Here the time dependent Navier-Stokes equations for viscous fluid flow are solved in 2D, using a scheme by Guermond and Quartapelle, along with a pressure stabilization term. The two velocity components and pressure are computed in time. The curl of the velocity field, the vorticity, is also computed, as well as a scalar quantity that is convected with the flow.

The geometry is a flow past a cylinder, which exhibits the well known periodic shedding of vortices behind the cylinder. The mesh is contained in the file area.scratch. The scalar quantity is diffusing out from the cylinder and is convected away.