Recent gravitational wave observations of neutron star mergers (NSMs) by LIGO have increased the need for more detailed and complex simulations of these events. State-of-the-art simulations are necessary for interpreting the observational data and gaining insight into the underlying physics of NSMs, such as r-process nucleosynthesis and the nuclear equation of state. Numerically solving the Einstein field equations of general relativity (GR) in addition to the GR hydrodynamic equations is essential for accurate NSM simulations.
In this project I explore particle methods for the GR hydrodynamic equations used to model NSMs. Particle methods offer several advantages over the commonly used grid-based approach: they have excellent conservation properties and a naturally adaptive resolution and do not require artificial atmospheres or costly conversion from conserved to primitive quantities. Furthermore, I experiment with coupling the particle hydrodynamics with dynamical geometry, which is evolved by solving the Einstein field equations in a generalized harmonic (GH) formulation. This has a number of advantages over the more commonly used BSSN formulation, such as explicit symmetric hyperbolicity, a constraint damping scheme and provable stability
To this end, I demonstrate the stable and efficient evolution of a single, rotating, relativistic star in a full dynamical three-dimensional geometry. These first results demonstrate the potential of particle methods in applications to NSMs (and possibly binary neutron star-black hole mergers). While simulating these merger events will be significantly more computationally expensive, the promising scaling results from the simpler model demonstrated here show that an extension to these more complicated models is achievable.