In the method of manufactured solutions (MMS) one postulates an exact solution, substitutes it in the equations and calculates the corresponding source term. The solution is then used for code verification.

For incompressible Navier-Stokes equations, MMS easily leads to a (non-zero) source term in the continuity equation. But not all codes allow source terms in the continuity equations, so for these codes only manufactured solutions with a divergence-free velocity fields will do. I found this example for a domain $\Omega=[0,1]^2$ \begin{align} u_1 &= -\cos(\pi x) \sin(\pi y) \\ u_2 &= \sin(\pi x) \cos(\pi y) \end{align} In general 3D cases, how does one manufacture a divergence-free velocity field?