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

[Frank T. <fx...@ma...>]

hi kent,

thanks! waiting several days for a calculation to finish is not an issue
in my world. i agree though, that having some subgrid front propagation 
methods in mesa would pay dividendson a number of interesting problems.

fxt



On Mar 22, 2011, at 11:00 AM, Kent Budge wrote:

> 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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