Black hole excision with multiple grid patches
Thornburg, Jonathan (2004) Black hole excision with multiple grid patches. Classical and Quantum Gravity, 21, (15), 36653691. (doi:10.1088/02649381/21/15/004).
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Description/Abstract
When using blackhole excision to numerically evolve a blackhole
spacetime with no continuous symmetries, most 3+1 finite differencing
codes use a Cartesian grid. It is difficult to do excision on such
a grid because the natural r = constant excision surface must be
approximated either by a very different shape such as a contained
cube, or by an irregular and nonsmooth `LEGO1 sphere' which may
introduce numerical instabilities into the evolution. In this paper
I describe an alternate scheme which uses multiple
{r × (angular coordinates)} patches,
each patch using a different (nonsingular)
choice of angular coordinates. This allows excision on a smooth
r = constant 2sphere. I discuss the key design choices in such a
multiplepatch scheme, including the choice of ghostzone versus
internalboundary treatment of the interpatch boundaries (I use a
ghostzone scheme), the number and shape of the patches (I use a
6patch `inflatedcube' scheme), the details of how the ghost zones
are `synchronized' by interpolation from neighbouring patches, the
tensor basis for the Einstein equations in each patch, and the
handling of nontensor field variables such as the BSSN ??? (I use a scheme which requires ghost zones which are twice as wide for the
BSSN conformal factor ? as for ??? and the other
BSSN field variables). 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 fourthorder finite differencing
in space and time. Using Kerr initial data with J/m^2 = 0.6, I
present evolutions to t ? 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
multiplepatch scheme.
Item Type:  Article  

Digital Object Identifier (DOI):  doi:10.1088/02649381/21/15/004  
ISSNs:  02649381 (print) 

Related URLs:  
Subjects:  Q Science > QB Astronomy Q Science > QC Physics Q Science > QA Mathematics > QA76 Computer software 

Divisions :  University Structure  Pre August 2011 > School of Mathematics > Applied Mathematics 

ePrint ID:  45845  
Accepted Date and Publication Date: 


Date Deposited:  16 Apr 2007  
Last Modified:  31 Mar 2016 12:20  
URI:  http://eprints.soton.ac.uk/id/eprint/45845 
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