**3. Conclusions**

Numerical diffusion is the main source of errors in computational calculations. In this study the performance of various numerical schemes is evaluated in order to find the limitations of the convection formulations. The first-order UPWIND scheme presents more stability and overcomes the streamwise diffusion but such the higher-order schemes do not deal at all with the cross-stream diffusion. The second-order hybrid numerical schemes take into account the influence of more neighboring points but appears unstable at high Peclet numbers. The nonlinear van LEER numerical scheme is highly stable and reduces satisfactory the false diffusion errors. The flow oriented SUPER scheme overcomes the phenomenon of the numerical diffusion in most of the cases investigated without increasing the computational cost.
