[Users] separation of simulation domain

[林家暉]

Dear Erik,
Thanks for your reply.It is conceptually helpful.
I think I would use other codes to deal with the exterior after the interior is simulated by ET like you said.
Best regards,
Chia-Hui
________________________________
寄件者: Erik Schnetter <schnetter at protonmail.com>
寄件日期: 2018年10月11日 下午 09:14:49
收件者: 林家暉
副本: Einstein Toolkit Users
主旨: Re: [Users] separation of simulation domain

Chia-Hui

I think you are asking a question about physics, not about the Einstein Toolkit.

To simulate a system, you need to have a mathematical description to start with. If you want to combine a general relativistic interior with a Newtonian (?) exterior, then you first need to come up with a physically consistent description, for example a consistent set of PDEs with respective interface conditions. I believe this is very difficult. At the least this is a mathematical question, not one about software engineering.

What we have been doing in the past is to simple use general relativity everywhere, even in the exterior. If you use adaptive mesh refinement (AMR), then you can have a central region where small length and time scales are resolve, and an exterior region that is much larger and where only coarser length and time scales are resolved. As Roland mentions, using approximately spherical coordinates in the exterior via Llama allows you to have a constant angular resolution there, which is convenient for tracking gravitational waves generated by a point source.

If you need to resolve hours and days, then in general the following approximations hold:
- from the point of view of the interior, the exterior is constant in time
- from the point of view of the exterior, only the temporally averaged interior is relevant

People would thus first perform a calculation of the interior, and once this has reached a "steady state", use this to motivate certain inner boundary conditions for a second simulation that treats only the exterior.

-erik

> On Oct 11, 2018, at 0:29 , 林家暉 <r06222015 at ntu.edu.tw> wrote:
>
> Hello,
> I have a question about whether it is possible to separate the domain of the simulation.  I want to simulate with a larger scale such as (1 million km )^3 , however it is too computation-consuming to simulate the whole domain with GR and it is not necessary to consider GR because GR could be ignored in such large scale. But in the region near center with high density , GR is important .
> Therefore I am wondering if it is possible that GR is included in the center region ,say (1000 km)^3, but not included in the other region. However another problem is that timescale is also very different. ET's time scale is about ~ ms but what I need is around hours to days. Is there some suggestion for me to deal with it ?
> Thanks,
> Best regards,
> Chia-Hui

--
Erik Schnetter <schnetter at protonmail.com>
http://www.perimeterinstitute.ca/personal/eschnetter/



-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://lists.einsteintoolkit.org/pipermail/users/attachments/20181012/4a1a3744/attachment.html