SPHINCS_BSSN: A general relativistic Smooth Particle Hydrodynamics code for dynamical spacetimes
Abstract
We present a new methodology for simulating selfgravitating generalrelativistic fluids. In our approach the fluid is modelled by means of Lagrangian particles in the framework of a generalrelativistic (GR) Smooth Particle Hydrodynamics (SPH) formulation, while the spacetime is evolved on a mesh according to the BSSN formulation that is also frequently used in Eulerian GRhydrodynamics. To the best of our knowledge this is the first Lagrangian fully general relativistic hydrodynamics code (all previous SPH approaches used approximations to GRgravity). A core ingredient of our particlemesh approach is the coupling between the gas (represented by particles) and the spacetime (represented by a mesh) for which we have developed a set of sophisticated interpolation tools that are inspired by other particlemesh approaches, in particular by vortexparticle methods. One advantage of splitting the methodology between matter and spacetime is that it gives us more freedom in choosing the resolution, so that  if the spacetime is smooth enough  we obtain good results already with a moderate number of grid cells and can focus the computational effort on the simulation of the matter. Further advantages of our approach are the ease with which ejecta can be tracked and the fact that the neutron star surface remains wellbehaved and does not need any particular treatment. In the hydrodynamics part of the code we use a number of techniques that are new to SPH, such as reconstruction, slope limiting and steering dissipation by monitoring entropy conservation. We describe here in detail the employed numerical methods and demonstrate the code performance in a number of benchmark problems ranging from shock tube tests, over Cowling approximations to the fully dynamical evolution of neutron stars in selfconsistently evolved spacetimes.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 arXiv:
 arXiv:2012.13954
 Bibcode:
 2020arXiv201213954R
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  High Energy Astrophysical Phenomena;
 Astrophysics  Instrumentation and Methods for Astrophysics
 EPrint:
 41 pages, 16 figures