A hybrid approach to long-term binary neutron-star simulations

One of the main challenges in the numerical modeling of binary neutron-star (BNS) mergers is long-term simulations of the post-merger remnant over timescales of the order of seconds. When this modeling includes all the aspects of complex physics, the computational costs can easily become enormous. To address this challenge in part, we have developed a novel hybrid approach in which the solution from a general-relativistic magnetohydrodynamics (GRMHD) code solving the full set of the Einstein equations in Cartesian coordinates is coupled with another GRMHD code in which the Einstein equations are solved under the Conformally Flat Condition (CFC). The latter approximation has a long history and has been shown to provide an accurate description of compact objects in non-vacuum spacetimes. An important aspect of the CFC is that the elliptic equations need to be solved only for a fraction of the steps needed for the underlying HD/MHD evolution, thus allowing for a gain in computational efficiency that can be up to a factor of $\sim 6~(230)$ in three-dimensional (two-dimensional) simulations. We present the basic features of the new code, the strategies necessary to interface it when importing both two- and three-dimensional data, and a novel and robust approach to the recovery of the primitive variables. To validate our new framework, we have carried out code tests with various coordinate systems and different numbers of spatial dimensions, involving a variety of astrophysical scenarios, including the evolution of the post-merger remnant of a BNS merger over a timescale of one second. \texttt{BHAC+}, can accurately reproduce the evolution of compact objects in non-vacuum spacetimes and that, when compared with the evolution in full general relativity, the CFC reproduces accurately both the gravitational fields and the matter variables at a fraction of the computational costs.