Black hole excision with multiple grid patches


Thornburg, Jonathan (2004) Black hole excision with multiple grid patches. Classical and Quantum Gravity, 21, (15), 3665-3691. (doi:10.1088/0264-9381/21/15/004).

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Description/Abstract

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 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 non-smooth `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 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 (I use a
ghost-zone scheme), the number and shape of the patches (I use a
6-patch `inflated-cube' 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 non-tensor field variables such as the BSSN Γ̃ί (I use a scheme which requires ghost zones which are twice as wide for the
BSSN conformal factor φ as for Γ̃ί 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 fourth-order 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
multiple-patch scheme.

Item Type: Article
ISSNs: 0264-9381 (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
Date Deposited: 16 Apr 2007
Last Modified: 27 Mar 2014 18:30
Contact Email Address: J.Thornburg@soton.ac.uk
URI: http://eprints.soton.ac.uk/id/eprint/45845

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