Re: [ff3d-users] a question about improving accuracy in ff3d

[Stephane Del Pino]

Hello Wei.

Le vendredi 19 janvier 2007 17:09, Wei Huang a écrit :
> Thank you Stephane! This does work!
> I am curious on how to choose the right mesh size (for
> example, why use (9,9,5),(17,17,5),(33,33,5), not others?)
> I tried a few others such as (34,34,5), and saw relatively
> big deviation from the exact result.
In fact, according to your geometry, the "center" part is
        ]-0.005,0.005[*]-0.005,0.005[
and your total domain is
        ]-0.01,0.01[*]-0.01,0.01[
So, if you use a 4*4 uniform mesh, the 4 middle cells will describe *exactly* 
the "center" zone, the other 12 cells will describe the remaining part of the 
domain : there is *no* jump of the conductivity *inside* any cell of this 
mesh.

If you want a good approximation, you need to respect this rule. If you do 
not, it will converge well, but not very well near the conductivity jump. 
This is mainly due to the quadrature formulae which assume that the solution 
integrated function is smooth in each cell...

Since in ff3d, mesh refinement of structured meshes are defined using 
vertices, the smallest mesh describing *exactly* your geometry is defined by
        n=(5,5,2)
To get finer mesh in x and z directions you can use the meshes:
        n=(4*n1+1,4*n2+1,n3+1)
where n1,n2 and n3 are integers bigger than 1.

Is that more clear?

Best regards,
Stéphane.