[Mesa-users] resolution study

[Francis Timmes]

hi amber,

is the blurb below pragmatically useful?

fxt


------------------------------------------------------------------------------------

i will mostly restrict my comments here to mass and temporal resolution
with respect to convergence studies. 

obviously if one's stellar model depends on free parameters, one
should investigate the robustness of model to variations in
the free parameters. an example of this is the radial stellar pulsation
capability in section 2 of the recent mesa V instrument paper 
(https://ui.adsabs.harvard.edu/?#abs/2019arXiv190301426P/abstract) 
where variations with respect to the convective parameter sets are highlighted.

controls for energy conservation are also discussed in the mesa V instrument paper,
and i will not mention them further here.


mess resolution:

mesa has two coarse level controls for the mass resolution
max_dq = 0.01
mesh_delta_coeff = 1.0
where the default values are given.

max_dq is the maximum size for cell as fraction of total mass,
perhaps more conveniently said as 1/max_dq being the minimum number of cells in a model.
the default value means there is a minimum baseline grid of 100 cells.
the smaller dq_max, the larger the minimum number of cells
and a larger dq_max means a smaller number of cells.

mesh_delta_coeff controls the relative magnitude of changes between adjacent cells.
see appendix B.4 of the mesa II instrument paper, https://ui.adsabs.harvard.edu/?#abs/2013ApJS..208....4P/abstract ,
for a more complete discussion. a larger value of mesh_delta_coeff increases the maximum allowed changes between
cells and thus decreases the number of grid points. a smaller of mesh_delta_coeff does the opposite.

my method of madness for mass resolution convergence studies is to set mesh_delta_coeff = 1.0 
and vary the underlying grid max_dq = 0.01. for normal science exploration runs 
i routinely use max_dq = 0.001 (1000 cells). when i get closer to publishing a model
i always conduct a mass resolution study. usually i will run models with max_dq = 0.0005 (2000 cells) 
and max_dq = 0.00025 (4000 cells) and plot the behavior of a quantity of interest with 
respect to the number of cells. what i'm looking for, crudely, is that the quantity of interest 
does not change with ever increasing amounts of mass resolution. based on what i see, 
i may run additional models with max_dq = 0.002 (500 cells) or max_dq = 1.25e-4 (8000 cells).

others may prefer to set or leave max_dq = 0.01, fixing the baseline grid,
and varying mesh_delta_coeff. 

mesa has numerous fine-level controls for the setting the mass resolution
http://mesa.sourceforge.net/controls_defaults.html#mesh_adjustment .
for example, if i am using log_kap_function_weight to put more cells
where the opacity changes (e.g., He II or Z bump or sharp composition interfaces), 
then, with everything else held fixed, i will explore how changing this mesh setting 
impacts the quantity of interest.


temporal resolution:

mesa has a coarse level control for time resolution
varcontrol_target = 1.0d-4
where the default values is given.

varcontrol_target modulates the relative variation in the structure from one model to the next. 
if the relative variations from one time step to the next time step is larger than varcontrol_target,
then the time step is reduced. if the the relative variations between time steps is smaller than
varcontrol_target, then the time step is increased see appendix B.3 of the mesa II instrument paper, 
https://ui.adsabs.harvard.edu/?#abs/2013ApJS..208....4P/abstract , fir a more complete discussion.

for normal science exploration runs i routinely set varcontrol_target = 1.0d-4.
when i get closer to publishing  a model i always conduct a temporal resolution study. 
usually i will run models with varcontrol_target = 5.0d-5 and varcontrol_target = 1.0d-5,
with the latter value requiring patience for the longer run times.

mesa has numerous fine-level controls for the setting the time resolution,
http://mesa.sourceforge.net/controls_defaults.html#timestep_controls .
of these, my favorites are delta_lg_*_cntr_limit, delta_lg_*_cntr_max , and delta_lg_*_cntr_min
as they enforce smaller time steps as a nuclear fuel depletes in the core. this is important for,
say, helium burning when it is the final few percent of burnt helium that largely determine 
the o16/c12 ratio of the ashes. as above, when i get closer to publication, i will always 
explore how my "extra" time step controls impacts the quantity of interest.


mass and temporal resolution:

mesa is solving a discrete version of continuum partial differential equations.
formal verification error models usually have a first-order term that couples the
mass and time discreteness (e.g., error ~ b*(delta m * delta t)**a ).
i have not yet explored the importance of this cross-term for mesa.
if my experiences exploring this cross-term for various explicit hydro instruments 
applies for mesa, then this cross term is smaller in magnitude and power than the
first-order terms that isolate the individual space and time dependencies.

------------------------------------------------------------------------------------






> On Mar 8, 2019, at 5:02 PM, Francis Timmes <fxt44 at mac.com> wrote:
> 
> hi amber,
> 
> usually this topic is emphasized during the labs in a mesa summer school,
> and one year we had an evening session on the subject. i cannot recall
> a write-up or stored presentation outside of a mesa instrument paper 
> or other science paper (e.g., https://ui.adsabs.harvard.edu/?#abs/2016ApJS..227...22F),
> so i'm not too surprised you didn't find one. i'll take a shot at crafting
> a verification-with-mesa message, or at least how i do it.
> 
> fxt
> 
> 
> 
> 
>> On Mar 8, 2019, at 3:00 PM, amber lauer via Mesa-users <mesa-users at lists.mesastar.org> wrote:
>> 
>> I've searched the mailing list archives, as well as the educational materials on the marketplace, and I can't find something I know existed. 
>> 
>> At one time there were instructions, possibly a tutorial, on how to do convergence and resolution studies, and just various in-depth explanations of adjustments to these variables. 
>> 
>> I've exhausted the resourcess I know of. Can anyone help? Thanks.
>> 
>> -- 
>> Amber Lauer
>> Postdoctoral Researcher
>> Triangle Universities Nuclear Lab
>> Duke University
>> amber.lauer at tunl.duke.edu
>> _______________________________________________
>> mesa-users at lists.mesastar.org
>> https://lists.mesastar.org/mailman/listinfo/mesa-users
>> 
>