[mesa-users] mass loss, rotation, binaries, and a hydrodynamic surface boundary conditions

Wed Jun 17 17:16:51 EDT 2015

"Eulerian codes generally do not conserve the angular momentum, and there
is no easy way to conserve it in the discrete world in general."

This argument gets thrown at Eulerian codes fairly consistently, but
conservation of angular momentum isn't really a serious problem at modern
resolutions. At even a fairly mediocre grid sizing of 256**3 the maximum
deviation in angular momentum is much less than 1% over the course of many
orbits, at least for the white dwarf binaries I study. And if you really
want to conserve angular momentum to machine precision you can write your
fluid equations to do that (see, e.g., Byerly et al. 2014
<http://adsabs.harvard.edu/abs/2014ApJS..212...23B>). I will agree with
this statement to the extent that stellar astrophysics problems cannot get
away with periodic boundaries and so there is always some leaking of energy
and momentum even for "conservative" methods.

There are much more serious problems than angular momentum conservation.
Mainly, representing the surface of the stars and advecting the stars along
the grid while maintaining HSE. (Related to the so-called violation of
"Galilean invariance" of static mesh Eulerian codes, though that is not
really what is going on. If you try to put a single star on a grid and have
it maintain equilibrium while moving at some non-zero velocity, it will do
*really* badly on a static mesh at low resolution.) All sorts of weird
things are going on near the stellar edges because that's where the density
gradient is sharpest. At low resolutions I am skeptical of what is going on
near stellar surfaces in these binary simulations. But resolution can
probably help with this, either with AMR or with generally greater
resolution everywhere due to greater computing resources. Also, increased
resolution results in decreased advection errors, and a better maintenance
of equilibrium. Possibly that can be coupled with some of the ideas from
the moving mesh codes to really nail that issue.

"As for the methods, simply increasing the number of discrete elements is
not a sufficient condition for obtaining a convergent solution."

Cannot be repeated often enough!

Max Katz
Ph.D. Candidate, Department of Physics and Astronomy
Stony Brook University
http://astro.sunysb.edu/mkatz/

On Wed, Jun 17, 2015 at 4:35 PM, Tomasz Plewa <tomekplewa at gmail.com> wrote:

>  Hi Dave -
>
> Eulerian codes generally do not conserve the angular momentum, and there
> is no easy way to conserve it in the discrete world in general.
> Lagrangian codes can conserve the angular momentum by construction, but
> suffer from a number of other problems on their own (be it a mesh
> deformation or numerical diffusion for particle codes, to name just the
> major problems).
>
> As for the methods, simply increasing the number of discrete elements is
> not a sufficient condition for obtaining a convergent solution. For that
> one also needs stability, and those two pieces are encapsulated in the Lax
> equivalence theorem.  The third element is consistency, which is probably
> the least difficult to demonstrate, and which has most to do with the mesh
> resolution you mentioned. Well, equivalence actually implies only two out
> of three conditions must be demonstrated.
>
> Apart from the fact that the physics model may not be complete and
> numerical solution converging to unphysical solution, most mesh-convergence
> studies are rudimentary and at times limited for all wrong reasons. I
> remember one study in which the number of discrete elements was doubled but
> at the same time the evolutionary time used for comparison was halved
> (seemingly due to lack of computational resources). The problem is that the
> main conclusions of that work were drawn based on the final problem time,
> which the convergence study simply did not reach. In another study, the
> authors claimed the outcome was different likely due to floating point
> errors. Well, how come? But in most cases, no convergence study is
> presented. Instead computational model quality is claimed based on the
> previous experience (based on the previous experience, and again, etc.).
> This seems good enough even though the code has been extended and used in
> the new regime.
>
> The mesh is actually both time and space, and it is temporal convergence
> and coupling between various physics that is usually overlooked or quietly
> avoided in our studies. Who knows what happens if we couple everything as
> the nature does. And in reality there is no need to evolve systems for
> several ten- or hundred thousand discrete steps. How about 1 million steps?
> Is it still okay? Do we know what is the accumulated error after all those
> steps? I do not quite recall any work in stellar astrophysics that provided
> global error estimates.
>
> As for turbulence, it really depends on the application. There are some
> problems in stellar astrophysics which are on the verge of being resolved
> in terms of viscosity, and that huge Reynolds number frequently quoted
> simply does not apply (because of additional physics involved). There are
> many recent studies of "turbulence" that never demonstrated they were
> studying real turbulence. That is, producing a kinetic energy spectrum that
> spans 2.5 decades in wavenumber is not really a proof of turbulent
> behavior, perhaps a mere hint of what might be coming. Yet, the conclusions
> are drawn about turbulent nature of the system under study, even the role
> of turbulence, which is a clear overstatement if not simply wrong. One has
> to wonder about the reviewers' training.
>
> So one should probably be a little careful trying to "engineer" stars. The
> discussion about wind accretion is a good example of navigating muddy
> waters of approximations, parametrizations, features and switches available
> in complex computational tools. None of this increases my confidence in
> this kind of tools. (Not that these tools are wrong, but confidence is not
> judged by the number of available options.)
>
> Do not take me wrong: It is absolutely fine to explore things. I love
> "poking" around, more or less systematically myself. What is not fine is
> extending conclusions beyond model's actual limitations. I  am confdent
> someone will attempt to study the wind accretion problem in massive
> binaries. Ideally it should give us the ultimate answer, and if not then
> provide some estimate of how well or otherwise how badly it has been done.
> I doubt, though... But in which part? ;-)
>
> Tomek
> --
>
> On 06/17/15 14:06, David Arnett wrote:
>
>  OK Tomasz, maybe we should be explicit. It would be useful for people
> who are using approximate methods to know the cause of errors.
>
> First, what worries you about the equations? We can write them out
> generally in an inertial frame in 3D; conservation of mass, momentum and
> energy, with radiative transfer and MHD. We just can't solve them
> accurately. Are you thinking of something else?
>
> Second, what is wrong with the methods? My favorite worry is that a grid
> code will have errors because the fluid sweeps through the mesh rapidly,
> and an SPH code, which can move with the matter, will have resolution too
> low to represent turbulence. I suppose the issue is a general one with
> zoning for high Reynolds number and optically thick-thin plasmas.
>
>  What are your favorites?
>
>  Dave
>
> On Wed, Jun 17, 2015 at 11:39 AM, Tomasz Plewa <tomekplewa at gmail.com>
> wrote:
>
>>  No. There is no code in existence that could solve this problem in 3D,
>> regardless computational resources. The problem is with equations, then
>> with methods, and perhaps only then with the available computing power.
>>
>> Tomek
>> --
>>
>> On 06/17/15 10:44, David Arnett wrote:
>>
>>   Hmmm.  It sounds like a problem that can be done, but probably not
>> with sufficient resolution to be believed in detail, unfortunately. Maybe
>> when Moore's law has more time to help us.
>>  Dave
>>
>> On Tue, Jun 16, 2015 at 11:55 PM, Pablo Marchant <pamarca at gmail.com>
>> wrote:
>>
>>> There is a big uncertainty in accretion when you reach critical
>>> rotation. Whether or not the material gets ejected, and how much angular
>>> momentum it would carry with it has a very large impact on the final fates
>>> of several binary systems. 3D simulations would certainly be enlightening
>>> here, but my experience on 3D hydro is definitely insufficient to attempt
>>> this on my own.
>>>
>>> On Mon, Jun 15, 2015 at 9:19 PM, David Arnett <wdarnett at gmail.com>
>>> wrote:
>>>
>>>> This sounds interesting. It seems that you are exploring a region of
>>>> parameter space in which some of our approximations need to be merged into
>>>> a more wholistic formulation. We encounter the same sort of issue when we
>>>> simulate turbulent convection near a boundary in a star. When the flow is
>>>> no longer radial, interesting new things may happen. We should look for
>>>> instances in which the purely 1D representation needs more careful thought,
>>>> and maybe 3D simulation "spot checks" for guidance.
>>>>
>>>> --
>>>> David Arnett
>>>> Regents Professor
>>>> Steward Observatory
>>>> University of Arizona
>>>>
>>>> Facts are stubborn, but statistics are more pliable.  Mark Twain
>>>> Facts do not cease to exist because they are ignored.  Aldous Huxley
>>>>
>>>
>>>
>>>
>>>   --
>>> Pablo Marchant Campos
>>> M.Sc on Astrophysics, Universidad Católica de Chile
>>> PhD student, Argelander-Institut für Astronomie
>>>
>>
>>
>>
>> --
>> David Arnett
>> Regents Professor
>> Steward Observatory
>> University of Arizona
>>
>> Facts are stubborn, but statistics are more pliable.  Mark Twain
>> Facts do not cease to exist because they are ignored.  Aldous Huxley
>>
>>
>>  ------------------------------------------------------------------------------
>>
>>
>>
>> _______________________________________________
>> mesa-users mailing listmesa-users at lists.sourceforge.nethttps://lists.sourceforge.net/lists/listinfo/mesa-users
>>
>>
>>
>
>
> --
> David Arnett
> Regents Professor
> Steward Observatory
> University of Arizona
>
> Facts are stubborn, but statistics are more pliable.  Mark Twain
> Facts do not cease to exist because they are ignored.  Aldous Huxley
>
>
>
>
> ------------------------------------------------------------------------------
>
> _______________________________________________
> mesa-users mailing list
> mesa-users at lists.sourceforge.net
> https://lists.sourceforge.net/lists/listinfo/mesa-users
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://lists.mesastar.org/pipermail/mesa-users/attachments/20150617/4fa16915/attachment.html>