[FLASH-USERS] Parameters for outer zone structure in new multipole gravity

[Dean Townsley]

Hi everyone,

I think I could figure this out digging through the code, but I figured 
others might be interested and someone might be able to give just give 
some quick answers.

Or if this is in the documentation somewhere please bump my nose on it, 
as I didn't find it among the descriptions that are there.  I also don't 
recall this coming up on the mailing list before.


How do the different outer zones fit together for the new multipole 
poisson solver?  I assume there is only one grid, and the different 
zones define how the spacing is chosen.  But the zones are "nested" 
correct?  But this is just used to generate the grid.  The "outer" outer 
zone doesn't influence the spacing in the inner outer zones, right?

Also, how is the "maximum domain size" that mpole_zone_radius_fraction_n 
acts upon determined?  i.e. does it matter where the zero of the 
coordinates system is?  or is it just "corner to corner" of the whole 
domain?

Do I need to tune the parameters so that the bin sizes match near the 
zone borders?  Assuming that's what I want, so that I have a smooth 
transition in zone sizes.

Also, is there any problem with changing these parameters 
mid-calculation? Or if the maximum refinement level changes?


It seems useful to have a partially concrete example...
Say I want the grid for the multipole moment calculation to be uniform 
out to some radius R, and then logarithmic from there out. My maximum 
radius is Rmax, and my domain size is 2*Rmax, since my origin is in the 
middle of the domain.  Are these the right parameters?

mpole_max_radial_zones = 2

mpole_zone_radius_fraction_1 = R/(2*Rmax)
mpole_zone_radius_fraction_2 = 1

mpole_zone_type_1 = "exponential"
mpole_zone_exponent_1 = 1    # this is actually uniformly spaced

mpole_zone_type_2 = "logarithmic"
mpole_zone_exponent_2 = delta r/R

mpole_zone_scalar_1 = 1
mpole_zone_scalar_2 = 1

where delta r is my grid spacing, and therefore also the size of the 
bins in the first zone.

I think this choice of zone_exponent_2 = t_2 is right, as it gives me 
dr/dQ|_{r(Q)=R} \approx t*R = delta r.  As best I can tell, the other 
parameter, s, doesn't help in setting the size of the bins near r=R in 
this example.


Any thoughts are welcome from someone who knows more about the new 
multipole solver than I do.


Thanks!
Dean