[Mesa-users] Clarification about extra heat arrays in `run_star_extras`

[Francis Timmes]

hi ian,

your interpretation is correct. for cell k, the variable notation is "p1" (plus one) for cell k+1
and "m1 (minus one) for cell k-1. if one's heating term relies only on values in cell k, then
the p1 and m1 partials are zero. if one's heating term relies on values in neighboring cells,
then the p1 and d1 partials will in general not be zero. it should be clear from how one 
formulates one's extra heating term. for example, if e = constant * (T_{k+1} - 2*T_{k} + T_{k-1}) then 
de/d(T_{k+1}) = constant, so T_{k+1} * de/d(T_{k+1}) = de/d(lnT_{k+1}) = T_{k+1} * constant = d_extra_heat_dlnTp1.

clearer?

fxt





> On Apr 18, 2021, at 1:58 PM, Ian Bania '21 via Mesa-users <mesa-users at lists.mesastar.org> wrote:
> 
> Hi all,
> 
> I have been working on a run_star_extras routine which makes use of the other_energy_implicit hook. I have a pretty good grasp on the extra_heat array itself, but I was wondering if anyone might be able to provide some insight on, or point me to some documentation about these arrays:
>           d_extra_heat_dlndm1, d_extra_heat_dlnd00, d_extra_heat_dlndp1, &
>           d_extra_heat_dlnTm1, d_extra_heat_dlnT00, d_extra_heat_dlnTp1, &
>           d_extra_heat_dlnR00, d_extra_heat_dlnRp1.
> My current understanding is that these are partial derivatives of the extra_heat array, with lnd** being with respect to the log of the density, lnT** the log of the temperature, and lnR** the log of the radius. I'm mostly confused about what is notated by the *00, *p1, and *m1 suffixes. Looking through star_data/public/star_data.inc it appears that *00 just refers to a normal partial, whereas *p1 and *m1 refer to the same partial derivative but the variable we are differentiating with respect to is offset up or down a cell? Is this the correct interpretation, and if so does anyone have any advice for the best way to go about actually computing these offset partials?
> 
> Thanks for any help!
> Best,
> Ian K. Bania
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