Constraint-preserving boundary conditions in the Z4 Numerical Relativity formalism
Abstract
The constraint-preserving approach, which aim is to provide consistent boundary conditions for Numerical Relativity simulations, is discussed in parallel with other recent developments. The case of the Z4 system is considered, and constraint-preserving boundary conditions of the Sommerfeld type are provided. A necessary condition for the stability of the proposed boundary conditions is obtained, which amounts to the requirement of a symmetric ordering of space derivatives. This requirement is numerically seen to be also sufficient in the absence of corners and edges. Maximally dissipative boundary conditions are also implemented. In this case, a less restrictive stability condition is obtained, which is shown numerically to be also sufficient even in the presence of corners and edges.
Keywords
Cite
@article{arxiv.gr-qc/0411110,
title = {Constraint-preserving boundary conditions in the Z4 Numerical Relativity formalism},
author = {C. Bona and T. Ledvinka and C. Palenzuela-Luque and M. Zacek},
journal= {arXiv preprint arXiv:gr-qc/0411110},
year = {2009}
}
Comments
Enhanced version, including a new Appendix on maximally dissipative boundary conditions (12 pages, 5 figures)