[mesa-users] questions about the "Eulerian" scheme for eps_grav

Sun Nov 9 23:04:45 EST 2014

Hi Dean,

I appreciate that you gave me the comments so quickly!

Thank you for the suggestion. I will update to ver 7184 and use the transition region set by eps_grav_time_deriv_separation. In ver. 6596, I set that the transition region is ten cells or more (namely, “min_cells_for_Eulerian_to_Lagrangian_transition = 10”).

I am sorry for the misleading sentence. I can change the Eulerian region with “min_dxm_Eulerian_div_dxm_added” even in ver. 6596, but sometimes the Eulerian region disappears when the timestep (and then dm) is very small. I wanted to maintain a large Eulerian region even in such a case.

I am glad to have your comments on the CpTMdot controls! I wondered why CpTMdot/L is still used to limit the Eulerian region. Since in our study the accretion is highly adiabatic, I set “min_dxm_Eulerian_div_dxm_CpTMdot_lt_L = -1”.

As for my second question, I am still not sure the two assumptions are physically valid: (1) a parcel of accreting material can instantaneously enter the stellar interior and (2) its entropy is the same as that of the stellar interior. I think your “compressional heating” in Townsley and Bildsten (2004) considers the heat leak of the accreting material, but here we do not take into account such a energy release...

Best wishes,
Masanobu

> On Nov 10, 2014, at 11:27, Dean Townsley <Dean.M.Townsley at ua.edu> wrote:
> 
> Hi Masanobu,
> 
> Nice to have you using this stuff!  Hopefully I can help you a bit with your questions.
> 
> First, if it's not too much trouble, you might want to use the most recent release (7184).  This release contains some changes to how the boundaries for the Eulerian vs. Lagrangian forms for eps_grav are determined, and some updates for consistency with how the mesh behaves (constant dq or constant dm) in these regions.  With this new version min_dxm_Eulerian_div_dxm_added should work.  Please let me know if it doesn't do what you expect and I can investigate.
> 
> I think the CpTMdot controls aren't being used anymore because either the "Eulerian" or Lagrangian form of eps_grav is valid in the whole star so that it doesn't make sense to limit on this quantity anymore.   I still need to clear this control out cleanly, sorry about that.  The control used to adjust for accuracy  (or validity) is now eps_grav_time_deriv_separation, but you shouldn't need to adjust it if you push the transition region far into the star anyway.  I reproduce the comment about it below, since it may be that you don't need to push the Eulerian region over the whole star and you can just let this control adjust to the mass added each time step for you.
> 
> 
>          !### eps_grav_time_deriv_separation
> 
>          ! Separation (in grid cells) over which eps_grav can be time-differenced when Mstar changes
>          ! The mesh has two major regions - an interior region where the cells are
>          ! Lagrangian and an outer region where they are homologous (constant dq =dm/M).
>          ! There is also a small transition region between these two.  In the Lagrangian
>          ! region Ds/dt is evaluated with a Lagrangian finite difference in time, while in the
>          ! homologous region Ds/dt is evaluated with a finite difference in time at constant q
>          ! plus an advection-like term accounting for the movement of the q boundaries in mass.
>          ! In the transition region, these two derivatives are combined.  This means that at
>          ! the edges of the transition region, finite differences may cross cell boundaries.
>          ! This control determines how the mesh for the end of the current timestep is
>          ! placed to ensure that finite differences cross no more than this many cell
>          ! boundaries.
> 
>       eps_grav_time_deriv_separation = 1.5
> 
> 
> 
> 
> On your second question:  The new material is added at the outside of the star - not throughout the star.  The size of the mesh zones change in the "Eulerian" or "constant q" part of the star (which may be the whole star if you push the boundary that deep), but the entropy and its derivatives are evaluated locally, not with respect to the surface.  So a parcel of material enters the star at the surface with the same entropy as the surface, but its entropy then evolves appropriately as it moves down through the star.
> 
> 
> Hopefully that helps.  Like I said, let me know if the newer version doesn't do what you expect.
> 
> Dean
> 
> 
> On 11/09/2014 07:06 PM, Masanobu Kunitomo wrote:
>> Dear all,
>> 
>> 
>> I would like to ask two questions about (1) changing the region of “Eulerian scheme” (s% k_below_Eulerian_eps_grav) and (2) the validity of the Eulerian scheme. I am using ver. 6596 and working on a protostar’s evolution with intense accretion (the mass accretion rate is 1e-5Msun/yr and CpTMdot/L is at most ~100).
>> 
>> 
>> (1)
>> I would like to try the case that eps_grav is calculated by the “Eulerian” scheme in the entire star, namely s% k_below_Eulerian_eps_grav = s% nz (although this may not be good because the Eulerian scheme can cause a numerical diffusion). 
>> I tried to set a large “min_dxm_Eulerian_div_dxm_added” in the inlist file, but this did not work. Next I tried to modify the subroutine "set_Eulerian_Lagrangian_for_eps_grav” in “mesa/star/private/evolve.f”. I tried some modifications such as “dxm_kA = s% xmstar”, but it did not work. (In fact, even if I write “stop”, it was not reflected...) Is it inappropriate to modify the evolve.f file?
>> 
>> (2)
>> If my understanding is correct, in the Eulerian scheme, the newly accreted mass is distributed in the entire star uniformly and instantaneously, and its entropy is assumed to match the local value of the stellar interior as shown in the Fig. 6 of Sugimoto et al. 1981 (I have attached this figure). If the star is radiative, the accreting material’s entropy can be much lower than that of the stellar surface. Thus, I think this underestimates the accreting material’s entropy. Is this correct?
>> 
>> 
>> 
>> I apologise if these are already discussed in this mailing list. 
>> I appreciate any comments. Thanks in advance!
>> 
>> Best wishes,
>> Masanobu
>> 
>> --
>> Masanobu Kunitomo
>> Ph.D. student / JSPS Research Fellow
>> Tokyo Institute of Technology
>> Dept. of Earth and Planetary Sciences
>> Email: kunitomo at geo.titech.ac.jp <mailto:kunitomo at geo.titech.ac.jp>
>> 
>> 
>> 
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