A numerical simulation is used to evaluate the curvature effects of the wall on features of the interaction between discrete jets and cross flow, and therefore on the efficiency of the cooling. The injection is realized in a turbulent limit layer through only one row of openings. Our study was especially based on the SST model that is efficient in the capture of the phenomena near and in the wall. Three turbulence models are used; the k-, the RSM and the SST on a flat plate crossed by throw in order to identify which of these models are more capable to capture the near wall interaction phenomena. Discrete jets are arranged across a surface exposed to a wall boundary layer of parallel compressible stream, as occurs in certain discrete-hole cooling systems for turbine blades. Comparisons of the results of this study are presented in the case of a flat plate crossed by throw inclined of 45° with a rate injection Ra=0.6. These results compared to experimental data proved the aptitude of the SST model, in relation to the other models in this case of problems. Applied for a NACA0012 profile, this model (SST) revealed us the distinct difference of features of the interaction in relation to the flat plate.