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Spherical excision for moving black holes and summation by parts for axisymmetric systems

Spherical excision for moving black holes and summation by parts for axisymmetric systems
Spherical excision for moving black holes and summation by parts for axisymmetric systems
It is expected that the realization of a convergent and long-term stable numerical code for the simulation of a black hole inspiral collision will depend greatly upon the construction of stable algorithms capable of handling smooth and, most likely, time dependent boundaries. After deriving single grid, energy conserving discretizations for axisymmetric systems containing the axis of symmetry, we present a new excision method for moving black holes using multiple overlapping coordinate patches, such that each boundary is fixed with respect to at least one coordinate system. This multiple coordinate structure eliminates all need for extrapolation, a commonly used procedure for moving boundaries in numerical relativity. We demonstrate this excision method by evolving a massless Klein-Gordon scalar field around a boosted Schwarzschild black hole in axisymmetry. The excision boundary is defined by a spherical coordinate system comoving with the black hole. Our numerical experiments indicate that arbitrarily high boost velocities can be used without observing any sign of instability.
2470-0029
1-21
Calabrese, Gioel
b6d18b27-64cd-426f-b86e-1b3a848f03ed
Neilsen, David
f1187d99-0b22-4126-830a-0d238e32e680
Calabrese, Gioel
b6d18b27-64cd-426f-b86e-1b3a848f03ed
Neilsen, David
f1187d99-0b22-4126-830a-0d238e32e680

Calabrese, Gioel and Neilsen, David (2004) Spherical excision for moving black holes and summation by parts for axisymmetric systems. Physical Review D, 69 (44020), 1-21. (doi:10.1103/PhysRevD.69.044020).

Record type: Article

Abstract

It is expected that the realization of a convergent and long-term stable numerical code for the simulation of a black hole inspiral collision will depend greatly upon the construction of stable algorithms capable of handling smooth and, most likely, time dependent boundaries. After deriving single grid, energy conserving discretizations for axisymmetric systems containing the axis of symmetry, we present a new excision method for moving black holes using multiple overlapping coordinate patches, such that each boundary is fixed with respect to at least one coordinate system. This multiple coordinate structure eliminates all need for extrapolation, a commonly used procedure for moving boundaries in numerical relativity. We demonstrate this excision method by evolving a massless Klein-Gordon scalar field around a boosted Schwarzschild black hole in axisymmetry. The excision boundary is defined by a spherical coordinate system comoving with the black hole. Our numerical experiments indicate that arbitrarily high boost velocities can be used without observing any sign of instability.

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Published date: 2004

Identifiers

Local EPrints ID: 40853
URI: http://eprints.soton.ac.uk/id/eprint/40853
ISSN: 2470-0029
PURE UUID: 1a9c53d5-a017-4c81-80d1-032590487121

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Date deposited: 11 Jul 2006
Last modified: 15 Jul 2019 18:58

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Author: Gioel Calabrese
Author: David Neilsen

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