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 <[email protected]>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 <[email protected]>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 >> >> _______________________________________________ >> Users mailing list >> [email protected] >> http://lists.einsteintoolkit.org/mailman/listinfo/users >> >> > > > -- > Erik Schnetter <[email protected]> > http://www.perimeterinstitute.ca/personal/eschnetter/ >
_______________________________________________ Users mailing list [email protected] http://lists.einsteintoolkit.org/mailman/listinfo/users
