TY - JOUR

T1 - Symmetry without symmetry

T2 - Numerical simulation of axisymmetric systems using Cartesian grids

AU - Alcubierre, Miguel

AU - Brügmann, Bernd

AU - Holz, Daniel

AU - Takahashi, Ryoji

AU - Brandt, Steven

AU - Seidel, Edward

AU - Thornburg, Jonathan

N1 - Funding Information:
The basic idea for this work was suggested by Steven Brandt. Special thanks are due to Paul Walker for early input on this idea. This work was supported by the AEI, NSF PHY 98-00973, and FWF P12754-PHY. The calculations were performed at the AEI. We thank many colleagues at the AEI, NCSA, Univeristat de les Illes Balears, and Washington University for the co-development of the Cactus code.

PY - 2001/6

Y1 - 2001/6

N2 - 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 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 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 ≠ 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.

AB - 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 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 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 ≠ 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.

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U2 - 10.1142/S0218271801000834

DO - 10.1142/S0218271801000834

M3 - Article

AN - SCOPUS:0142207503

VL - 10

SP - 273

EP - 289

JO - International Journal of Modern Physics D

JF - International Journal of Modern Physics D

SN - 0218-2718

IS - 3

ER -