A Multiple-Grid-Patch Evolution Scheme for 3-D Black Hole Excision

Details A Multiple-Grid-Patch Evolution Scheme for 3-D Black Hole Excision A Multiple-Grid-Patch Evolution Scheme for 3-D Black Hole Excision

2000-12-04

arxiv.org/abs/gr-qc/0012012v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX, 2 pages including 1 postscript figure; uses World Scientific style file ws-p9-75x6-50.cls (enclosed); to appear in Proc

Scientific paper

When using black hole excision to numerically evolve a fully generic black hole spacetime, most 3-D 3+1 codes use an $xyz$-topology (spatial) grid. In such a grid, an $r = \constant$ excision surface must be approximated by an irregular and non-smooth "staircase-shaped" excision grid boundary, which may introduce numerical instabilities into the evolution. In this paper I describe an alternate scheme, which uses multiple grid patches, each with topology $\{r \times ({\rm angular coordinates})\}$, to cover the slice outside the $r = \constant$ excision surface. The excision grid boundary is now smooth, so the evolution should be less prone to instabilities. With 4th order finite differencing, this code evolves Kerr initial data to ${\sim} 60M$ using the ADM equations; I'm currently implementing the BSSN equations in it in the hope that this will improve the stability.

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