Dear all, I am working on natural convection problems in cavities. with my code in FV i can't go up Rayleigh=1d6. Is there code, books, references trying hight Ra number. thank you for advicing

I don't know what you have tried, these are general comments:

1) Are you using some king of upwinding ?(mandatory for High Ra numbers)

2) Are you solving your problem using in transient mode ? Then what kind of time discretisation are you using (explicit, implicit, Crank-Nickolson...)

3) Were you able to get a good solution at smaller Ra numbers (10^5, 10^4...)

Thank you Sebastien 1) I have used the Control Volume based Finit Element method. I did not use th Upwind Schema. 2) In transient case i have used the implicit schema. 3) I have obtained good resultes until Ra=10^6. but up this value my code did no converge.

When the local (on a cell) Peclet number or local Reybolds number is bigger than 2, non-physical oscillatgions will appear and may cause the non-convergence of your scheme.

Solutions:

1) Upwinding 2) Artificial diffusion 3) mesh adaptation

Thanks again Sebastien, What are you mean by artificial diffusion? do you know some references?

There is another thing to consider. It isn't clear exactly what physical problem is being solved, but generally if the Rayleigh number is sufficiently high, the flow is turbulent. It may be necessary to use one of the standard turbulence models.

When you use an upwind discretization of the convective term, the result is similar to introducing a second derivative term (artificial diffusion).

A good reference:

C. Hirsh, Numerical computation of internal and external flows (volume 2), 1988, Wiley and Sons

Sorry, the lastname of the Author is: Hirsch