[mesa-users] accretion

[Bill Paxton]

Hi Dean,

On Oct 3, 2013, at 11:54 AM, Dean Townsley wrote:

> Just to follow myself up with some more concrete things...
> 
> 
> Just to say, my description of timescales is pretty much the same as in section 5.3 of the second MESA paper, sorry I didn't reference that.

I'll forgive you this time --- just never again miss an opportunity to reference a MESA paper! ;p

> Also, I see that figure 26 does show a problem at the depth where eps_grav is switched from the explicit lagragian form to the quasi-steady form.  Bill, just to be sure, is this the issue that you are trying to improve?  are there others?

The glitch in fig 26 you noticed is indeed coming at the location where we switch between different schemes for calculating eps_grav.  (btw: I tried blending the schemes near the boundary in hope of reducing the glitch, but that seemed to make things worse!  Perhaps I just had a bug.)

So, yes, getting a consistent method of calculating eps_grav was a major motivation for the new scheme.  Also, the Townsley&Bildsten scheme is for thin radiative shells, and we were applying it even when there was convection present (maybe that didn't matter).

Both the radiative restriction and the uniformity of method might be addressed by using the Sugimoto&Nomoto scheme everywhere in the star.  But I'm reluctant to introduce an advection term if I can avoid it.  I'm okay with advection when the cells are large and the timesteps are small enough so that dt*advection_velocity is comparable to the neighboring cell size -- i.e., you are advecting from a near neighbor rather than from far away. But we have extremely tiny cells in the surface regions so we can resolve the action (recall, 100's of cells for the newly added material), so we'd need extremely small timesteps  to satisfy that restriction.   Perhaps I'm just being paranoid about this.  For an explicit method, you can use the CFL condition to set limits on dt given cell sizes and velocities, but the situation isn't so clear for implicit methods -- at least it isn't clear to me.  What do you think?  We compromised by using the Townsley&Bildsten scheme with advection in spite of my misgivings, but we limited timesteps based on thermal timescale arguments (see below).   But I prefer using a scheme without advection if possible.

Note:  I should emphasize that we still use the relative mass to create the initial guess for the newton iterations when we have added or removed mass.   This is an important application of the fact illustrated by Sugimoto&Nomoto in their Fig 6.   Near the surface, the new structure is much better predicted from the old one by using values at the same relative mass.   In mesa we do that, while for locations deeper in the star, we predict the new values based on the same absolution mass location.  There's a short sketch of this in appendix B.5 of MESA2.  You can find the code in star/private/adjust_mass.
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> A question: is the spot for the switch between the two eps_grav just at some constant multiple of the Mdot*dt?  (sorry I'm not familiar enough with the code to figure this out for myself yet.)  

Like just about everything in mesa, this is a user selected parameter.  The transition happens at "k_below_recently_added" -- recall that mesa cell numbering starts with 1 at the surface.  So for cell k, if k < k_below_recently_added, then we do the thin radiative version of eps_grav instead of the the scheme we use deeper in the star.   The value for k_below_recently_added is set so that it is just below some multiple of the mass added in the current timestep, the multiple being determined by the control parameter called "factor_for_recently_added" which can be found in controls.defaults.   Here's the default value:

         factor_for_recently_added = 5
            ! multiply delta_m of current timestep times this to set mass to be
            ! considered to be recently accreted.

And there is another critical parameter you need to consider which limits the timesteps.

            ! limit on added mass to keep L > Cp T Mdot in new material
            L_div_CpTMdot_limit = 2 ! reduce next timestep if L/(Cp T Mdot) < this in new material
            L_div_CpTMdot_hard_limit = -1 ! retry with smaller timestep if ratio < this

So in runs with previous versions of mesa you will want to check these controls rather than just using defaults! ;D

> From reading the accompanying discussion, I am surprised that the point at which the form is changed and the point at the base of the newly accreted material are different.  Maybe I missed something?  Is there a stability reason for this or something like that?

You should experiment with different locations to see what you find!   I recall we had problems if we set factor_for_recently_added = 1.  What happens when you try it?

Also, what timesteps to you get when you change L_div_CpTMdot_limit?    
Can you make it large and still get okay results?   
How small do the timesteps become if you reduce this down to 1?

Cheers,
Bill

p.s. in case anyone would like to look at the Sugimoto&Nomoto paper, I've attached it.   It's a classic!
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