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

[Kent B. <kg...@la...>]

The problem is not so much resolving the front. There's no particular
limit on the number of levels of refinement in an adaptive method. I'm
told some early universe simulations span thirty orders of magnitude.
The problem is the restriction on the time step that results, a common
problem with spatially adaptive time-dependent hydro methods. You have
to take a very small time step to avoid rapid changes in the variables
in the fine zones, or you might even take the burn front into a coarsely
refined zone faster than the mesh can adapt if the time step is too
small.

I haven't run a calculation with a very thin shell all the way up the
AGB. I'm not that patient. My guess, based on my attempts, is: At
*least* several days even with four threads running. Sometimes it may be
worth the brute calculation, but it seems to me that it would be
worthwhile to experiment with some kind of front propagator method.
Frank, you pointed me at some leads; I'll take a look at these but I
can't promise I'll be able to put anything useful in the code anytime
soon. (Or ever.)

On Sun, 2011-03-20 at 14:31 -0700, Frank Timmes wrote:
> hi alfred (& kent & theodore),
> 
> i'm curious what "taking forever" means for these "brute force"
> thin shell calculations. an hour, a day, a week, on how may threads?
> 
> i agree with you that adaptive grids can help in a number
> of situations, including maybe these particular thin shell problems.
> there are limits though as to what adaptive grids can do. for example,
> laminar flame fronts in nascent sn1a have widths on the order of microns, 
> and are unlikely to be resolved in full star calculations, even those 
> with 1d adaptive meshes. other examples where 1d adaptive grids may have 
> limited utility include off-center neon burning in ~10 msun zams stars, 
> edge-lit co white dwarfs, various dredge-up scenarios, or the thin shell instability. 
> 
> for cases that involve a subsonic propagating front, which is one way
> of looking at the thin shell evolution, one might want to examine level-set 
> or fat-flame technologies. both are general, fairly flexible 
> methods of transporting a propagating front. of course, any such sub-grid models 
> will need input that is guided by resolved microphysics calculations 
> (e.g., how fast is the flame or thin shell propagating). such sub-grid models 
> will also probably have to be explicitly toggled on/off by a user for 
> specific regions at specific times in a given model.
> 
> just my thoughts at the moment ...
> 
> fxt
> 
> 
> 
> 
> On Mar 17, 2011, at 12:26 PM, Alfred Gautschy wrote:
> 
> > 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. 
> > 
> > 
> > 
> > 
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