Applicability of some numerical schemes in generalized curvilinear coordinate forms on a density current is examined focusing on the conservation and numerical diffusion. Various models with different spatial schemes for convective terms, grid fineness, turbulence models and methods of pressure calculation are applied to the mixing of two fluids with different density in a simple rectangular domain (Flat Model), a rectangular domain with a small mound (Mound Model) and a trapezoidal domain with steep bed slope (Slope Model). The numerical results show that the un-conservative spatial schemes yield significant error in total salinity and grid fineness affects not only the vertical density profile but also the phase velocity of density wave. A simple modification is also proposed in order to suppress unreasonable current in a stable stratified flow over a steep bed slope.