General-relativistic neutron star evolutions with the discontinuous Galerkin method

TL;DR

This paper demonstrates the application of the discontinuous Galerkin method to simulate general-relativistic neutron stars, achieving high accuracy, stability, and improved convergence in complex astrophysical scenarios.

Contribution

It introduces a novel implementation of the discontinuous Galerkin method for evolving both spacetime and matter in neutron star simulations, including dynamical spacetimes.

Findings

Long-term stable evolutions of neutron stars and black holes

Higher convergence rates compared to finite-volume methods

Successful 3D simulations of complex relativistic systems

Abstract

Simulations of relativistic hydrodynamics often need both high accuracy and robust shock-handling properties. The discontinuous Galerkin method combines these features --- a high order of convergence in regions where the solution is smooth and shock-capturing properties for regions where it is not --- with geometric flexibility and is therefore well suited to solve the partial differential equations describing astrophysical scenarios. We present here evolutions of a general-relativistic neutron star with the discontinuous Galerkin method. In these simulations, we simultaneously evolve the spacetime geometry and the matter on the same computational grid, which we conform to the spherical geometry of the problem. To verify the correctness of our implementation, we perform standard convergence and shock tests. We then show results for evolving, in three dimensions, a Kerr black hole; a neutron star in the Cowling approximation (holding the spacetime metric fixed); and, finally, a neutron star where the spacetime and matter are both dynamical. The evolutions show long-term stability, good accuracy, and an improved rate of convergence versus a comparable-resolution finite-volume method.