Constraint-preserving boundary conditions in the 3+1 first-order approach
| Autor: | Bona, C., Bona-Casas, C. |
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| Rok vydání: | 2010 |
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| Zdroj: | Phys.Rev.D82:064008,2010 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevD.82.064008 |
| Popis: | 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. Comment: Revised version, with conclusive numerical evidence. 23 pages, 12 figures |
| Databáze: | arXiv |
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