[mesa-users] accretion

[Bill Paxton]

Hi Ben,

Gak!  That's important information.  Thank you.

I haven't carefully checked the numbers for mesa, but here's a rough estimate.
This is the 1st case I looked at -- 8M on the AGB.  It has fewer than
typical number of grid points (I was just doing some rough tests).
It only has 465 cells --- much less than you'd use normally, so the
cells sizes are perhaps larger than you'd use in "real" runs.
Even so, we are resolving the outer envelope with tiny cells.
Here's the plot of logdq vs grid point:
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The mass for this model is down to about 1 Msun, so the cells at the surface
have about 10^-14 Msun.  If we use Mdot = 10-^6 Msun/year then we get
dm/Mdot = 10^-14/10^-6 = 10^-8 years = about 0.3 second.  That's a tiny timestep!

Perhaps we can get away with much less resolution near the surface.
If we cut off at logdq = -7 we could get dt up to 1 year --- but I don't
think we'll be happy with the spatial resolution if we do that.
We probably wouldn't want to go below dq = 10^-10 at the surface giving us
a timestep limit of about 1 day.

Concerning other advection schemes, I think the most interesting
that I've seen recently is the "semi-lagrangian" method.  I implemented
that in an advection-diffusion op-split for element diffusion, but
for that particular case it wasn't a good match.  Element diffusion
is often running close to equilibrium where the advection cancels
the diffusion.  But that means that you are particularly sensitive
to operating splitting errors that ruined the element diffusion results.
So I went back to coupled advection diffusion --- based on your
email, I'm probably happily settling for stable solutions that have
dubious reality!  Sigh....    

It will be interesting to see what responses you provoke with this!!!!

Cheers,
Bill






On Oct 3, 2013, at 1:57 PM, Ben Brown wrote:

> Bill,
>    Regarding your question about implicit handling of advection:
> 
> "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?"
> 
> Even for implicit methods, you're limited by the CFL.  Exceeding the CFL gives stable but unphysical behavior.  That was my takeaway message from
> Viallet, Baraffe, & Walder (2011):
> 
> 	"Towards a new generation of multi-dimensional stellar evolution
> 	models: development of an implicit hydrodynamic code"
> 	Viallet, M.; Baraffe, I.; Walder, R.
> 	http://adsabs.harvard.edu/abs/2011A%26A...531A..86V
> 
> and from a quick skim of their 2013 followup:
> 
> 	Comparison of different nonlinear solvers for 2D time-implicit
> 	stellar hydrodynamics
> 	Viallet, M.; Baraffe, I.; Walder, R.
> 	http://adsabs.harvard.edu/abs/2013A%26A...555A..81V
> 
> They've built in a 2-D fully implicit hydro solver and found (no surprise) that you have to resolve the eddy advection (e.g., CFL) timescale to have anything physical.  That's partly owing to the nonlinearities in the flow.
> 
> For simple advection diffusion problems, where there's no non-linearity, you should be able to do a fully implicit solve that's longer than the advective CFL.  The real way to test this is to test the stability of the timestepping scheme against the equations we're trying to solve; I'm not familiar enough with what we're solving to offer anything more concrete, but I'd be happy to brainstorm with you (and anyone else) if we'd like to test this out.  There may be too many moving parts in MESA star, but if we could break the advection scheme out on it's own we should be able to do these tests.   I'm doing similar tests on a stellar fluid code we're developing, so it's an opportune time.
> 
> 
> --Ben