Microphysics in computational relativistic astrophysics
I review different approaches to the kinematics and dynamics of (hyper)elasticity in GR, and describe one that is now being implemented in joint work with Ian Hawke.
Nonlinear numerical relativistic elasticity may be necessary for simulations including neutron star crusts. Basic simulations of large deformations in relativistic elastic matter will be detailed, and issues necessary for more realistic simulations covered. This work is in collaboration with Carsten Gundlach.
I present a relativistic study of axisymmetric magnetohydrodynamic Bondi--Hoyle accretion onto a moving Kerr black hole. The equations of general relativistic magnetohydrodynamics are solved using high resolution shock capturing methods, involving the use of linearised Riemann solvers. In this study I use the ideal MHD limit, which assumes no viscosity and infinite conductivity. The fluid flow is completely specified by the adiabatic constant $Gamma$, the asymptotic speed of sound $c_s^infty$, and the plasma beta parameter $beta_P$.
Alfven oscillations of strongly magnetized neutron stars coupled to shear modes in the solid crust could possibly explain the quasi-periodic oscillations (QPOs) observed in the giant flares of soft gamma repeaters. We present results of two-dimensional simulations of Alfven torsional oscillations in magnetars, modeled as relativistic stars with a dipolar magnetic field. We use a general relativistic magnetohydrodynamics code in the anelastic approximation, which allows for an effective suppression of fluid modes and an accurate description of the Alfven waves.
I will discuss the techniques that can be used to include arbitrary equations of state in MHD simulations, particularly the ways in which one may perform conservative to primitive variable conversion numerically for such simulations.
GPUs can offer a less costly solution to large-scale calculations of astrophysical systems. I will outline the basics of the CUDA libraries and also compare with various metrics our in-development GPU code for molecular dynamics versus our hybrid OpenMP/MPI version.
I will present the formalism needed for the application of discontinuous Galerkin methods to general relativistic hydrodynamics and the results obtained in the spherically symmetric case.