[FLASH-USERS] Minor bugs in MacLaurin spheroid test

[Norbert Flocke]

Sorry, there is a typo in the last AA3 equations. It should read:

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

Norbert

On Wed, 14 Aug 2013, Norbert Flocke wrote:

> 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
>> 
>