[FLASH-USERS] Minor bugs in MacLaurin spheroid test

[Norbert Flocke]

Hi Charles,

The answer to your first question I can provide. As written in the code on 
line 78, the value of AA3 is

   AA3 = (2*sqrt(1-e^2)/e^2) * (1/sqrt(1-e^2) - asin (e)/e)

or, written out

   AA3 = 2/e^2 - 2*sqrt(1-e^2)*asin (e) / e^3

where e is the eccentricity. If e -> zero, then the MacLaurin (what 
coincidence!) expansions are:

   asin (e)     -> e
   sqrt (1-e^2) -> 1 - e^2/2

When you insert these limits into the AA3 equation, then:

   AA3 -> 2/e^2 - 2*(1-e^2/2)*e / e^3
       -> 2/e^2 - 2/e^2 + 2*e^2/2
       -> 1

so there is no error in the formula.

Cheers,
Norbert


On Wed, 14 Aug 2013, Chenchong Zhu wrote:

> Hi FLASH users,
>
> I'm currently playing with the MacLaurin spheroid example that comes with
> FLASH to see how well the spheroid can be represented hydrodynamically.
> I'm not entirely certain, but I think I might have found two bugs in the
> code though.
>
> On line 78 of Simulation_init.F90 AA3 as written approaches 2/3 rather than
> 1 as sim_eccentricity goes to 0.  It obeys the proper limit if it's changed
> to "AA3 = (3.0*sqrt...".
>
> In Simulation_initBlock.F90, under case(sim_geom3DCartesian), vxfac and
> vyfac have z-dependencies on their velocities.  They should be multiplied
> by rxyinv = 1./sqrt(xdist**2 + ydist**2) rather than rinv if we want rigid
> rotation.
>
> Best,
>
> Charles
>