Influence of the mesh

Meshes description :

We used two kind of rectangular meshes, the first one is a 20x40 nodes mesh and second is a 50x100 nodes mesh. We also used a square mesh.

We studied the mesh influence with the Rayleigh critical number. For each mesh we determined the Rayleigh critical number. We obtained interesting results.

The 20x40 mesh : it measures 0.02 m long and 0.01 m high. The 50x100 mesh : it measures 0.02 m long and 0.01 m high. The square 40x40 mesh : it measures 0.02 m long. Simulation results :

We present here the results of the steady calculation for a case where the Rayleigh number is equal to 2500. Hence we have a of 0.16 K for the rectangular box and of 0.02 K for the square box (the square box is 2 time as high as the rectangular one so the temperature has to 8=23 time higher).

The rectangular box :

20x40 mesh :

Velocity vectors : Temperature contours : 50x100 mesh :

Velocity vectors : Temperature contours : When we compare the results of the simulations with the two different rectangular meshes, we notice that the velocity amplitude are different. They have the same shape, they decrease and increase at the same place but they don't have the same amplitude, the ratio between the amplitudes is around 5 but it doesn't seem to be constant. We think that this difference between the results of the simulations is related to the problems of convergence of the calculus on the refined grid. The square box (40x40 mesh) :

Velocity vectors : Temperature contour : The calculus on the square grid leeds to a single roll whose size is twice the size of the rolls in the rectangular box. This shows that the rolls are the taller they can be, they use the whole height of the box they're in. The convergence of those calculus was "harder" than with the rectangular grid (20x40) because of a much lower temperature for the same Rayleigh number ( ratio of 8 because the distance between the two walls is in a ratio of 2) hence the heat flux between the two walls is much smaller too.

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