  In the given paper, we confront three finite difference approximations to the
Navier--Stokes equations for the two-dimensional viscous incomressible fluid
flows. Two of these approximations were generated by the computer algebra
assisted method proposed based on the finite volume method, numerical
integration, and difference elimination. The third approximation was derived by
the standard replacement of the temporal derivatives with the forward
differences and the spatial derivatives with the central differences. We prove
that only one of these approximations is strongly consistent with the
Navier--Stokes equations and present our numerical tests which show that this
approximation has a better behavior than the other two.
