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;

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Modelling Convection in OpenFOAM

As you may know by now, the Navier-Stokes equations are composed from three parts: a time component, a convection component and a diffusion component.
The time component accounts for the change in time of the given scalar or vector; the convection component accounts for the transport of the scalar due to the velocity of the fluid; and the diffusion components determines the transport due to scalar concentration and will make the scalar to spread from high concentration to low concentration even with zero velocity.
In the previous post we've seen that when computing only the convection we had some diffusion also, and said that it was a numerical error.

In this post we will see this in more detail; we'll use the same shockTube problem as before, changed to work for the scalar transport solver, and model the convection only problem for 3 seconds.
For the convection, which mathematically is a divergence we'll use different schemes and see their effects.

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