[mesa-users] accretion

[Bill Paxton]

Hi Dave,

Thanks for your words of hope!   However, the advection I've been discussing with Dean is not (necessarily) from the turbulent cascade of convection.  I've been talking about the advection term introduced in the Sugimoto&Nomoto and Townsley&Bildsten "Eulerian" treatments of the Lagrangian time derivatives for the calculation of eps_grav (= -T*Ds/Dt).  I don't know whether the CFL advection limits discussed by Viallet et al 2013 also apply to the advection terms in this case.  In these schemes we are getting a Lagrangian time derivative by splitting it into a time derivative at constant relative mass coordinate and an advection term with the velocity of mass flowing by the constant relative mass location determined by the accretion rate.  My hunch has been that "super CFL" advection was dubious for the entropy time derivative for eps_grav.  The Viallet et al paper suggests a CFL_advection limit of 2 for implicit solution of convection related advection.   It is a jump from their case to ours -- but it is suggestive.   And I still don't like to have an advection term if I can avoid it -- at least not until someone can explain to me why my concern is unfounded in spite of the Viallet et al findings.

But you also suggest that we don't necessarily need to be thinking about resolving the advection at the level of the evolution steps in order to get useful results.   That's what I was getting at by suggesting the possibility of a "side-computation" to calculate an effective accretion heating in surface layers to be used in place of the standard calculation of eps_grav in mesa/star.  Perhaps that side computation would use substeps that were small enough to capture the advection effects --- or perhaps you and Dean and friends will look at your 3D results and give us a nice simple recipe for calculating eps_grav in the presence of large mass changes.  Please do!

Cheers,
Bill




On Oct 3, 2013, at 6:21 PM, David Arnett wrote:

> I think (actually I am quite sure) I agree with Ben. 
> 
> Some further thoughts:
> 
> There are two different time scales which are important here. One is the "entrainment: time scale which is how fast the turbulence is eating into the stable regions at the boundary (this tends to be slow), and the other is the "cycle" time scale, which is how fast the integral scale convection takes to move matter from the top to the bottom (or vice versa) of the turbulent region. If we are lucky we can implicitly solve the cycle time scale, and increase the delta t allowed for MESA stability.
> 
> In a turbulent cascade the largest scale (the "integral" scale) is the dominant transport mode and probably the physically relevant CFL (causality) time scale. This is a global feature of the turbulent layer, not of the zoning, and should be much larger than the CFL for the smallest zone. Have hope Bill, the presence of fluctuations may not mean that we have to resolve them in time, just that we have to approximate their average behavior.
> 
> Dave
> 
> 
> -- 
> 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
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