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Numerical stability of the Z4c formulation of general relativity

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arxiv 1111.2177 v1 pith:JHXUZDHC submitted 2011-11-09 gr-qc

Zhoujian Cao , David Hilditch This is my paper · ORCID
classification gr-qc
keywords testsevolutionsnumericalbssnokstabilityapplesconstraintdiscretization
verification ladder T0 review T1 audit T2 compute T3 formal
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We study numerical stability of different approaches to the discretization of a conformal decomposition of the Z4 formulation of general relativity. We demonstrate that in the linear, constant coefficient regime a novel discretization for tensors is formally numerically stable with a method of lines time-integrator. We then perform a full set of apples with apples tests on the non-linear system, and thus present numerical evidence that both the new and standard discretizations are, in some sense, numerically stable in the non-linear regime. The results of the Z4c numerical tests are compared with those of BSSNOK evolutions. We typically do not employ the Z4c constraint damping scheme and find that in the robust stability and gauge wave tests the Z4c evolutions result in lower constraint violation at the same resolution as the BSSNOK evolutions. In the gauge wave tests we find that the Z4c evolutions maintain the desired convergence factor over many more light-crossing times than the BSSNOK tests. The difference in the remaining tests is marginal.

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Cited by 3 Pith papers

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