# 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 |
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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: | 06 Aug 2015 02:38 |

URI: | http://eprints.soton.ac.uk/id/eprint/45845 |

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