[Users] question about ML_BSSN::fixAdvectionTerms

[Jonah Miller]

Hi Kyle,


I am not sure the origin of this parameter, but it is indeed necessary. 
With fixAdvectionTerms=0, the evolution of the time derivative of the 
lapse A is given by

partial_t A = (partial_t - Lie_beta) K - A

where K is the trace of the extrinsic curvature, beta is the shift, and 
Lie is the Lie derivative. It turns out that this prescription is 
incompatible with 1+log slicing. Worse, if you try to impose 1+log like 
gauge conditions the gauge for a static black hole will in fact be 
dynamic. In other words, the coordinates will evolve.


To get 1+log slicing, you need to set fixAdvectionTerms=1, which gives 
the prescription

( partial_t  - Lie_beta ) A = (partial_t - Lie_beta) K

which is compatible with 1+log slicing and with a static coordinate 
system for a black hole.

As you can see, it's called "fixAdvectionTerms" because it changes the 
partial time derivative of A into an advective total derivative.

I'm not sure the origin of the parameter so I don't know the reason for 
the current default settings. Somebody else should have some insight there.

Best,
Jonah

On 16-09-29 12:47 PM, Slinker, Kyle Patrick wrote:
> Hello,
>
> I'm wondering if anybody can tell me about the
> ML_BSSN::fixAdvectionTerms parameter (which I think was new in
> Somerville). I have been trying to reproduce some old results and
> discovered this morning that having this parameter set to "off" is what
> was causing the discrepancy.
>
> What does it do? The description "Modify driver and advection terms to
> work better?" is vague enough I don't know what to make of it. From
> McLachlan_BSSN.m it looks like it's switching how the advection terms in
> the 1+log and Gamma-driver conditions are handled. What changes is it
> making to these equations? And what is the purpose of them? If setting
> the parameter to "on" reproduces old results (and if it lives up to its
> name and fixes things), should "on" be the default behavior?
>
> Thanks.
>
> Kyle Slinker
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