[Users] outer boundary conditions

[Erik Schnetter]

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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