[mesa-users] accretion

[Bill Paxton]

Hi Dean,

On Oct 2, 2013, at 1:35 PM, Dean Townsley wrote:

> The way I understand this has been handled in other codes of the Sugimoto and Nomoto heritage is that the coordinate used for gridding the star is not a truly Lagrangian one. 

The Sugimoto & Nomoto paper is full of great stuff -- and indeed your scheme with Lars was basically very similar (you avoided doing a numerical difference for ds/dlnq by a clever use of difference in temperature gradients).   But as you well know, this introduces an advection term that becomes questionable exactly in the case we care about where we have a large number of grid points resolving the newly added material.   And mesa/star can have LOTS of resolution in the new material -- I've often see 100's of cells holding nothing but new material; very-very different than codes that impose a requirement that dt*mdot < dm(1).   Our old attempt to deal with this was to limit the timesteps using the control I mentioned in a previous email to you, L_div_CpTMdot_limit.  That would force small timesteps which it was hoped would keep the accuracy okay.   It is also intesting to note that Sugimoto & Nomoto explicity point out that for large change in mass that their scheme will not magically take care of the timestep requirements:  

"In some other models, however, change in mass is very rapid, and mass elements of the stellar interior suffer from almost adiabatic change... In such models this scheme does not save the number of time steps any more, but we need inevitably many time-steps in order to follow a greatly non-homologous change whatever the numerical scheme may be."  (bottom of page 129 and top of 130)

So I'm also a fan of the Sugimoto & Nomoto scheme, but I don't think it is a solution for your case of dt >> dm(1)/mdot.  (Perhaps Ken would like to correct me on this one!)  Similarly, the previous implementation in mesa using the Townsley&Bildsten inspired method also required strictly limited timesteps.

> (Forgive me if this is oversimplified, as I realize that I have not written a stellar evolution code myself as both you, Dave, and Bill have! (gulp))  They use q = 1-m(r)/M.  Then the rate of change in mass, Mdot, appears in various terms in the stellar structure equations, rather than as mass added to any particular zone, and material is naturally added at the same entropy as the photosphere without any particularly special treatment.


This seems to be hard to explain (for me at least) -- it might well be beyond the limits of what I can do via email.   For now just let me say I don't have a clue what you are saying at the end of your last sentence after the "and".    Or perhaps you simply are reaffirming that Sugimoto & Notomo or Townsley & Bildsten schemes work when the timesteps are small enough?  If so, I agree.

Cheers,
Bill


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