Constraint-preserving boundary conditions in the 3+1 first-order approach
Abstract
A set of energy-momentum constraint-preserving boundary conditions is proposed for the first-order Z4 case. The stability of a simple numerical implementation is tested in the linear regime (robust stability test), both with the standard corner and vertex treatment and with a modified finite-differences stencil for boundary points which avoids corners and vertices even in cartesian-like grids. Moreover, the proposed boundary conditions are tested in a strong field scenario, the Gowdy waves metric, showing the expected rate of convergence. The accumulated amount of energy-momentum constraint violations is similar or even smaller than the one generated by either periodic or reflection conditions, which are exact in the Gowdy waves case. As a side theoretical result, a new symmetrizer is explicitly given, which extends the parametric domain of symmetric hyperbolicity for the Z4 formalism. The application of these results to first-order BSSN-like formalisms is also considered.
Keywords
Cite
@article{arxiv.1003.3328,
title = {Constraint-preserving boundary conditions in the 3+1 first-order approach},
author = {C. Bona and C. Bona-Casas},
journal= {arXiv preprint arXiv:1003.3328},
year = {2014}
}
Comments
Revised version, with conclusive numerical evidence. 23 pages, 12 figures