comparisons are
made on the results of RANS simulations using the LANN and Spalart-Allmaras
(SA) models. It is shown that the LANN model performs better than the SA model
in the prediction of the average velocity, wall-shear stress and average
pressure, which gives the results that are essentially indistinguishable from
the direct numerical simulation (DNS) data. The LANN model trained in low
Reynolds number Re = 2800 can be directly applied in the cases of high Reynolds
numbers Re = 5600, 10595, 19000, 37000 with accurate predictions. Furthermore,
the LANN model is verified for flows over periodic hills with varying slopes.
These results suggest that the LANN framework has a great potential to be
applied to complex turbulent flows with curved walls.
