First and Second order scheme:
In order to compare the influence
of first and second order schemes on the calculations, we have run some
simulations with two different kind of meshes.








We have used first and second
order schemes for flow and energy equations because they are coupled in
the problem studied.
As expected, two main points
can be observed. First of all, it is clear that second order scheme leads
to a longer convergence time. On the other hand, this kind of scheme gives
more accurate results. For example, for the critical Rayleigh number, we
obtain values closer from the theorical critical Rayleigh number.
Moreover, as it is underlined
in the Fluent help, it is better to use a second order scheme when the
flow doesn't remain parallel to the grid as it is the case here.
SIMPLE and SIMPLEC:
The case we ran here is a
case with a Rayleigh number of 3692 and 465 nodes (15*31). As expected,
in the two cases, we obtain some convective rolls as we are quite above
the critical Rayleigh number.
Concerning the number of
iterations necessary to converge, it is of 185 for SIMPLE and 164 for SIMPLEC.
Considering the relatively low number of iterations required, the difference
between the two cases is quite important.




This case had been run with
the same Rayleigh number but with a mesh of 2592 nodes. The solution
converges in 936 iterations with SIMPLE and in 1016 with SIMPLEC.




The following case is run
with a Rayleigh number of 1723 and with a higher number of nodes (2592
nodes). It is clear that the number of iterations is much more important
in this case. With the SIMPLE scheme, the solution converge in 384 iterations
whereas with the SIMPLEC scheme, it converges in 345 iterations.




















What can be noticed here
is that SIMPLEC seems to give better results considering convergence speedup
when the Rayleigh number doesn't get too high. This is related to a remark
made in Fluent's help that for relatively uncomplicated problems in which
convergence is limited by the pressurevelocity coupling, you can often
obtain a converged solution more quickly using SIMPLEC.
However, when the Rayleigh
number gets higher, ie the flow tends to be less stable, SIMPLEC converges
more slowly. The difference is not very important but it marks a changing
considering the others results.