[mesa-users] density and sound speed profiles with "ripples" in solar calibration example

[Warrick Ball]

Hi Ana,

I thought I'd chip in here because I have a small amount of experience 
with CESAM, and some knowledge of how it works.  I'm not sure if my 
variant of the code is the same as yours, but here's what I know anyway. 
And keep in mind that I'm no CESAM expert, so invite any to overrule me!

The numerical method in CESAM is unlike other stellar evolution codes: 
there is no finite differencing or relaxation.  Instead, the structure of 
the star is expressed as a sum of basis functions that span some 
functional space.  In CESAM, it boils down to supposing that the functions 
are something like piecewise polynomials with compact support i.e. 
restricted to a small region of the dependent variable.  (These are basis 
splines, or B-splines, if I remember correctly.)  This method is known as 
"collocation".

In this scheme, the differential equations of stellar structure become 
equations relating the coefficients of the basis functions in the sums 
that define the functions, and the "meshpoints" in the stellar model 
correspond to the locations at which these equations are formulated.  The 
splines have derivatives that can also be evaluated at those same points. 
The block-diagonal form of the matrix returns because the coefficients 
then depend on some number of neighbouring points, depending on the order 
of the polynomials.

But the long and short is that, yes, I think all the structure variables 
are defined at the same collocation points, rather than distinguishing 
between cell averages and faces.

Hope that helps!

Cheers,
Warrick


On Fri, 22 Aug 2014, Ana Olímpia wrote:

> Hi again!
> 
> I was reading the cesam's manual and it looks like it does not use the concept of cell. I think it works with a
> system of concentric spheres with different values of R (radius) and the other parameters are taken at the surface
> of these spheres.
> 
> Regards,
> Ana
> 
> 
> 
> On Fri, Aug 22, 2014 at 12:54 AM, Ana Olímpia <anaolimpiabrito at gmail.com> wrote:
>       Hi Francis,
> 
> I always thought they were defined all at cell centers but now that you are asking I realize that I have to
> take a look at the manual. I'm not sure about that.
> 
> Regards,
> Ana
> 
> 
> On Thu, Aug 21, 2014 at 4:32 AM, Francis Timmes <fxt44 at mac.com> wrote:
>       hi ana,
>
>       … and along the lines of bill’s earlier message, are the
>       cesam numbers defined at cell centers, cell edges, or something else?
>
>       fxt
> 
> 
> 
> 
>
>       On Aug 20, 2014, at 8:20 PM, Bill Paxton <paxton at kitp.ucsb.edu> wrote:
>
>       > Hi Ana,
>       >
>       > Thanks for sending your solar results.  They are certainly smooth, but the sound speed match
>       to the solar data isn't quite up to the other codes.   I image this is just a result of not
>       doing as many cycles of calibration.  I've attached the data being used for the comparisons in
>       this plot in case you'd like to check that I've correctly represented your results in the plot.
> > <solar_comparison.pdf>
> >
> > here are the corresponding rms deviations:
> >
> > MESA rms 0.000632728747717372
> > BBP98 rms 0.000930645900227312
> > S09 rms 0.00113436296074351
> > Ana using CESAM rms 0.0057738746271799
> >
> > Let me know how things go with the "ripples".
> >
> > Cheers,
> > Bill
> >
> > <csound.data>
> >
> >
> >
> >
> > On Aug 20, 2014, at 7:13 PM, Ana Olímpia wrote:
> >
> >> Hi Bill,
> >>
> >> thank you for replying so quickly!
> >> I will follow your suggestions (I have not done any of them yet) and then I will let you know the
> results.
> >>
> >> I am sending attached the file with the cesam output for my solar calibration (radius is the first
> column and csound^2 the last one).
> >> If you need something else, please let me know.
> >>
> >> Regards,
> >> Ana
> >> <sun_cesam.txt>
> >
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> 
>


------------
Warrick Ball
Postdoc, Institut für Astrophysik Göttingen
wball at astro.physik.uni-goettingen.de
+49 (0) 551 39 5069