Fluent was probably not the best model to simulate the Rayleigh Benard convectipn rolls in the mantle, nevertheless, thanks to our study, we were able to view the developement of the rolls in differents situation.
We used User Defined Function to separate the domain in two differents zones of fluid.
The purpose was to create two regions similar to the superior and inferior mantle distinct by their temperature, viscosity, composition , density...
In this report we didn't consider the difference of composition, effectivly, we could have used the VOF method but, this would not have enable us to resolve the equation of energy.

After visualising the influence of the initial condition on the number of rolls for a constant Rayleigh number and a constant viscosity in the fluid, we can notice that, the convection easily invade the all domain even if part of it is a lot more viscous.
Depending on the position of the viscosity gradient and the difference of temperature between the two walls, the convergence is more or less fast, and the rolls are more or less in the middle of the mesh.

Finally, the initial condition in velocity is supposed to force the creation of 2 rolls, one upon the other, but , this situation is unstable, probably because of the viscosity gradient.
The fluid is drafted to the top of the domain because of the Archimede strengh, and the initialisation unables the movement of the fluid above the bottom rolls. We don't manage to make it move as a separated roll: when we
take a bigger Rayleigh number, the model convergs to one roll.

In fact, the viscosity gradient goes against the creation of the two levels convection that we would obtain with the same velocity initialisation and a constant viscosity.
This last remark could lead us to conclude in favor of the hypothesis of one global convection in the mantle, but we msut keep in mind the gap between our simulation and the real situation in the mantle.

Finally, the scientists seem to valid a brand new idea suggesting that the convection is partly separated in two levels, but that a global convection movement exists in the mantle, and that the subduction has a bigger responsability than we though in the of evolution of the magma.

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