Symmetry without Symmetry: Numerical Simulation of Axisymmetric Systems using Cartesian Grids

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dc.creatorAlcubierre, M.
dc.creatorBrandt, S.
dc.creatorBruegmann, B.
dc.creatorHolz, D.
dc.creatorSeidel, E.
dc.creatorTakahashi, R.
dc.creatorThornburg, J.
dc.date1999-08-04
dc.date.accessioned2026-07-07T12:01:27Z
dc.date.available2026-07-07T12:01:27Z
dc.descriptionWe 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 tensor partial differential equations like those of 3+1 numerical relativity. For a system axisymmetric about the z axis, the basic idea is to use a 3-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 \neq 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.
dc.description17 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/gr-qc/9908012
dc.identifierhttp://arxiv.org/abs/gr-qc/9908012
dc.identifierInt.J.Mod.Phys.D10:273-290,2001
dc.identifierdoi:10.1142/S0218271801000834
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/207099
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleSymmetry without Symmetry: Numerical Simulation of Axisymmetric Systems using Cartesian Grids
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