Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-04-13
Class.Quant.Grav. 21 (2004) 3665-3692
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
31 pages, revtex4, includes color postscript figures, mpeg movies available at http://www.aei.mpg.de/~jthorn/research/mpe/movi
Scientific paper
10.1088/0264-9381/21/15/004
When using black hole excision to numerically evolve a black hole spacetime with no continuous symmetries, most 3+1 finite differencing codes use a Cartesian grid. It's difficult to do excision on such a grid, because the natural $r = \text{constant}$ excision surface must be approximated either by a very different shape such as a contained cube, or by an irregular and non-smooth "LEGO(tm) sphere" which may introduce numerical instabilities into the evolution. In this paper I describe an alternate scheme, which uses multiple $\{r \times (\text{angular coordinates}) \}$ grid patches, each patch using a different (nonsingular) choice of angular coordinates. This allows excision on a smooth $r = \text{constant}$ 2-sphere. I discuss the key design choices in such a multiple-patch scheme, including the choice of ghost-zone versus internal-boundary treatment of the interpatch boundaries, the number and shape of the patches, the details of how the ghost zones are "synchronized" by interpolation from neighboring patches, the tensor basis for the Einstein equations in each patch, and the handling of non-tensor field variables such as the BSSN $\tilde{\Gamma}^i$. I present sample numerical results from a prototype implementation of this scheme. This code simulates the time evolution of the (asymptotically flat) spacetime around a single (excised) black hole, using 4th-order finite differencing in space and time. Using Kerr initial data with $J/m^2 = 0.6$, I present evolutions to $t \gtsim 1500m$. The lifetime of these evolutions appears to be limited only by outer boundary instabilities, not by any excision instabilities or by any problems inherent to the multiple-patch scheme.
No associations
LandOfFree
Black Hole Excision with Multiple Grid Patches does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Black Hole Excision with Multiple Grid Patches, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Black Hole Excision with Multiple Grid Patches will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-247207