[mesa-users] On "modus videndi with very thin shell burning"

[Alfred G. <al...@ga...>]

The thin-shell evolution problem is indeed quite an old one; it is also
well described together with a numerical solution to solve it in the
Kippenhahn, Weigert, Hofmeister article of 1967 in "Methods in
Computational Physics", vol. 7, 129 - 190. The solution that was adopted
then was appropriate for the time when computers were slow and memory
was small and after all it was implemented during a first expedition to
the field of stellar evolution where much was terra incognita. Up to
now, I assumed that the adaptive-grid approach of Eggleton & Co.
actually solved the kludge solution of Schwarzschild et al. and
Kippenhahn et al. and whomever it concerns too. 

As Sande correctly observes, in the frame of the thin shell, the
structure of its environment stays almost stationary, this is just what
the adaptive grid (properly tuned, i.e. if made sensitive to the proper
physical quantities) takes advantage of to let the star evolve easily
through this phase of life. Of course there is a price to pay, namely
that mass advection has to be dealt with numerically. Eggleton's code
applies essentially a donor-cell method (as far as I have seen); this is
first order accurate and might be good enough for all quasistatic phases
of evolution (I am not so sure regarding the nuclear species movement in
diffusion like equations) but it might degrade inacceptably the quality
of models in dynamical phases. (This was never a point for the Eggleton
code, but might be one for MESA). 

Finally, the point I would like to make is: If MESA is intended to play
the role in the future of a core set of numerically reliable and robust
routines for 1d stellar evolution, one should refrain from adding
klutches on a deep level just to get through whatever phases of
evolution for whatever classes of stars. Such kludges will accumulate as
there are always phases that need separate treatement. This will
diminish the usefulness of such a collection of modules in the long run.
I would prefer to see innovative numerical methods being implemented to
get the best results for the problem at hand. After all, there is quite
advanced software engineering going into the project already, why then
fall back on quick-fix solutions that were invented in the 1960s to deal
physical problems. After all, I think for the thin-shell problem there
is a better solution already having been put forth: this is the adaptive
grid. It is not unlikely that also other tricky phases of stellar
evolution (whereever strong gradients occur that have to be resolved)
would benefit from such a treatment.   

Actually, Bill Paxton (and possibly others in the group of MESA
users/developers) should have gained some experience with the behavior
of Eggleton's scheme in the thin-shell regime.