Abstract: A 2 D depth averaged numerical model in boundary fitted coordinates for non staggered grids, taking contravariant velocity as an independent variable, is developed. The momentum interpolation method is used to calculate the interpolation at the interface to avoid the pressure oscillation in non staggered grids. The discretization equations are solved using pressure correction algorithms(SIMPLE, SIMPLEC or SIMPLER). Finally, the model is applied in numerical calculation of a S type meandering channel.