[mesa-users] accretion

[Ben Brown]

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