Combining spectral and shock-capturing methods: A new numerical approach for 3D relativistic core collapse simulations

  title={Combining spectral and shock-capturing methods: A new numerical approach for 3D relativistic core collapse simulations},
  author={Harald Dimmelmeier and J. Novak and Jos{\'e} A. Font and Jos{\'e} Ma. Ib{\'a}{\~n}ez and E. R. Mueller},
  journal={Physical Review D},
We present a new three-dimensional general relativistic hydrodynamics code which is intended for simulations of stellar core collapse to a neutron star, as well as pulsations and instabilities of rotating relativistic stars. Contrary to the common approach followed in most existing three-dimensional numerical relativity codes which are based in Cartesian coordinates, in this code both the metric and the hydrodynamics equations are formulated and solved numerically using spherical polar… 
High-resolution shock capturing scheme for ideal hydrodynamics in general relativity optimized for quasistationary solutions
In this article, we present a numerical scheme for relativistic ideal hydrodynamics on arbitrary curved spacetimes in up to three spatial dimensions. The aim of this scheme is an improved treatment
General relativistic magnetohydrodynamics in axisymmetric dynamical spacetimes: the X-ECHO code
We present a new numerical code, X-ECHO, for general relativistic magnetohydrodynamics (GRMHD) in dynamical spacetimes. This aims at studying astrophysical situations where strong gravity and
Gmunu: toward multigrid based Einstein field equations solver for general-relativistic hydrodynamics simulations
We present a new open-source axisymmetric general relativistic hydrodynamics code Gmunu (general-relativistic multigrid numerical solver) which uses a multigrid method to solve the elliptic metric
CFC+: Improved dynamics and gravitational waveforms from relativistic core collapse simulations
Received date / Accepted date Abstract. Core collapse supernovae are a promising source of detectable gravitational waves. Most of the existing (multidimensional) numerical simulations of core
Exploring the relativistic regime with Newtonian hydrodynamics: an improved effective gravitational potential for supernova simulations
We investigate the possibility approximating relativistic effects in hydrodynamical simulations of stellar core collapse and post-bounce evolution by using a modified gravitational potential in an
A new open-source code for spherically symmetric stellar collapse to neutron stars and black holes
We present the new open-source spherically symmetric general-relativistic (GR) hydrodynamics code GR1D. It is based on the Eulerian formulation of GR hydrodynamics (GRHD) put forth by
An introduction to relativistic hydrodynamics
We review formulations of the equations of (inviscid) general relativistic hydrodynamics and (ideal) magnetohydrodynamics, along with methods for their numerical solution. Both systems can be cast as
Gravitational waves in dynamical spacetimes with matter content in the fully constrained formulation
The Fully Constrained Formulation (FCF) of General Relativity is a novel framework introduced as an alternative to the hyperbolic formulations traditionally used in numerical relativity. The FCF
A Novel multidimensional Boltzmann neutrino transport scheme for core-collapse supernovae.
A new discrete-ordinate scheme for solving the general relativistic Boltzmann transport equation in the context of core-collapse supernovae (CCSNe) using an intuitive particle-like approach that has excellent conservation properties and fully accounts for Lorentz boosts, GR effects, and grid geometry terms is introduced.
Spectral Methods for Time-dependent Studies of Accretion Flows. II. Two-dimensional Hydrodynamic Disks with Self-Gravity
Spectral methods are well suited for solving hydrodynamic problems in which the self-gravity of the flow needs to be considered. Because Poisson's equation is linear, the numerical solution for the


Relativistic simulations of rotational core collapse I. Methods, initial models, and code tests
We describe an axisymmetric general relativistic code for rotational core collapse. The code evolves the coupled system of metric and fluid equations using the ADM 3 + 1 formalism and a conformally
Three-dimensional numerical general relativistic hydrodynamics. 1. Formulations, methods, and code tests
This is the first in a series of papers on the construction and validation of a three-dimensional code for general relativistic hydrodynamics, and its application to general relativistic
Three-dimensional relativistic simulations of rotating neutron-star collapse to a Kerr black hole
We present a new three-dimensional fully general-relativistic hydrodynamics code using high-resolution shock-capturing techniques and a conformal traceless formulation of the Einstein equations.
Non-linear hydrodynamical evolution of rotating relativistic stars: numerical methods and code tests
ABSTRA C T We present numerical hydrodynamical evolutions of rapidly rotating relativistic stars, using an axisymmetric, non-linear relativistic hydrodynamics code. We use four different
Gravitational waves from axisymmetric rotating stellar core collapse to a neutron star in full general relativity
Axisymmetric numerical simulations of rotating stellar core collapse to a neutron star are performed in the framework of full general relativity. The so-called Cartoon method, in which the Einstein
Relativistic numerical model for close neutron-star binaries.
The evidence that general relativistic effects may cause the stars to individually collapse into black holes prior to merging and the strong fields cause the last stable orbit to occur at a larger separation distance and lower frequency than previously estimated is discussed.
Relativistic simulations of rotational core collapse - II. Collapse dynamics and gravitational radiation
We have performed hydrodynamic simulations of relativistic rotational supernova core collapse in axisymmetry and have computed the gravitational radiation emitted by such an event. The Einstein
Axisymmetric general relativistic hydrodynamics: Long term evolution of neutron stars and stellar collapse to neutron stars and black holes
We report a new implementation for axisymmetric simulation in full general relativity. In this implementation, the Einstein equations are solved using the Nakamura-Shibata formulation with the
Axisymmetric core collapse simulations using characteristic numerical relativity
We present results from nonrotating axisymmetric stellar core collapse simulations in general relativity. Our hydrodynamics code has proved robust and accurate enough to allow for a detailed analysis
Fully General Relativistic Simulation of Coalescing Binary Neutron Stars
We present our first successful numerical results of 3D general relativistic simulations in which the Einstein equation and the hydrodynamic equations are fully solved. This paper is especially