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  Gauge and constraint shocks in one-dimensional numerical relativity

Reimann, B., Alcubierre, M., Gonzalez, J. A., & Nunez, D. (2005). Gauge and constraint shocks in one-dimensional numerical relativity. Physical Review D, 71: 064021.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4E94-D Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4E95-B
Genre: Journal Article

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0411094.pdf (Preprint), 607KB
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 Creators:
Reimann, Bernd1, Author
Alcubierre, Miguel, Author
Gonzalez, Jose A., Author
Nunez, Dario, Author
Affiliations:
1Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24013              

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 Abstract: We study how different types of blow-ups can occur in systems of hyperbolic evolution equations of the type found in general relativity. In particular, we discuss two independent criteria that can be used to determine when such blow-ups can be expected. One criteria is related with the so-called geometric blow-up leading to gradient catastrophes, while the other is based upon the ODE-mechanism leading to blow-ups within finite time. We show how both mechanisms work in the case of a simple one-dimensional wave equation with a dynamic wave speed and sources, and later explore how those blow-ups can appear in one-dimensional numerical relativity. In the latter case we recover the well known ``gauge shocks'' associated with Bona-Masso type slicing conditions. However, a crucial result of this study has been the identification of a second family of blow-ups associated with the way in which the constraints have been used to construct a hyperbolic formulation. We call these blow-ups ``constraint shocks'' and show that they are formulation specific, and that choices can be made to eliminate them or at least make them less severe.

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Language(s): eng - English
 Dates: 2005
 Publication Status: Published in print
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 Identifiers: eDoc: 205707
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Title: Physical Review D
Source Genre: Journal
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Pages: - Volume / Issue: 71 Sequence Number: 064021 Start / End Page: - Identifier: -