We present a new fully first-order strongly hyperbolic representation of the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's equations with optional constraint damping terms. We describe the characteristic fields of the system, discuss its hyperbolicity properties, and present two numerical implementations and simulations: one using finite differences, adaptive mesh refinement, and, in particular, binary black holes, and another one using the discontinuous Galerkin method in spherical symmetry. The results of this paper constitute a first step in an effort to combine the robustness of Baumgarte-Shapiro-Shibata-Nakamura evolutions with very high accuracy numerical techniques, such as spectral collocation multidomain or discontinuous Galerkin methods. © 2012 American Physical Society.
Publication Source (Journal or Book title)
Physical Review D - Particles, Fields, Gravitation and Cosmology
Brown, J., Diener, P., Field, S., Hesthaven, J., Herrmann, F., Mroué, A., Sarbach, O., Schnetter, E., Tiglio, M., & Wagman, M. (2012). Numerical simulations with a first-order BSSN formulation of Einstein's field equations. Physical Review D - Particles, Fields, Gravitation and Cosmology, 85 (8) https://doi.org/10.1103/PhysRevD.85.084004