[mesa-users] The MLT Jacobian

[Ehsan Moravveji]

HI Pablo,

Thanks for your words on this.
So, perhaps the Newton solver, at the current stage is so robust that an improved partials would not change the accuracy/performance to better.
It’s like giving a Ferrari for a Lamborghini ;-)

Best wishes,
Ehsan.

> On 26 Aug 2016, at 09:44, Pablo Marchant <pamarca at gmail.com> wrote:
> 
> Hi Ehsan. In general, the better the partials are, the easier it will be for the newton solver to provide an answer. But whatever solution the solver ends up accepting needs to satisfy the stellar structure equations. Sure, if you modify the partials provided by mlt you won't have the same results up to machine precision, but the solutions should be physically equivalent.
> 
> 
> Am 26.08.2016 1:15 vorm. schrieb "Ehsan Moravveji" <e.moravveji at gmail.com <mailto:e.moravveji at gmail.com>>:
> Dear mesa users,
> 
> I’ve been taking a peek at the ml.f90 module, and came across two naive questions. So, I thought of sharing them with you, and ask for your kind feedbacks.
> 
> 1. The MLT module returns the Jacobian of the output quantities w.r.t. the input, e.g. partial_gradT_div_partial_grada and so on.
> On the other hand, the cgrav, mixing_length_alpha, and gradr_factor are three additional inputs, which are allowed to have spatial dependence too, e.g. s% cgrav(:).
> Furthermore, gradr in the convective region depends on alpha_MLT; e.g. see Eqs. (14.98), (14.94), and (14.107) in Cox and Giuli.
> 
> Consequently, I was speculating that derivatives of cgrav, mixing_length_alpha and grad_factor may also need be incorporated in the Jacobian matrix.
> Is anyone willing to enlighten me on this?
> 
> 2. Currently, the derivative of gradL_composition_term w.r.t. to all quantities is ignored when evaluating the derivative of Ledoux temperature gradient; see line 485 in mlt.f90. From Eq. (8) in MESA_II paper, the B-term depends explicitly on chi_T. So, I was wondering, as a rough, first-order estimate, it would be possible to include the derivative of B-term w.r.t. to chi_T, e.g.
> 
>          gradL = grada + gradL_composition_term
>          d_gradL_composition_term_dvb(mlt_dchiT) = - gradL_composition_term / chiT
>          d_gradL_dvb = d_grada_dvb + d_gradL_composition_term_dvb
> 
> I am aware that working out the composition dependence of gradL_composition_term could be involved; so, that might be ignored for now.
> It is possible that a modified gradL derivative would influence, even slightly, the behaviour of growing convective cores. This "might be" important for seismic modelling Kepler F stars. I have to admit this is my naive speculation, and shall be exploited and tested first.
> 
> I appreciate and welcome your feedbacks.
> 
> Best regards,
> Ehsan.
> 
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