A new method for computing the fluid flow in complex geometries using highly non-smooth and non-orthogonal staggered grid is presented. In a context of the SIMPLE algorithm, pressure and physical tangential velocity components are used as dependent variables in momentum equations. To reduce the sensitivity of the curvature terms in response to coordinate line orientation change, these terms are exclusively computed using Cartesian velocity components in momentum equations. The method is then used to solve some fairly complicated 2-D and 3-D flow field using highly non-smooth grids. The accuracy of results on rough grids (with sharp grid line orientation change and non-uniformity) was found to be high and the agreement with previous experimental and numerical results was quite good

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