A  standard benchmark for incompressible flow is the flow of an isothermal fluid in a square cavity with unit sides, as schematically represented; the velocity field has been set to zero along all the boundaries, except than the upper one, where a uniform unitary horizontal velocity has been imposed.
In order to make the problem solvable a zero pressure has been imposed to the lower left
corner of the cavity.




Velocity fields


The velocity vector (top) and the velocity magnitude (bottom) plotted superimposed to the mesh for (left), for (center) and for (right). The main vortex tends to the center of the cavity as the Reynolds numbers grows and secondary vortexes appear.


[3] J. Donea, A. Huerta, Finite Element Methods for Flow Problems, (2003) Wiley