4. Comparison between different cases

4.1 2D Cases

In this case, we focus on the results from two different grids: 40x20 and 20x10.
Results for Vmax are close for Ra<8000, ie DT< 1K. Nevertheless, there is a difference after this value due to a better precision with a thiner grid.
Moreover, the critical Rayleigh number is a little bit different:
- mesh 10x20: Rac=1772
- mesh 20x40: Rac=2013


The comparison of the theorical and numerical Vx_max values for the two grids is displayed below:

We can observe better results for the thiner grid. Nevertheless, there is a good adequacy for the lowest values of the Rayleigh number.

The following fields are the temperature and velocity fields for DT=0,5 K after convergence of the 10x20 mesh. We observe two steady rolls.



4.2 3D Case

Here, we use a 20x20x20 grid as follows:

This simulation, for a DT=1K and dimensions of 2cmx1cmx5cm, has converged after 67 iterations.

The velocity vector field obtained is:


The temperature field is:


When computing a new case (4cmx1cmx10cm), in the (y=0,5cm) temperature field, we can observe a sinuous mode of oscillation. This a physical phenomenon which is observed here.