[mesa-users] Misuse of Ledoux criterion in mesa MLT

[Arlette Grotsch]

Hi Falk,

I am fully aware of the fact that stars don’t know such a thing as a « mathematical » discontinuity. The trick is here a way to keep a structure coherent with the physical frame adopted in the computation (LMLT). This helps a lot to prevent a sort of numerical « scrubbing » and also to help applying convective criteria in a coherent way and obtain reliable extents of convective cores. Of course, it can be done with other techniques. A double mesh point is just an easy one.
Arlette



Le 16 juin 2014 à 22:26, Falk Herwig <fherwig at uvic.ca> a écrit :

> I have not followed all the details of this thread. But the notion that a convective boundary could be so thin that it would require in 1D a double mesh point is something I find difficult to contemplate in the context of today's numerical tools and resources. I would argue that there are no discontinuities inside a star that one could not resolve in 1D, except the shock during the final SN explosion and/or the flame in a thermo-nuclear explosion. The problem is of course that we can not resolve and simulate the relevant physics of the convective boundary in 1D. The answer to the physics of the convective boundary layer is still hidden in the global, non-linear solutions of the conservation laws in 3D, and would involve most of the hydrodynamic instabilities known. In the absence of a full quantitative understanding of this physics (something that can and will be improved in the not too distant future), we need to adopt a convective boundary model that mimics the behaviour of entropy and species mixing. A very simple model is the exponential convective-boundary mixing model in MESA, that is now available with some treatment of (partial, depth-dependent ...) entropy mixing. This model allows you to make the convective boundary as thin as you believe is physically justified, provided you can put enough zones in there to resolve that boundary, which in our days really should not provide much of a limitation. But I would argue that one should never approximate the convective boundary as a discontinuity. Besides the fact that a discontinuity is physically a poor choice for any convective boundary, it is also a choice that would resist reaching numerical convergence under grid refinement. 
> 
> Falk
> 
> 
> On 2014-06-16, at 1:56 AM, Arlette Grotsch wrote:
> 
>> The best way to deal with convective boundaries would be to insert a double mesh point, which can easily reflect the convective and radiative sides of this boundary.
> 
> --
> Falk Herwig
> Dept of Physics & Astronomy, U of Victoria
> fherwig at uvic.ca, tel: +1 (250) 721-7743
> 
> 
> 

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