Discontinuous Galerkin methods for general-relativistic hydrodynamics: formulation and application to spherically symmetric spacetimes

We have developed the formalism necessary to employ the discontinuous-Galerkin approach in general-relativistic hydrodynamics. The formalism is firstly presented in a general 4-dimensional setting and then specialized to the case of spherical symmetry within a 3+1 splitting of spacetime. As a direct application, we have constructed a one-dimensional code, EDGES, which has been used to asses the viability of these methods via a series of tests involving highly relativistic flows in strong gravity. Our results show that discontinuous Galerkin methods are able not only to handle strong relativistic shock waves but, at the same time, to attain very high orders of accuracy and exponential convergence rates in smooth regions of the flow. Given these promising prospects and their affinity with a pseudospectral solution of the Einstein equations, discontinuous Galerkin methods could represent a new paradigm for the accurate numerical modelling in relativistic astrophysics.Comment: 24 pages, 19 figures. Small changes; matches version to appear in PR

Twisted-torus configurations with large toroidal magnetic fields in relativistic stars

Understanding the properties of the internal magnetic field of neutron stars remains a theoretical challenge. Over the last years, twisted-torus geometries have been considered both in Newtonian and general-relativistic equilibrium models, as they represent a potentially good description of neutron star interiors. All of these works have found an apparent intrinsic limitation to geometries that are poloidal-field-dominated, with a toroidal-to-poloidal energy ratio inside the star that are <10%, unless surface currents are included and magnetic fields are allowed to be discontinuous. This limitation is in stark contrast with the general expectation that much higher toroidal fields should be present in the stellar interior and casts doubt about the stability and hence realism of these configurations. We here discuss how to overcome this limitation by adopting a new prescription for the azimuthal currents that leads to magnetized equilibria where the toroidal-to-total magnetic-field energy ratio can be as high as 90%, thus including geometries that are toroidal-field-dominated. Moreover, our results show that for a fixed exterior magnetic-field strength, a higher toroidal-field energy implies a much higher total magnetic energy stored in the star, with a potentially strong impact on the expected electromagnetic and gravitational-wave emission from highly magnetized neutron stars.Comment: 5 pages, 3 figures, 1 tabl

Universality and intermittency in relativistic turbulent flows of a hot plasma

With the aim of determining the statistical properties of relativistic turbulence and unveiling novel and non-classical features, we resent the results of direct numerical simulations of driven turbulence in an ultrarelativistic hot plasma using high-order numerical schemes. We study the statistical properties of flows with average Mach number ranging from $\sim 0.4$ to $\sim 1.7$ and with average Lorentz factors up to $\sim 1.7$. We find that flow quantities, such as the energy density or the local Lorentz factor, show large spatial variance even in the subsonic case as compressibility is enhanced by relativistic effects. The velocity field is highly intermittent, but its power-spectrum is found to be in good agreement with the predictions of the classical theory of Kolmogorov. Overall, our results indicate that relativistic effects are able to significantly enhance the intermittency of the flow and affect the high-order statistics of the velocity field, while leaving unchanged the low-order statistics, which instead appear to be universal and in good agreement with the classical Kolmogorov theory. To the best of our knowledge, these are the most accurate simulations of driven relativistic turbulence to date.Comment: 5 pages, 4 figures. Minor changes to match the version accepted on ApJ

Universality and intermittency in relativistic turbulent flows of a hot gas

With the aim of determining the statistical properties of relativistic turbulence and unveiling novel and non-classical features, we present the results of direct numerical simulations of driven turbulence in an ultrarelativistic hot plasma using high-order numerical schemes. We study the statistical properties of flows with average Mach number ranging from $\sim 0.4$ to $\sim 1.7$ and with average Lorentz factors up to $\sim 1.7$. We find that flow quantities, such as the energy density or the local Lorentz factor, show large spatial variance even in the subsonic case as compressibility is enhanced by relativistic effects. The velocity field is highly intermittent, but its power-spectrum is found to be in good agreement with the predictions of the classical theory of Kolmogorov.Comment: Talk given at the ASTRONUM2012 conference on the 25th of June 201

The Exact Solution of the Riemann Problem in Relativistic MHD

We discuss the procedure for the exact solution of the Riemann problem in special relativistic magnetohydrodynamics (MHD). We consider both initial states leading to a set of only three waves analogous to the ones in relativistic hydrodynamics, as well as generic initial states leading to the full set of seven MHD waves. Because of its generality, the solution presented here could serve as an important test for those numerical codes solving the MHD equations in relativistic regimes.Comment: 36 pages, 13 figures. Minor changes to match published versio