4.Comparison between different cases4.1

2D CasesIn 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 CaseHere, 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.

Next