2D Transport of a Passive Scalar with OpenFOAM

All the posts that have been written until now tackled the shockTube problem and the 1D transport problem; we've seen the convection and diffusion at work and we saw that there are a lot different schemes for divergences modelling.
In the following I will show the setup and results for 2D scalar transport problem. This was actually the first problem that I setup and solved from scratch on my own in OpenFOAM.
This may not be a physical problem but it has all the components of an actual CFD problem solved in OpenFOAM.

Problem statement:
- a 2D domain in a shape of a square with the side of 10 m;
- in the middle of the square we have a circle of radius 1 m;

- the square has an initial scalar set to zero and the circle has the scalar set to 1;
- the circle is moving in the domain in the manner shown below:

- each move will take 4 seconds and the velocity for each move is 1 m/s;
- during this transport convection and diffusion terms are active;

Solving in OpenFOAM is really straight and I will point out only the things that worth mention:
- the mesh dictionary is much like the one from cavity tutorial but needs some changes at the boundary definition:

- secondly, the setFields dictionary must be changed in order to set the scalar to be 1 in a circular area:

- the analysis is run for 4 seconds with a velocity (1 0 0); afterwards, the velocity is changed to (0 1 0) and the analysis is started from second 4 for another 4 seconds; in the last section the velocity will be (-1 -1 0).

The initial step is given in the following:

All results can be seen in the following tables:

The evolution of the solution can be seen in the following video:

This is it, if you have any questions please leave a comment below.