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          Institute: MPI für Gravitationsphysik     Collection: Astrophysical Relativity     Display Documents



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ID: 206107.0, MPI für Gravitationsphysik / Astrophysical Relativity
Symmetry without symmetry: Numerical simulation of axisymmetric systems using Cartesian grids.
Authors:Alcubierre, Miguel; Brandt, Steven; Brügmann, Bernd; Holz, Daniel; Seidel, Edward; Takahashi, Ryoji; Thornburg, Jonathan
Date of Publication (YYYY-MM-DD):2001-06
Title of Journal:International Journal of Modern Physics D
Volume:10
Issue / Number:3
Start Page:273
End Page:289
Copyright:Jahrbuch 2000, Copyright MPG 2000
Review Status:not specified
Audience:Not Specified
Intended Educational Use:No
Abstract / Description:We present a new technique for the numerical simulation of axisymmetric systems. This technique avoids the coordinate singularities which often arise when cylindrical or polar-spherical coordinate finite difference grids are used, particularly in simulating tenser partial differential equations like those of 3 + 1 numerical relativity. For a system axisymmetric about the r axis, the basic idea is to use a three-dimensional Cartesian (x,y,z) coordinate grid which covers (say) the y = 0 plane, but is only one finite-difference-molecule-width thick in the y direction. The field variables in the central y = 0 grid plane can be updated using normal (x, y, z)-coordinate finite differencing, while those in the y not equal 0 grid planes can be computed from those in the central plane by using the axisymmetry assumption and interpolation. We demonstrate the effectiveness of the approach on a set of fully nonlinear test computations in 3 + 1 numerical general relativity, involving both black holes and collapsing gravitational waves.
External Publication Status:published
Document Type:Article
Communicated by:Bernhard F. Schutz
Affiliations:MPI für Gravitationsphysik/Astrophysical Relativity
Identifiers:URL:http://xxx.lanl.gov/archive/gr-qc/
LOCALID:16362
DOI:10.1142/S0218271801000834
ISSN:0218-2718
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