Abstract. The current paper presents comparisons between four different discretization schemes for non-orthogonal grids in the skewed cavity and highly skewed flow in the curved cavity. These schemes are upwind differencing scheme (UDS), upwind differencing scheme with numerical diffusion (UDS-ND), central differencing scheme (CDS), and Quadratic upwind interpolation for convective kinematics (QUICK). The comparison between the selected schemes for highly skewed flow in curved cavity indicated that the upwind differencing scheme with numerical diffusion is the best choice in terms of accuracy and computational cost. In addition, the comparisons between the present results and previous results from the literature indicate that the current procedure which is more suitable for general purpose codes can produce computational results which are in close agreement with those obtained from body fitted and polar coordinates systems. For the non-orthogonal grids in the skewed cavity, all the tested schemes produce close results when they are compared with the benchmark solution. However, the UDS-ND requires fewer number of iteration and shorter computational time. Despite the upwind differencing scheme with numerical diffusion being the first-order scheme, its accuracy is very close to the second and third-order schemes. Therefore, the UDS-ND is recommended for general-purpose code because its stability is higher than the higher-order scheme and the computational time is lower.