[Users] outer boundary conditions

[Comer Duncan]

Hi Eric,

Thanks for your reply.

I found a reference to an old paper by Vulcanov in which he mentions a
thorn he calls Cosmo which is purported to begin to include cosmological
backgrounds and expanding outer bc.  However, I can not seem to find such
nowadays in ET.  Do you remember it? If so, is it now defunct and/or
inadequate?

Treating the expanding background as an asymptotic bc with a gauge choice
is something I thought about.  I was just thinking of running some problems
using McLachlan with say FRW outer bc and was wondering whether McLachlan
has been used by anyone in this context? I have not seen such.

Comer


On Tue, May 28, 2013 at 10:25 PM, Erik Schnetter <schnetter at cct.lsu.edu>wrote:

> Comer
>
> I am aware of two general types of boundary conditions: either outgoing
> radiative boundary conditions, or periodic boundary conditions. The latter
> are commonly used in cosmology, where one may want to simulate a box of a
> certain (large) size, and then identifies the box faces to avoid the need
> for an artificial outer boundary.
>
> The other type is commonly used for simulating compact objects. Instead of
> imposing asymptotic flatness, one sets up a particular geometry via initial
> conditions, and then uses a boundary condition that lets (approximately)
> all gravitational radiation exit the simulation domain, while not injecting
> any gravitational radiation. The true story is a bit more complex, and what
> is often done numerically is only a crude approximation of this.
>
> What particular feature of an expanding edge do you want to model? If it
> is already encoded in the initial condition, then the boundary condition
> may not look particularly complex. On the other hand, if you want to model
> a simulation domain with a volume that grows in time, then this may
> correspond to a gauge choice that moves the location of the outer boundary
> (which is fixed in coordinate space) in a certain way.
>
> To start, you probably need to choose a foliation (since this is about a
> time evolution), and describe your boundary condition in this foliation. If
> you can describe the boundary condition via a set of PDEs and gauge
> conditions, then it should be fairly straightforward to implement. There
> may be certain special cases that correspond to what is already implemented
> in the Einstein Toolkit, but being unfamiliar with the matter I cannot say
> without seeing a description of the boundary condition in terms of PDEs.
>
> -erik
>
>
>
> On Tue, May 28, 2013 at 4:16 PM, Comer Duncan <comer.duncan at gmail.com>wrote:
>
>> I am wondering what existing support there is in the einsteintoolkit for
>> outer boundary conditions appropriate to cosmological problems?  I do not
>> seem to find anything directly relevant, so please let me know if I have
>> missed something.  Suppose one has a given interior problem which uses
>> spatially asymptotically flat boundary conditions for all variables. Given
>> that I was wondering how hard it would be to redo the problem replacing the
>> asymptotically flat with asymptotically expanding at the edge of the
>> spatial mesh?
>>
>> Thanks for any help.
>>
>> Comer
>>
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>>
>
>
> --
> Erik Schnetter <schnetter at cct.lsu.edu>
> http://www.perimeterinstitute.ca/personal/eschnetter/
>
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