With the recent first detection of gravitational waves, numerical relativity provides us with the most promising tools of astronomical discovery, particularly for strong dynamical gravity phenomena where analytic solutions remain elusive. However, finding numerical solutions to the Einstein field equations of General Relativity and their accompanying matter source equations often comes at a steep computational cost. In this thesis, I present a Lagrangian formalism for solving the equations of relativistic hydrodynamics in a dynamical 3+1 spacetime using `smoothed particle hydrodynamics' (SPH) techniques. This method comes with numerous advantages over more traditional Eulerian methods. In particular, the resolution of SPH naturally follows the density distribution of the fluid: a distribution that may span many orders of magnitude in relevant astrophysical problems. The accuracy and validity of this method is then established by showing agreement with well-established analytical test cases in relativistic hydrodynamics. Additionally, I highlight the parallel properties of this method and discuss how this approach naturally lends itself well to a scientific computing environment that is increasingly seeing gains, not from higher clock rates, but rather a push towards massive parallelism.
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General Relativistic Smoothed Particle Hydrodynamics: a Multi-Scale Formulation of Fluid Flow in Numerical Relativity
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